%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PRO009+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:23:02 AM UTC 2025
% Result : Theorem 34.18s 34.37s
% Output : Proof 34.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PRO009+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:31:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 34.18/34.37 % SZS status Theorem
% 34.18/34.37 % SZS output start Proof
% 34.18/34.37 tff(min_precedes_type, type, (
% 34.18/34.37 min_precedes: ( $i * $i * $i ) > $o)).
% 34.18/34.37 tff(tptp0_type, type, (
% 34.18/34.37 tptp0: $i)).
% 34.18/34.37 tff(tptp_fun_X97_15_type, type, (
% 34.18/34.37 tptp_fun_X97_15: $i > $i)).
% 34.18/34.37 tff(tptp_fun_X99_17_type, type, (
% 34.18/34.37 tptp_fun_X99_17: $i)).
% 34.18/34.37 tff(tptp_fun_X93_13_type, type, (
% 34.18/34.37 tptp_fun_X93_13: ( $i * $i ) > $i)).
% 34.18/34.37 tff(tptp_fun_X96_16_type, type, (
% 34.18/34.37 tptp_fun_X96_16: $i > $i)).
% 34.18/34.37 tff(tptp_fun_X73_8_type, type, (
% 34.18/34.37 tptp_fun_X73_8: ( $i * $i * $i ) > $i)).
% 34.18/34.37 tff(root_occ_type, type, (
% 34.18/34.37 root_occ: ( $i * $i ) > $o)).
% 34.18/34.37 tff(occurrence_of_type, type, (
% 34.18/34.37 occurrence_of: ( $i * $i ) > $o)).
% 34.18/34.37 tff(subactivity_occurrence_type, type, (
% 34.18/34.37 subactivity_occurrence: ( $i * $i ) > $o)).
% 34.18/34.37 tff(root_type, type, (
% 34.18/34.37 root: ( $i * $i ) > $o)).
% 34.18/34.37 tff(tptp_fun_X34_1_type, type, (
% 34.18/34.37 tptp_fun_X34_1: ( $i * $i ) > $i)).
% 34.18/34.37 tff(tptp_fun_X53_6_type, type, (
% 34.18/34.37 tptp_fun_X53_6: $i > $i)).
% 34.18/34.37 tff(activity_type, type, (
% 34.18/34.37 activity: $i > $o)).
% 34.18/34.37 tff(activity_occurrence_type, type, (
% 34.18/34.37 activity_occurrence: $i > $o)).
% 34.18/34.37 tff(leaf_occ_type, type, (
% 34.18/34.37 leaf_occ: ( $i * $i ) > $o)).
% 34.18/34.37 tff(tptp2_type, type, (
% 34.18/34.37 tptp2: $i)).
% 34.18/34.37 tff(tptp1_type, type, (
% 34.18/34.37 tptp1: $i)).
% 34.18/34.37 tff(tptp3_type, type, (
% 34.18/34.37 tptp3: $i)).
% 34.18/34.37 tff(tptp_fun_X98_14_type, type, (
% 34.18/34.37 tptp_fun_X98_14: $i > $i)).
% 34.18/34.37 tff(next_subocc_type, type, (
% 34.18/34.37 next_subocc: ( $i * $i * $i ) > $o)).
% 34.18/34.37 tff(tptp4_type, type, (
% 34.18/34.37 tptp4: $i)).
% 34.18/34.37 tff(tptp_fun_X18_0_type, type, (
% 34.18/34.37 tptp_fun_X18_0: ( $i * $i * $i ) > $i)).
% 34.18/34.37 tff(atomic_type, type, (
% 34.18/34.37 atomic: $i > $o)).
% 34.18/34.37 tff(1,plain,
% 34.18/34.37 ((occurrence_of(X99!17, tptp0) & ![X100: $i, X101: $i] : (~(occurrence_of(X100, tptp3) & root_occ(X100, X99!17) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99!17)))) <=> (occurrence_of(X99!17, tptp0) & ![X100: $i, X101: $i] : (~(occurrence_of(X100, tptp3) & root_occ(X100, X99!17) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99!17))))),
% 34.18/34.37 inference(rewrite,[status(thm)],[])).
% 34.18/34.37 tff(2,plain,
% 34.18/34.37 ((~![X99: $i] : ((~occurrence_of(X99, tptp0)) | ?[X100: $i, X101: $i] : (occurrence_of(X100, tptp3) & root_occ(X100, X99) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99)))) <=> (~![X99: $i] : ((~occurrence_of(X99, tptp0)) | ?[X100: $i, X101: $i] : (occurrence_of(X100, tptp3) & root_occ(X100, X99) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99))))),
% 34.18/34.37 inference(rewrite,[status(thm)],[])).
% 34.18/34.37 tff(3,plain,
% 34.18/34.37 ((~![X99: $i] : (occurrence_of(X99, tptp0) => ?[X100: $i, X101: $i] : ((((occurrence_of(X100, tptp3) & root_occ(X100, X99)) & (occurrence_of(X101, tptp2) | occurrence_of(X101, tptp1))) & min_precedes(X100, X101, tptp0)) & leaf_occ(X101, X99)))) <=> (~![X99: $i] : ((~occurrence_of(X99, tptp0)) | ?[X100: $i, X101: $i] : (occurrence_of(X100, tptp3) & root_occ(X100, X99) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99))))),
% 34.18/34.37 inference(rewrite,[status(thm)],[])).
% 34.18/34.37 tff(4,axiom,(~![X99: $i] : (occurrence_of(X99, tptp0) => ?[X100: $i, X101: $i] : ((((occurrence_of(X100, tptp3) & root_occ(X100, X99)) & (occurrence_of(X101, tptp2) | occurrence_of(X101, tptp1))) & min_precedes(X100, X101, tptp0)) & leaf_occ(X101, X99)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 34.18/34.37 tff(5,plain,
% 34.18/34.37 (~![X99: $i] : ((~occurrence_of(X99, tptp0)) | ?[X100: $i, X101: $i] : (occurrence_of(X100, tptp3) & root_occ(X100, X99) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 34.18/34.37 tff(6,plain,
% 34.18/34.37 (~![X99: $i] : ((~occurrence_of(X99, tptp0)) | ?[X100: $i, X101: $i] : (occurrence_of(X100, tptp3) & root_occ(X100, X99) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 34.18/34.37 tff(7,plain,
% 34.18/34.37 (~![X99: $i] : ((~occurrence_of(X99, tptp0)) | ?[X100: $i, X101: $i] : (occurrence_of(X100, tptp3) & root_occ(X100, X99) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 34.18/34.37 tff(8,plain,
% 34.18/34.37 (~![X99: $i] : ((~occurrence_of(X99, tptp0)) | ?[X100: $i, X101: $i] : (occurrence_of(X100, tptp3) & root_occ(X100, X99) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 34.18/34.37 tff(9,plain,
% 34.18/34.37 (occurrence_of(X99!17, tptp0) & ![X100: $i, X101: $i] : (~(occurrence_of(X100, tptp3) & root_occ(X100, X99!17) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99!17)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[8, 1])).
% 34.18/34.37 tff(10,plain,
% 34.18/34.37 (occurrence_of(X99!17, tptp0)),
% 34.18/34.37 inference(and_elim,[status(thm)],[9])).
% 34.18/34.37 tff(11,plain,
% 34.18/34.37 (^[X89: $i, X90: $i] : refl(((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90))))) <=> ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90))))))),
% 34.18/34.37 inference(bind,[status(th)],[])).
% 34.18/34.37 tff(12,plain,
% 34.18/34.37 (![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90))))) <=> ![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90)))))),
% 34.18/34.37 inference(quant_intro,[status(thm)],[11])).
% 34.18/34.37 tff(13,plain,
% 34.18/34.37 (^[X89: $i, X90: $i] : rewrite(((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90))) <=> ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90))))))),
% 34.18/34.37 inference(bind,[status(th)],[])).
% 34.18/34.37 tff(14,plain,
% 34.18/34.37 (![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90))) <=> ![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90)))))),
% 34.18/34.37 inference(quant_intro,[status(thm)],[13])).
% 34.18/34.37 tff(15,plain,
% 34.18/34.37 (![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90))) <=> ![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90)))),
% 34.18/34.37 inference(rewrite,[status(thm)],[])).
% 34.18/34.37 tff(16,plain,
% 34.18/34.37 (^[X89: $i, X90: $i] : rewrite((occurrence_of(X90, X89) => (activity(X89) & activity_occurrence(X90))) <=> ((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90))))),
% 34.18/34.37 inference(bind,[status(th)],[])).
% 34.18/34.37 tff(17,plain,
% 34.18/34.37 (![X89: $i, X90: $i] : (occurrence_of(X90, X89) => (activity(X89) & activity_occurrence(X90))) <=> ![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90)))),
% 34.18/34.37 inference(quant_intro,[status(thm)],[16])).
% 34.18/34.37 tff(18,axiom,(![X89: $i, X90: $i] : (occurrence_of(X90, X89) => (activity(X89) & activity_occurrence(X90)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_29')).
% 34.18/34.37 tff(19,plain,
% 34.18/34.37 (![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 34.18/34.37 tff(20,plain,
% 34.18/34.37 (![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 34.18/34.37 tff(21,plain,(
% 34.18/34.37 ![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (activity(X89) & activity_occurrence(X90)))),
% 34.18/34.37 inference(skolemize,[status(sab)],[20])).
% 34.18/34.37 tff(22,plain,
% 34.18/34.37 (![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90)))))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 34.18/34.37 tff(23,plain,
% 34.18/34.37 (![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90)))))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[22, 12])).
% 34.18/34.37 tff(24,plain,
% 34.18/34.37 (((~![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90)))))) | ((~occurrence_of(X99!17, tptp0)) | (~((~activity(tptp0)) | (~activity_occurrence(X99!17)))))) <=> ((~![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90)))))) | (~occurrence_of(X99!17, tptp0)) | (~((~activity(tptp0)) | (~activity_occurrence(X99!17)))))),
% 34.18/34.37 inference(rewrite,[status(thm)],[])).
% 34.18/34.37 tff(25,plain,
% 34.18/34.37 ((~![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90)))))) | ((~occurrence_of(X99!17, tptp0)) | (~((~activity(tptp0)) | (~activity_occurrence(X99!17)))))),
% 34.18/34.37 inference(quant_inst,[status(thm)],[])).
% 34.18/34.37 tff(26,plain,
% 34.18/34.37 ((~![X89: $i, X90: $i] : ((~occurrence_of(X90, X89)) | (~((~activity(X89)) | (~activity_occurrence(X90)))))) | (~occurrence_of(X99!17, tptp0)) | (~((~activity(tptp0)) | (~activity_occurrence(X99!17))))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 34.18/34.37 tff(27,plain,
% 34.18/34.37 (~((~activity(tptp0)) | (~activity_occurrence(X99!17)))),
% 34.18/34.37 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 34.18/34.37 tff(28,plain,
% 34.18/34.37 (((~activity(tptp0)) | (~activity_occurrence(X99!17))) | activity_occurrence(X99!17)),
% 34.18/34.37 inference(tautology,[status(thm)],[])).
% 34.18/34.37 tff(29,plain,
% 34.18/34.37 (activity_occurrence(X99!17)),
% 34.18/34.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 34.18/34.37 tff(30,plain,
% 34.18/34.37 (^[X52: $i] : refl(((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52)))))) <=> ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52)))))))),
% 34.18/34.37 inference(bind,[status(th)],[])).
% 34.18/34.37 tff(31,plain,
% 34.18/34.37 (![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52)))))) <=> ![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52))))))),
% 34.18/34.37 inference(quant_intro,[status(thm)],[30])).
% 34.18/34.37 tff(32,plain,
% 34.18/34.37 (^[X52: $i] : rewrite(((~activity_occurrence(X52)) | (activity(tptp_fun_X53_6(X52)) & occurrence_of(X52, tptp_fun_X53_6(X52)))) <=> ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52)))))))),
% 34.18/34.37 inference(bind,[status(th)],[])).
% 34.18/34.37 tff(33,plain,
% 34.18/34.37 (![X52: $i] : ((~activity_occurrence(X52)) | (activity(tptp_fun_X53_6(X52)) & occurrence_of(X52, tptp_fun_X53_6(X52)))) <=> ![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52))))))),
% 34.18/34.37 inference(quant_intro,[status(thm)],[32])).
% 34.18/34.37 tff(34,plain,
% 34.18/34.37 (![X52: $i] : ((~activity_occurrence(X52)) | ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53))) <=> ![X52: $i] : ((~activity_occurrence(X52)) | ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53)))),
% 34.18/34.37 inference(rewrite,[status(thm)],[])).
% 34.18/34.37 tff(35,plain,
% 34.18/34.37 (^[X52: $i] : rewrite((activity_occurrence(X52) => ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53))) <=> ((~activity_occurrence(X52)) | ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53))))),
% 34.18/34.37 inference(bind,[status(th)],[])).
% 34.18/34.37 tff(36,plain,
% 34.18/34.37 (![X52: $i] : (activity_occurrence(X52) => ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53))) <=> ![X52: $i] : ((~activity_occurrence(X52)) | ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53)))),
% 34.18/34.37 inference(quant_intro,[status(thm)],[35])).
% 34.18/34.37 tff(37,axiom,(![X52: $i] : (activity_occurrence(X52) => ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_18')).
% 34.18/34.37 tff(38,plain,
% 34.18/34.37 (![X52: $i] : ((~activity_occurrence(X52)) | ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 34.18/34.37 tff(39,plain,
% 34.18/34.37 (![X52: $i] : ((~activity_occurrence(X52)) | ?[X53: $i] : (activity(X53) & occurrence_of(X52, X53)))),
% 34.18/34.37 inference(modus_ponens,[status(thm)],[38, 34])).
% 34.18/34.37 tff(40,plain,(
% 34.18/34.37 ![X52: $i] : ((~activity_occurrence(X52)) | (activity(tptp_fun_X53_6(X52)) & occurrence_of(X52, tptp_fun_X53_6(X52))))),
% 34.18/34.37 inference(skolemize,[status(sab)],[39])).
% 34.18/34.37 tff(41,plain,
% 34.18/34.37 (![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52))))))),
% 34.18/34.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 34.18/34.38 tff(42,plain,
% 34.18/34.38 (![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52))))))),
% 34.18/34.38 inference(modus_ponens,[status(thm)],[41, 31])).
% 34.18/34.38 tff(43,plain,
% 34.18/34.38 (((~![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52))))))) | ((~activity_occurrence(X99!17)) | (~((~activity(tptp_fun_X53_6(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))))) <=> ((~![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52))))))) | (~activity_occurrence(X99!17)) | (~((~activity(tptp_fun_X53_6(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))))),
% 34.18/34.38 inference(rewrite,[status(thm)],[])).
% 34.18/34.38 tff(44,plain,
% 34.18/34.38 ((~![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52))))))) | ((~activity_occurrence(X99!17)) | (~((~activity(tptp_fun_X53_6(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))))),
% 34.18/34.38 inference(quant_inst,[status(thm)],[])).
% 34.18/34.38 tff(45,plain,
% 34.18/34.38 ((~![X52: $i] : ((~activity_occurrence(X52)) | (~((~activity(tptp_fun_X53_6(X52))) | (~occurrence_of(X52, tptp_fun_X53_6(X52))))))) | (~activity_occurrence(X99!17)) | (~((~activity(tptp_fun_X53_6(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17)))))),
% 34.18/34.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 34.18/34.38 tff(46,plain,
% 34.18/34.38 (~((~activity(tptp_fun_X53_6(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))),
% 34.18/34.38 inference(unit_resolution,[status(thm)],[45, 42, 29])).
% 34.18/34.38 tff(47,plain,
% 34.18/34.38 (((~activity(tptp_fun_X53_6(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17)))) | occurrence_of(X99!17, tptp_fun_X53_6(X99!17))),
% 34.18/34.38 inference(tautology,[status(thm)],[])).
% 34.18/34.38 tff(48,plain,
% 34.18/34.38 (occurrence_of(X99!17, tptp_fun_X53_6(X99!17))),
% 34.18/34.38 inference(unit_resolution,[status(thm)],[47, 46])).
% 34.18/34.38 tff(49,plain,
% 34.18/34.38 (^[X32: $i, X33: $i] : refl((~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))))) <=> (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))))))),
% 34.18/34.38 inference(bind,[status(th)],[])).
% 34.18/34.38 tff(50,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))))) <=> ![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))),
% 34.18/34.38 inference(quant_intro,[status(thm)],[49])).
% 34.18/34.38 tff(51,plain,
% 34.18/34.38 (^[X32: $i, X33: $i] : rewrite((~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))))) <=> (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))))))),
% 34.18/34.38 inference(bind,[status(th)],[])).
% 34.18/34.38 tff(52,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))))) <=> ![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))),
% 34.18/34.38 inference(quant_intro,[status(thm)],[51])).
% 34.18/34.38 tff(53,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))))) <=> ![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))),
% 34.18/34.38 inference(transitivity,[status(thm)],[52, 50])).
% 34.18/34.38 tff(54,plain,
% 34.18/34.38 (^[X32: $i, X33: $i] : trans(monotonicity(rewrite(((~root_occ(X32, X33)) | (occurrence_of(X33, tptp_fun_X34_1(X33, X32)) & subactivity_occurrence(X32, X33) & root(X32, tptp_fun_X34_1(X33, X32)))) <=> ((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))), rewrite((root_occ(X32, X33) | ![X34: $i] : (~(occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34)))) <=> (root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))), ((((~root_occ(X32, X33)) | (occurrence_of(X33, tptp_fun_X34_1(X33, X32)) & subactivity_occurrence(X32, X33) & root(X32, tptp_fun_X34_1(X33, X32)))) & (root_occ(X32, X33) | ![X34: $i] : (~(occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34))))) <=> (((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32)))))) & (root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))))), rewrite((((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32)))))) & (root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34))))) <=> (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))), ((((~root_occ(X32, X33)) | (occurrence_of(X33, tptp_fun_X34_1(X33, X32)) & subactivity_occurrence(X32, X33) & root(X32, tptp_fun_X34_1(X33, X32)))) & (root_occ(X32, X33) | ![X34: $i] : (~(occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34))))) <=> (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))))),
% 34.18/34.38 inference(bind,[status(th)],[])).
% 34.18/34.38 tff(55,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (((~root_occ(X32, X33)) | (occurrence_of(X33, tptp_fun_X34_1(X33, X32)) & subactivity_occurrence(X32, X33) & root(X32, tptp_fun_X34_1(X33, X32)))) & (root_occ(X32, X33) | ![X34: $i] : (~(occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34))))) <=> ![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))),
% 34.18/34.38 inference(quant_intro,[status(thm)],[54])).
% 34.18/34.38 tff(56,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (root_occ(X32, X33) <=> ?[X34: $i] : (occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34))) <=> ![X32: $i, X33: $i] : (root_occ(X32, X33) <=> ?[X34: $i] : (occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34)))),
% 34.18/34.38 inference(rewrite,[status(thm)],[])).
% 34.18/34.38 tff(57,plain,
% 34.18/34.38 (^[X32: $i, X33: $i] : rewrite((root_occ(X32, X33) <=> ?[X34: $i] : ((occurrence_of(X33, X34) & subactivity_occurrence(X32, X33)) & root(X32, X34))) <=> (root_occ(X32, X33) <=> ?[X34: $i] : (occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34))))),
% 34.18/34.38 inference(bind,[status(th)],[])).
% 34.18/34.38 tff(58,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (root_occ(X32, X33) <=> ?[X34: $i] : ((occurrence_of(X33, X34) & subactivity_occurrence(X32, X33)) & root(X32, X34))) <=> ![X32: $i, X33: $i] : (root_occ(X32, X33) <=> ?[X34: $i] : (occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34)))),
% 34.18/34.38 inference(quant_intro,[status(thm)],[57])).
% 34.18/34.38 tff(59,axiom,(![X32: $i, X33: $i] : (root_occ(X32, X33) <=> ?[X34: $i] : ((occurrence_of(X33, X34) & subactivity_occurrence(X32, X33)) & root(X32, X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_10')).
% 34.18/34.38 tff(60,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (root_occ(X32, X33) <=> ?[X34: $i] : (occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34)))),
% 34.18/34.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 34.18/34.38 tff(61,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (root_occ(X32, X33) <=> ?[X34: $i] : (occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34)))),
% 34.18/34.38 inference(modus_ponens,[status(thm)],[60, 56])).
% 34.18/34.38 tff(62,plain,(
% 34.18/34.38 ![X32: $i, X33: $i] : (((~root_occ(X32, X33)) | (occurrence_of(X33, tptp_fun_X34_1(X33, X32)) & subactivity_occurrence(X32, X33) & root(X32, tptp_fun_X34_1(X33, X32)))) & (root_occ(X32, X33) | ![X34: $i] : (~(occurrence_of(X33, X34) & subactivity_occurrence(X32, X33) & root(X32, X34)))))),
% 34.18/34.38 inference(skolemize,[status(sab)],[61])).
% 34.18/34.38 tff(63,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))),
% 34.18/34.38 inference(modus_ponens,[status(thm)],[62, 55])).
% 34.18/34.38 tff(64,plain,
% 34.18/34.38 (![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))),
% 34.18/34.38 inference(modus_ponens,[status(thm)],[63, 53])).
% 34.18/34.38 tff(65,plain,
% 34.18/34.38 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))) | (~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))) | (~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))))))),
% 34.18/34.38 inference(rewrite,[status(thm)],[])).
% 34.18/34.38 tff(66,plain,
% 34.18/34.38 ((~((~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))))) <=> (~((~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))) | (~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))))))))),
% 34.18/34.38 inference(rewrite,[status(thm)],[])).
% 34.18/34.38 tff(67,plain,
% 34.18/34.38 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34)))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))) | (~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))))))),
% 34.18/34.38 inference(monotonicity,[status(thm)],[66])).
% 34.18/34.38 tff(68,plain,
% 34.18/34.38 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34)))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))) | (~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))))))),
% 34.18/34.38 inference(transitivity,[status(thm)],[67, 65])).
% 34.18/34.38 tff(69,plain,
% 34.18/34.38 ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34)))))))),
% 34.18/34.38 inference(quant_inst,[status(thm)],[])).
% 34.18/34.38 tff(70,plain,
% 34.18/34.38 ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))) | (~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))))))))),
% 34.18/34.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 34.18/34.38 tff(71,plain,
% 34.18/34.38 (~((~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))) | (~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))))),
% 34.18/34.38 inference(unit_resolution,[status(thm)],[70, 64])).
% 34.18/34.38 tff(72,plain,
% 34.18/34.38 (((~(root_occ(tptp_fun_X96_16(X99!17), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~root(tptp_fun_X96_16(X99!17), X34))))) | (~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))))))) | ((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))),
% 34.22/34.38 inference(tautology,[status(thm)],[])).
% 34.22/34.38 tff(73,plain,
% 34.22/34.38 ((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))))),
% 34.22/34.38 inference(unit_resolution,[status(thm)],[72, 71])).
% 34.22/34.38 tff(74,plain,
% 34.22/34.38 (^[X95: $i] : refl(((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95))))) <=> ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95))))))),
% 34.22/34.38 inference(bind,[status(th)],[])).
% 34.22/34.38 tff(75,plain,
% 34.22/34.38 (![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95))))) <=> ![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))),
% 34.22/34.38 inference(quant_intro,[status(thm)],[74])).
% 34.22/34.38 tff(76,plain,
% 34.22/34.38 (^[X95: $i] : rewrite(((~occurrence_of(X95, tptp0)) | (occurrence_of(tptp_fun_X96_16(X95), tptp3) & root_occ(tptp_fun_X96_16(X95), X95) & occurrence_of(tptp_fun_X97_15(X95), tptp4) & next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0) & (occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2)) & next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0) & leaf_occ(tptp_fun_X98_14(X95), X95))) <=> ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95))))))),
% 34.22/34.38 inference(bind,[status(th)],[])).
% 34.22/34.38 tff(77,plain,
% 34.22/34.38 (![X95: $i] : ((~occurrence_of(X95, tptp0)) | (occurrence_of(tptp_fun_X96_16(X95), tptp3) & root_occ(tptp_fun_X96_16(X95), X95) & occurrence_of(tptp_fun_X97_15(X95), tptp4) & next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0) & (occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2)) & next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0) & leaf_occ(tptp_fun_X98_14(X95), X95))) <=> ![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))),
% 34.22/34.38 inference(quant_intro,[status(thm)],[76])).
% 34.22/34.38 tff(78,plain,
% 34.22/34.38 (![X95: $i] : ((~occurrence_of(X95, tptp0)) | ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95))) <=> ![X95: $i] : ((~occurrence_of(X95, tptp0)) | ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95)))),
% 34.22/34.38 inference(rewrite,[status(thm)],[])).
% 34.22/34.38 tff(79,plain,
% 34.22/34.38 (^[X95: $i] : trans(monotonicity(quant_intro(proof_bind(^[X96: $i, X97: $i, X98: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4))), ((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) <=> ((occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)))), rewrite(((occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0))), ((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0)))), rewrite((occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1)) <=> (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2))), (((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) <=> ((occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2))))), rewrite(((occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2))) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)))), (((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2))))), ((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) <=> ((occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2))) & next_subocc(X97, X98, tptp0)))), rewrite(((occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2))) & next_subocc(X97, X98, tptp0)) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0))), ((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0)))), (((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95)) <=> ((occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95)))), rewrite(((occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95)) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95))), (((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95)) <=> (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95))))), (?[X96: $i, X97: $i, X98: $i] : ((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95)) <=> ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95)))), ((occurrence_of(X95, tptp0) => ?[X96: $i, X97: $i, X98: $i] : ((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95))) <=> (occurrence_of(X95, tptp0) => ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95))))), rewrite((occurrence_of(X95, tptp0) => ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95))) <=> ((~occurrence_of(X95, tptp0)) | ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95)))), ((occurrence_of(X95, tptp0) => ?[X96: $i, X97: $i, X98: $i] : ((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95))) <=> ((~occurrence_of(X95, tptp0)) | ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95)))))),
% 34.22/34.38 inference(bind,[status(th)],[])).
% 34.22/34.38 tff(80,plain,
% 34.22/34.38 (![X95: $i] : (occurrence_of(X95, tptp0) => ?[X96: $i, X97: $i, X98: $i] : ((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95))) <=> ![X95: $i] : ((~occurrence_of(X95, tptp0)) | ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95)))),
% 34.22/34.38 inference(quant_intro,[status(thm)],[79])).
% 34.22/34.38 tff(81,axiom,(![X95: $i] : (occurrence_of(X95, tptp0) => ?[X96: $i, X97: $i, X98: $i] : ((((((occurrence_of(X96, tptp3) & root_occ(X96, X95)) & occurrence_of(X97, tptp4)) & next_subocc(X96, X97, tptp0)) & (occurrence_of(X98, tptp2) | occurrence_of(X98, tptp1))) & next_subocc(X97, X98, tptp0)) & leaf_occ(X98, X95)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_32')).
% 34.22/34.38 tff(82,plain,
% 34.22/34.38 (![X95: $i] : ((~occurrence_of(X95, tptp0)) | ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95)))),
% 34.22/34.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 34.22/34.38 tff(83,plain,
% 34.22/34.38 (![X95: $i] : ((~occurrence_of(X95, tptp0)) | ?[X96: $i, X97: $i, X98: $i] : (occurrence_of(X96, tptp3) & root_occ(X96, X95) & occurrence_of(X97, tptp4) & next_subocc(X96, X97, tptp0) & (occurrence_of(X98, tptp1) | occurrence_of(X98, tptp2)) & next_subocc(X97, X98, tptp0) & leaf_occ(X98, X95)))),
% 34.22/34.38 inference(modus_ponens,[status(thm)],[82, 78])).
% 34.22/34.38 tff(84,plain,(
% 34.22/34.38 ![X95: $i] : ((~occurrence_of(X95, tptp0)) | (occurrence_of(tptp_fun_X96_16(X95), tptp3) & root_occ(tptp_fun_X96_16(X95), X95) & occurrence_of(tptp_fun_X97_15(X95), tptp4) & next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0) & (occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2)) & next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0) & leaf_occ(tptp_fun_X98_14(X95), X95)))),
% 34.22/34.38 inference(skolemize,[status(sab)],[83])).
% 34.22/34.38 tff(85,plain,
% 34.22/34.38 (![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))),
% 34.22/34.38 inference(modus_ponens,[status(thm)],[84, 77])).
% 34.22/34.38 tff(86,plain,
% 34.22/34.38 (![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))),
% 34.22/34.38 inference(modus_ponens,[status(thm)],[85, 75])).
% 34.22/34.38 tff(87,plain,
% 34.22/34.38 (((~![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))) | ((~occurrence_of(X99!17, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)))))) <=> ((~![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))) | (~occurrence_of(X99!17, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)))))),
% 34.22/34.38 inference(rewrite,[status(thm)],[])).
% 34.22/34.38 tff(88,plain,
% 34.22/34.38 ((~![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))) | ((~occurrence_of(X99!17, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)))))),
% 34.22/34.38 inference(quant_inst,[status(thm)],[])).
% 34.22/34.38 tff(89,plain,
% 34.22/34.38 ((~![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))) | (~occurrence_of(X99!17, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17))))),
% 34.22/34.38 inference(modus_ponens,[status(thm)],[88, 87])).
% 34.22/34.38 tff(90,plain,
% 34.22/34.38 (~((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)))),
% 34.22/34.38 inference(unit_resolution,[status(thm)],[89, 86, 10])).
% 34.22/34.38 tff(91,plain,
% 34.22/34.38 (((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17))) | root_occ(tptp_fun_X96_16(X99!17), X99!17)),
% 34.22/34.38 inference(tautology,[status(thm)],[])).
% 34.22/34.38 tff(92,plain,
% 34.22/34.38 (root_occ(tptp_fun_X96_16(X99!17), X99!17)),
% 34.22/34.38 inference(unit_resolution,[status(thm)],[91, 90])).
% 34.22/34.38 tff(93,plain,
% 34.22/34.38 ((~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))))),
% 34.22/34.38 inference(tautology,[status(thm)],[])).
% 34.22/34.38 tff(94,plain,
% 34.22/34.38 ((~((~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))))),
% 34.22/34.38 inference(unit_resolution,[status(thm)],[93, 92])).
% 34.22/34.38 tff(95,plain,
% 34.22/34.38 (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))),
% 34.22/34.38 inference(unit_resolution,[status(thm)],[94, 73])).
% 34.22/34.38 tff(96,plain,
% 34.22/34.38 (((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))) | occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))),
% 34.22/34.38 inference(tautology,[status(thm)],[])).
% 34.22/34.38 tff(97,plain,
% 34.22/34.38 (occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))),
% 34.22/34.38 inference(unit_resolution,[status(thm)],[96, 95])).
% 34.22/34.38 tff(98,plain,
% 34.22/34.38 (^[X64: $i, X65: $i, X66: $i] : refl(((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))) <=> ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))))),
% 34.22/34.38 inference(bind,[status(th)],[])).
% 34.22/34.38 tff(99,plain,
% 34.22/34.38 (![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))) <=> ![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))),
% 34.22/34.38 inference(quant_intro,[status(thm)],[98])).
% 34.22/34.38 tff(100,plain,
% 34.22/34.38 (^[X64: $i, X65: $i, X66: $i] : trans(monotonicity(trans(monotonicity(rewrite((occurrence_of(X64, X65) & occurrence_of(X64, X66)) <=> (~((~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))))), ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) <=> (~(~((~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))))))), rewrite((~(~((~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))))) <=> ((~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))), ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) <=> ((~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))))), (((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66)) <=> (((~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))) | (X65 = X66)))), rewrite((((~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65))) | (X65 = X66)) <=> ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))), (((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66)) <=> ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))))),
% 34.22/34.38 inference(bind,[status(th)],[])).
% 34.22/34.38 tff(101,plain,
% 34.22/34.38 (![X64: $i, X65: $i, X66: $i] : ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66)) <=> ![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))),
% 34.22/34.38 inference(quant_intro,[status(thm)],[100])).
% 34.22/34.38 tff(102,plain,
% 34.22/34.38 (![X64: $i, X65: $i, X66: $i] : ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66)) <=> ![X64: $i, X65: $i, X66: $i] : ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(103,plain,
% 34.22/34.39 (^[X64: $i, X65: $i, X66: $i] : rewrite(((occurrence_of(X64, X65) & occurrence_of(X64, X66)) => (X65 = X66)) <=> ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66)))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(104,plain,
% 34.22/34.39 (![X64: $i, X65: $i, X66: $i] : ((occurrence_of(X64, X65) & occurrence_of(X64, X66)) => (X65 = X66)) <=> ![X64: $i, X65: $i, X66: $i] : ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[103])).
% 34.22/34.39 tff(105,axiom,(![X64: $i, X65: $i, X66: $i] : ((occurrence_of(X64, X65) & occurrence_of(X64, X66)) => (X65 = X66))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_22')).
% 34.22/34.39 tff(106,plain,
% 34.22/34.39 (![X64: $i, X65: $i, X66: $i] : ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 34.22/34.39 tff(107,plain,
% 34.22/34.39 (![X64: $i, X65: $i, X66: $i] : ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[106, 102])).
% 34.22/34.39 tff(108,plain,(
% 34.22/34.39 ![X64: $i, X65: $i, X66: $i] : ((~(occurrence_of(X64, X65) & occurrence_of(X64, X66))) | (X65 = X66))),
% 34.22/34.39 inference(skolemize,[status(sab)],[107])).
% 34.22/34.39 tff(109,plain,
% 34.22/34.39 (![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[108, 101])).
% 34.22/34.39 tff(110,plain,
% 34.22/34.39 (![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[109, 99])).
% 34.22/34.39 tff(111,plain,
% 34.22/34.39 (((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))) <=> ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(112,plain,
% 34.22/34.39 (((tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17)))) <=> ((~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(113,plain,
% 34.22/34.39 (((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))) <=> ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))))),
% 34.22/34.39 inference(monotonicity,[status(thm)],[112])).
% 34.22/34.39 tff(114,plain,
% 34.22/34.39 (((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))) <=> ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))),
% 34.22/34.39 inference(transitivity,[status(thm)],[113, 111])).
% 34.22/34.39 tff(115,plain,
% 34.22/34.39 ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))),
% 34.22/34.39 inference(quant_inst,[status(thm)],[])).
% 34.22/34.39 tff(116,plain,
% 34.22/34.39 ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[115, 114])).
% 34.22/34.39 tff(117,plain,
% 34.22/34.39 (tptp_fun_X53_6(X99!17) = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[116, 110, 97, 48])).
% 34.22/34.39 tff(118,plain,
% 34.22/34.39 (((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp0))) <=> ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | (~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp0))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(119,plain,
% 34.22/34.39 (((tptp_fun_X53_6(X99!17) = tptp0) | (~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17)))) <=> ((~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp0))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(120,plain,
% 34.22/34.39 (((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((tptp_fun_X53_6(X99!17) = tptp0) | (~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))) <=> ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp0)))),
% 34.22/34.39 inference(monotonicity,[status(thm)],[119])).
% 34.22/34.39 tff(121,plain,
% 34.22/34.39 (((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((tptp_fun_X53_6(X99!17) = tptp0) | (~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))) <=> ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | (~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp0))),
% 34.22/34.39 inference(transitivity,[status(thm)],[120, 118])).
% 34.22/34.39 tff(122,plain,
% 34.22/34.39 ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | ((tptp_fun_X53_6(X99!17) = tptp0) | (~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))))),
% 34.22/34.39 inference(quant_inst,[status(thm)],[])).
% 34.22/34.39 tff(123,plain,
% 34.22/34.39 ((~![X64: $i, X65: $i, X66: $i] : ((X65 = X66) | (~occurrence_of(X64, X66)) | (~occurrence_of(X64, X65)))) | (~occurrence_of(X99!17, tptp0)) | (~occurrence_of(X99!17, tptp_fun_X53_6(X99!17))) | (tptp_fun_X53_6(X99!17) = tptp0)),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[122, 121])).
% 34.22/34.39 tff(124,plain,
% 34.22/34.39 (tptp_fun_X53_6(X99!17) = tptp0),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[123, 110, 10, 48])).
% 34.22/34.39 tff(125,plain,
% 34.22/34.39 (tptp0 = tptp_fun_X53_6(X99!17)),
% 34.22/34.39 inference(symmetry,[status(thm)],[124])).
% 34.22/34.39 tff(126,plain,
% 34.22/34.39 (tptp0 = tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))),
% 34.22/34.39 inference(transitivity,[status(thm)],[125, 117])).
% 34.22/34.39 tff(127,plain,
% 34.22/34.39 (root(tptp_fun_X96_16(X99!17), tptp0) <=> root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))),
% 34.22/34.39 inference(monotonicity,[status(thm)],[126])).
% 34.22/34.39 tff(128,plain,
% 34.22/34.39 (root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))) <=> root(tptp_fun_X96_16(X99!17), tptp0)),
% 34.22/34.39 inference(symmetry,[status(thm)],[127])).
% 34.22/34.39 tff(129,plain,
% 34.22/34.39 (((~subactivity_occurrence(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17))))) | root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))),
% 34.22/34.39 inference(tautology,[status(thm)],[])).
% 34.22/34.39 tff(130,plain,
% 34.22/34.39 (root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(X99!17, tptp_fun_X96_16(X99!17)))),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[129, 95])).
% 34.22/34.39 tff(131,plain,
% 34.22/34.39 (root(tptp_fun_X96_16(X99!17), tptp0)),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[130, 128])).
% 34.22/34.39 tff(132,assumption,(~root(tptp_fun_X96_16(X99!17), tptp0)), introduced(assumption)).
% 34.22/34.39 tff(133,plain,
% 34.22/34.39 ($false),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[132, 131])).
% 34.22/34.39 tff(134,plain,(root(tptp_fun_X96_16(X99!17), tptp0)), inference(lemma,lemma(discharge,[]))).
% 34.22/34.39 tff(135,assumption,(![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))), introduced(assumption)).
% 34.22/34.39 tff(136,plain,
% 34.22/34.39 (^[X15: $i, X16: $i, X17: $i] : rewrite((~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))) <=> (~((~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))) | (~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))))))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(137,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))) <=> ![X15: $i, X16: $i, X17: $i] : (~((~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))) | (~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17))))))))))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[136])).
% 34.22/34.39 tff(138,plain,
% 34.22/34.39 (^[X15: $i, X16: $i, X17: $i] : refl((~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))) <=> (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(139,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))) <=> ![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[138])).
% 34.22/34.39 tff(140,plain,
% 34.22/34.39 (^[X15: $i, X16: $i, X17: $i] : rewrite((~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))) <=> (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(141,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))) <=> ![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[140])).
% 34.22/34.39 tff(142,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))) <=> ![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))))),
% 34.22/34.39 inference(transitivity,[status(thm)],[141, 139])).
% 34.22/34.39 tff(143,plain,
% 34.22/34.39 (^[X15: $i, X16: $i, X17: $i] : trans(monotonicity(rewrite(((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) <=> ((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))), trans(monotonicity(rewrite((min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)) <=> (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))), ((next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))) <=> (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))), rewrite((next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))) <=> (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))), ((next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))) <=> (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))), ((((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))) <=> (((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17))))))) & (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))))), rewrite((((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17))))))) & (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))) <=> (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))))), ((((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))) <=> (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))))))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(144,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))) <=> ![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[143])).
% 34.22/34.39 tff(145,plain,
% 34.22/34.39 (^[X15: $i, X16: $i, X17: $i] : rewrite((((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | ((~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))) <=> (((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(146,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | ((~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))) <=> ![X15: $i, X16: $i, X17: $i] : (((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[145])).
% 34.22/34.39 tff(147,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (next_subocc(X15, X16, X17) <=> (min_precedes(X15, X16, X17) & (~?[X18: $i] : (min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) <=> ![X15: $i, X16: $i, X17: $i] : (next_subocc(X15, X16, X17) <=> (min_precedes(X15, X16, X17) & (~?[X18: $i] : (min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17)))))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(148,axiom,(![X15: $i, X16: $i, X17: $i] : (next_subocc(X15, X16, X17) <=> (min_precedes(X15, X16, X17) & (~?[X18: $i] : (min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_04')).
% 34.22/34.39 tff(149,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (next_subocc(X15, X16, X17) <=> (min_precedes(X15, X16, X17) & (~?[X18: $i] : (min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17)))))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[148, 147])).
% 34.22/34.39 tff(150,plain,(
% 34.22/34.39 ![X15: $i, X16: $i, X17: $i] : (((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | ((~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))),
% 34.22/34.39 inference(skolemize,[status(sab)],[149])).
% 34.22/34.39 tff(151,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (((~next_subocc(X15, X16, X17)) | (min_precedes(X15, X16, X17) & ![X18: $i] : (~(min_precedes(X15, X18, X17) & min_precedes(X18, X16, X17))))) & (next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17) & min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[150, 146])).
% 34.22/34.39 tff(152,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[151, 144])).
% 34.22/34.39 tff(153,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (~((~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17)))))))) | (~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17))))))))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[152, 142])).
% 34.22/34.39 tff(154,plain,
% 34.22/34.39 (![X15: $i, X16: $i, X17: $i] : (~((~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))) | (~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17))))))))))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[153, 137])).
% 34.22/34.39 tff(155,plain,
% 34.22/34.39 ((~![X15: $i, X16: $i, X17: $i] : (~((~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))) | (~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17))))))))))) | (~((~(next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0) | (~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X18_0(tptp0, tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17)), tptp0)) | (~min_precedes(tptp_fun_X18_0(tptp0, tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17)), tptp_fun_X97_15(X99!17), tptp0)))))) | (~((~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0))))))))))),
% 34.22/34.39 inference(quant_inst,[status(thm)],[])).
% 34.22/34.39 tff(156,plain,
% 34.22/34.39 (~((~(next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0) | (~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X18_0(tptp0, tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17)), tptp0)) | (~min_precedes(tptp_fun_X18_0(tptp0, tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17)), tptp_fun_X97_15(X99!17), tptp0)))))) | (~((~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0)))))))))),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[155, 154])).
% 34.22/34.39 tff(157,plain,
% 34.22/34.39 (((~(next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0) | (~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X18_0(tptp0, tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17)), tptp0)) | (~min_precedes(tptp_fun_X18_0(tptp0, tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17)), tptp_fun_X97_15(X99!17), tptp0)))))) | (~((~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0))))))))) | ((~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0)))))))),
% 34.22/34.39 inference(tautology,[status(thm)],[])).
% 34.22/34.39 tff(158,plain,
% 34.22/34.39 ((~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0))))))),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[157, 156])).
% 34.22/34.39 tff(159,plain,
% 34.22/34.39 (((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17))) | next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)),
% 34.22/34.39 inference(tautology,[status(thm)],[])).
% 34.22/34.39 tff(160,plain,
% 34.22/34.39 (next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[159, 90])).
% 34.22/34.39 tff(161,plain,
% 34.22/34.39 ((~((~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0)))))))) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0))))))),
% 34.22/34.39 inference(tautology,[status(thm)],[])).
% 34.22/34.39 tff(162,plain,
% 34.22/34.39 ((~((~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0)))))))) | (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0))))))),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[161, 160])).
% 34.22/34.39 tff(163,plain,
% 34.22/34.39 (~((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0)))))),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[162, 158])).
% 34.22/34.39 tff(164,plain,
% 34.22/34.39 (((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X97_15(X99!17), tptp0)) | (~min_precedes(tptp_fun_X96_16(X99!17), X18, tptp0))))) | min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)),
% 34.22/34.39 inference(tautology,[status(thm)],[])).
% 34.22/34.39 tff(165,plain,
% 34.22/34.39 (min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[164, 163])).
% 34.22/34.39 tff(166,plain,
% 34.22/34.39 (^[X70: $i, X71: $i, X72: $i] : refl(((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70)))))) <=> ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70)))))))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(167,plain,
% 34.22/34.39 (![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70)))))) <=> ![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[166])).
% 34.22/34.39 tff(168,plain,
% 34.22/34.39 (^[X70: $i, X71: $i, X72: $i] : rewrite(((~min_precedes(X71, X72, X70)) | (occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70) & subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70)) & subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70)))) <=> ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70)))))))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(169,plain,
% 34.22/34.39 (![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70) & subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70)) & subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70)))) <=> ![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[168])).
% 34.22/34.39 tff(170,plain,
% 34.22/34.39 (![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73))) <=> ![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73)))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(171,plain,
% 34.22/34.39 (^[X70: $i, X71: $i, X72: $i] : trans(monotonicity(quant_intro(proof_bind(^[X73: $i] : rewrite(((occurrence_of(X73, X70) & subactivity_occurrence(X71, X73)) & subactivity_occurrence(X72, X73)) <=> (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73)))), (?[X73: $i] : ((occurrence_of(X73, X70) & subactivity_occurrence(X71, X73)) & subactivity_occurrence(X72, X73)) <=> ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73)))), ((min_precedes(X71, X72, X70) => ?[X73: $i] : ((occurrence_of(X73, X70) & subactivity_occurrence(X71, X73)) & subactivity_occurrence(X72, X73))) <=> (min_precedes(X71, X72, X70) => ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73))))), rewrite((min_precedes(X71, X72, X70) => ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73))) <=> ((~min_precedes(X71, X72, X70)) | ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73)))), ((min_precedes(X71, X72, X70) => ?[X73: $i] : ((occurrence_of(X73, X70) & subactivity_occurrence(X71, X73)) & subactivity_occurrence(X72, X73))) <=> ((~min_precedes(X71, X72, X70)) | ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73)))))),
% 34.22/34.39 inference(bind,[status(th)],[])).
% 34.22/34.39 tff(172,plain,
% 34.22/34.39 (![X70: $i, X71: $i, X72: $i] : (min_precedes(X71, X72, X70) => ?[X73: $i] : ((occurrence_of(X73, X70) & subactivity_occurrence(X71, X73)) & subactivity_occurrence(X72, X73))) <=> ![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73)))),
% 34.22/34.39 inference(quant_intro,[status(thm)],[171])).
% 34.22/34.39 tff(173,axiom,(![X70: $i, X71: $i, X72: $i] : (min_precedes(X71, X72, X70) => ?[X73: $i] : ((occurrence_of(X73, X70) & subactivity_occurrence(X71, X73)) & subactivity_occurrence(X72, X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_24')).
% 34.22/34.39 tff(174,plain,
% 34.22/34.39 (![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73)))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[173, 172])).
% 34.22/34.39 tff(175,plain,
% 34.22/34.39 (![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | ?[X73: $i] : (occurrence_of(X73, X70) & subactivity_occurrence(X71, X73) & subactivity_occurrence(X72, X73)))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[174, 170])).
% 34.22/34.39 tff(176,plain,(
% 34.22/34.39 ![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70) & subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70)) & subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))),
% 34.22/34.39 inference(skolemize,[status(sab)],[175])).
% 34.22/34.39 tff(177,plain,
% 34.22/34.39 (![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[176, 169])).
% 34.22/34.39 tff(178,plain,
% 34.22/34.39 (![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[177, 167])).
% 34.22/34.39 tff(179,plain,
% 34.22/34.39 (((~![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))))) | ((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~subactivity_occurrence(tptp_fun_X97_15(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))))) <=> ((~![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))))) | (~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~subactivity_occurrence(tptp_fun_X97_15(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(180,plain,
% 34.22/34.39 ((~![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))))) | ((~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~subactivity_occurrence(tptp_fun_X97_15(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))))),
% 34.22/34.39 inference(quant_inst,[status(thm)],[])).
% 34.22/34.39 tff(181,plain,
% 34.22/34.39 ((~![X70: $i, X71: $i, X72: $i] : ((~min_precedes(X71, X72, X70)) | (~((~occurrence_of(tptp_fun_X73_8(X72, X71, X70), X70)) | (~subactivity_occurrence(X71, tptp_fun_X73_8(X72, X71, X70))) | (~subactivity_occurrence(X72, tptp_fun_X73_8(X72, X71, X70))))))) | (~min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~subactivity_occurrence(tptp_fun_X97_15(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))))),
% 34.22/34.39 inference(modus_ponens,[status(thm)],[180, 179])).
% 34.22/34.39 tff(182,plain,
% 34.22/34.39 (~((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~subactivity_occurrence(tptp_fun_X97_15(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[181, 178, 165])).
% 34.22/34.39 tff(183,plain,
% 34.22/34.39 (((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~subactivity_occurrence(tptp_fun_X97_15(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))) | subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))),
% 34.22/34.39 inference(tautology,[status(thm)],[])).
% 34.22/34.39 tff(184,plain,
% 34.22/34.39 (subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[183, 182])).
% 34.22/34.39 tff(185,plain,
% 34.22/34.39 (((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~subactivity_occurrence(tptp_fun_X97_15(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))) | occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)),
% 34.22/34.39 inference(tautology,[status(thm)],[])).
% 34.22/34.39 tff(186,plain,
% 34.22/34.39 (occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)),
% 34.22/34.39 inference(unit_resolution,[status(thm)],[185, 182])).
% 34.22/34.39 tff(187,plain,
% 34.22/34.39 (((~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))) | ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), tptp0)))) <=> ((~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), tptp0)))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(188,plain,
% 34.22/34.39 (((~root(tptp_fun_X96_16(X99!17), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0))) <=> ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), tptp0)))),
% 34.22/34.39 inference(rewrite,[status(thm)],[])).
% 34.22/34.39 tff(189,plain,
% 34.22/34.39 (((~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))) | ((~root(tptp_fun_X96_16(X99!17), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)))) <=> ((~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))) | ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.39 inference(monotonicity,[status(thm)],[188])).
% 34.22/34.39 tff(190,plain,
% 34.22/34.39 (((~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))) | ((~root(tptp_fun_X96_16(X99!17), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)))) <=> ((~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), tptp0)))),
% 34.22/34.40 inference(transitivity,[status(thm)],[189, 187])).
% 34.22/34.40 tff(191,plain,
% 34.22/34.40 ((~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))) | ((~root(tptp_fun_X96_16(X99!17), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)))),
% 34.22/34.40 inference(quant_inst,[status(thm)],[])).
% 34.22/34.40 tff(192,plain,
% 34.22/34.40 ((~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), tptp0))),
% 34.22/34.40 inference(modus_ponens,[status(thm)],[191, 190])).
% 34.22/34.40 tff(193,plain,
% 34.22/34.40 ($false),
% 34.22/34.40 inference(unit_resolution,[status(thm)],[192, 186, 184, 135, 134])).
% 34.22/34.40 tff(194,plain,(~![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))), inference(lemma,lemma(discharge,[]))).
% 34.22/34.40 tff(195,plain,
% 34.22/34.40 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34))))))))),
% 34.22/34.40 inference(rewrite,[status(thm)],[])).
% 34.22/34.40 tff(196,plain,
% 34.22/34.40 ((~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), X34))))))) <=> (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))))))),
% 34.22/34.40 inference(rewrite,[status(thm)],[])).
% 34.22/34.40 tff(197,plain,
% 34.22/34.40 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), X34)))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34))))))))),
% 34.22/34.40 inference(monotonicity,[status(thm)],[196])).
% 34.22/34.40 tff(198,plain,
% 34.22/34.40 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), X34)))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34))))))))),
% 34.22/34.40 inference(transitivity,[status(thm)],[197, 195])).
% 34.22/34.40 tff(199,plain,
% 34.22/34.40 ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root(tptp_fun_X96_16(X99!17), X34)))))))),
% 34.22/34.40 inference(quant_inst,[status(thm)],[])).
% 34.22/34.40 tff(200,plain,
% 34.22/34.40 ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))))))),
% 34.22/34.40 inference(modus_ponens,[status(thm)],[199, 198])).
% 34.22/34.40 tff(201,plain,
% 34.22/34.40 (~((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34))))))),
% 34.22/34.40 inference(unit_resolution,[status(thm)],[200, 64])).
% 34.22/34.40 tff(202,plain,
% 34.22/34.40 (((~((~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~((~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))) | (~root(tptp_fun_X96_16(X99!17), tptp_fun_X34_1(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp_fun_X96_16(X99!17)))))))) | (~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))))) | (root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34))))),
% 34.22/34.40 inference(tautology,[status(thm)],[])).
% 34.22/34.40 tff(203,plain,
% 34.22/34.40 (root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))),
% 34.22/34.40 inference(unit_resolution,[status(thm)],[202, 201])).
% 34.22/34.40 tff(204,plain,
% 34.22/34.40 ((~(root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34))))) | root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))),
% 34.22/34.40 inference(tautology,[status(thm)],[])).
% 34.22/34.40 tff(205,plain,
% 34.22/34.40 (root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) | ![X34: $i] : ((~root(tptp_fun_X96_16(X99!17), X34)) | (~subactivity_occurrence(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), X34)))),
% 34.22/34.40 inference(unit_resolution,[status(thm)],[204, 203])).
% 34.22/34.40 tff(206,plain,
% 34.22/34.40 (root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))),
% 34.22/34.40 inference(unit_resolution,[status(thm)],[205, 194])).
% 34.22/34.40 tff(207,plain,
% 34.22/34.40 (((~![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))) | ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp4)) | (~next_subocc(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp1) | occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp2))) | (~next_subocc(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~leaf_occ(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))))) <=> ((~![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp4)) | (~next_subocc(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp1) | occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp2))) | (~next_subocc(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~leaf_occ(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))))),
% 34.22/34.40 inference(rewrite,[status(thm)],[])).
% 34.22/34.40 tff(208,plain,
% 34.22/34.40 ((~![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))) | ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp4)) | (~next_subocc(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp1) | occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp2))) | (~next_subocc(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~leaf_occ(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))))),
% 34.22/34.40 inference(quant_inst,[status(thm)],[])).
% 34.22/34.40 tff(209,plain,
% 34.22/34.40 ((~![X95: $i] : ((~occurrence_of(X95, tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(X95), tptp3)) | (~root_occ(tptp_fun_X96_16(X95), X95)) | (~occurrence_of(tptp_fun_X97_15(X95), tptp4)) | (~next_subocc(tptp_fun_X96_16(X95), tptp_fun_X97_15(X95), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X95), tptp1) | occurrence_of(tptp_fun_X98_14(X95), tptp2))) | (~next_subocc(tptp_fun_X97_15(X95), tptp_fun_X98_14(X95), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X95), X95)))))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~((~occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp4)) | (~next_subocc(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp1) | occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp2))) | (~next_subocc(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~leaf_occ(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))))),
% 34.22/34.40 inference(modus_ponens,[status(thm)],[208, 207])).
% 34.22/34.40 tff(210,plain,
% 34.22/34.40 (~((~occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp4)) | (~next_subocc(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp1) | occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp2))) | (~next_subocc(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~leaf_occ(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.40 inference(unit_resolution,[status(thm)],[209, 86, 186])).
% 34.22/34.40 tff(211,plain,
% 34.22/34.40 (((~occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp4)) | (~next_subocc(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp1) | occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp2))) | (~next_subocc(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~leaf_occ(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))) | root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))),
% 34.22/34.40 inference(tautology,[status(thm)],[])).
% 34.22/34.40 tff(212,plain,
% 34.22/34.40 (root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))),
% 34.22/34.40 inference(unit_resolution,[status(thm)],[211, 210])).
% 34.22/34.40 tff(213,plain,
% 34.22/34.40 (^[X7: $i, X8: $i, X9: $i, X10: $i] : refl(((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))) <=> ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))))),
% 34.22/34.40 inference(bind,[status(th)],[])).
% 34.22/34.40 tff(214,plain,
% 34.22/34.40 (![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))) <=> ![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))),
% 34.22/34.40 inference(quant_intro,[status(thm)],[213])).
% 34.22/34.40 tff(215,plain,
% 34.22/34.40 (^[X7: $i, X8: $i, X9: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9)) <=> (~((~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))))), ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) <=> (~(~((~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))))))), rewrite((~(~((~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))))) <=> ((~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))), ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) <=> ((~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))))), (((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8)) <=> (((~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))) | (X7 = X8)))), rewrite((((~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9))) | (X7 = X8)) <=> ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))), (((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8)) <=> ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))))),
% 34.22/34.40 inference(bind,[status(th)],[])).
% 34.22/34.40 tff(216,plain,
% 34.22/34.40 (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8)) <=> ![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))),
% 34.22/34.40 inference(quant_intro,[status(thm)],[215])).
% 34.22/34.40 tff(217,plain,
% 34.22/34.40 (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8)) <=> ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8))),
% 34.22/34.40 inference(rewrite,[status(thm)],[])).
% 34.22/34.40 tff(218,plain,
% 34.22/34.40 (^[X7: $i, X8: $i, X9: $i, X10: $i] : trans(monotonicity(rewrite(((occurrence_of(X9, X10) & root_occ(X7, X9)) & root_occ(X8, X9)) <=> (occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))), ((((occurrence_of(X9, X10) & root_occ(X7, X9)) & root_occ(X8, X9)) => (X7 = X8)) <=> ((occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9)) => (X7 = X8)))), rewrite(((occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9)) => (X7 = X8)) <=> ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8))), ((((occurrence_of(X9, X10) & root_occ(X7, X9)) & root_occ(X8, X9)) => (X7 = X8)) <=> ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8))))),
% 34.22/34.40 inference(bind,[status(th)],[])).
% 34.22/34.40 tff(219,plain,
% 34.22/34.40 (![X7: $i, X8: $i, X9: $i, X10: $i] : (((occurrence_of(X9, X10) & root_occ(X7, X9)) & root_occ(X8, X9)) => (X7 = X8)) <=> ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8))),
% 34.22/34.40 inference(quant_intro,[status(thm)],[218])).
% 34.22/34.40 tff(220,axiom,(![X7: $i, X8: $i, X9: $i, X10: $i] : (((occurrence_of(X9, X10) & root_occ(X7, X9)) & root_occ(X8, X9)) => (X7 = X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_02')).
% 34.22/34.40 tff(221,plain,
% 34.22/34.40 (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8))),
% 34.22/34.40 inference(modus_ponens,[status(thm)],[220, 219])).
% 34.22/34.40 tff(222,plain,
% 34.22/34.40 (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8))),
% 34.22/34.40 inference(modus_ponens,[status(thm)],[221, 217])).
% 34.22/34.40 tff(223,plain,(
% 34.22/34.40 ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~(occurrence_of(X9, X10) & root_occ(X7, X9) & root_occ(X8, X9))) | (X7 = X8))),
% 34.22/34.40 inference(skolemize,[status(sab)],[222])).
% 34.22/34.40 tff(224,plain,
% 34.22/34.40 (![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))),
% 34.22/34.40 inference(modus_ponens,[status(thm)],[223, 216])).
% 34.22/34.40 tff(225,plain,
% 34.22/34.40 (![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))),
% 34.22/34.40 inference(modus_ponens,[status(thm)],[224, 214])).
% 34.22/34.40 tff(226,plain,
% 34.22/34.40 (((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))) <=> ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.40 inference(rewrite,[status(thm)],[])).
% 34.22/34.40 tff(227,plain,
% 34.22/34.40 (((tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))) <=> ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.40 inference(rewrite,[status(thm)],[])).
% 34.22/34.40 tff(228,plain,
% 34.22/34.40 (((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))) <=> ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))))),
% 34.22/34.40 inference(monotonicity,[status(thm)],[227])).
% 34.22/34.40 tff(229,plain,
% 34.22/34.40 (((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))) <=> ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.40 inference(transitivity,[status(thm)],[228, 226])).
% 34.22/34.40 tff(230,plain,
% 34.22/34.40 ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.41 inference(quant_inst,[status(thm)],[])).
% 34.22/34.41 tff(231,plain,
% 34.22/34.41 ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | (~occurrence_of(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0), tptp0)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~root_occ(tptp_fun_X96_16(X99!17), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[230, 229])).
% 34.22/34.41 tff(232,plain,
% 34.22/34.41 (tptp_fun_X96_16(X99!17) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[231, 225, 186, 212, 206])).
% 34.22/34.41 tff(233,plain,
% 34.22/34.41 (tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)) = tptp_fun_X96_16(X99!17)),
% 34.22/34.41 inference(symmetry,[status(thm)],[232])).
% 34.22/34.41 tff(234,plain,
% 34.22/34.41 (root_occ(tptp_fun_X96_16(X99!17), X99!17) <=> root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)),
% 34.22/34.41 inference(monotonicity,[status(thm)],[232])).
% 34.22/34.41 tff(235,plain,
% 34.22/34.41 (root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[92, 234])).
% 34.22/34.41 tff(236,assumption,(![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))), introduced(assumption)).
% 34.22/34.41 tff(237,plain,
% 34.22/34.41 ((~atomic(tptp0)) <=> (~atomic(tptp0))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(238,axiom,(~atomic(tptp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_34')).
% 34.22/34.41 tff(239,plain,
% 34.22/34.41 (~atomic(tptp0)),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[238, 237])).
% 34.22/34.41 tff(240,plain,
% 34.22/34.41 (^[X91: $i, X92: $i] : refl((atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))))) <=> (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))))))),
% 34.22/34.41 inference(bind,[status(th)],[])).
% 34.22/34.41 tff(241,plain,
% 34.22/34.41 (![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))))) <=> ![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))),
% 34.22/34.41 inference(quant_intro,[status(thm)],[240])).
% 34.22/34.41 tff(242,plain,
% 34.22/34.41 (^[X91: $i, X92: $i] : trans(monotonicity(trans(monotonicity(rewrite((occurrence_of(X92, X91) & (~atomic(X91))) <=> (~(atomic(X91) | (~occurrence_of(X92, X91))))), ((~(occurrence_of(X92, X91) & (~atomic(X91)))) <=> (~(~(atomic(X91) | (~occurrence_of(X92, X91))))))), rewrite((~(~(atomic(X91) | (~occurrence_of(X92, X91))))) <=> (atomic(X91) | (~occurrence_of(X92, X91)))), ((~(occurrence_of(X92, X91) & (~atomic(X91)))) <=> (atomic(X91) | (~occurrence_of(X92, X91))))), rewrite((root(tptp_fun_X93_13(X92, X91), X91) & subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)) <=> (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))))), (((~(occurrence_of(X92, X91) & (~atomic(X91)))) | (root(tptp_fun_X93_13(X92, X91), X91) & subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))) <=> ((atomic(X91) | (~occurrence_of(X92, X91))) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))))))), rewrite(((atomic(X91) | (~occurrence_of(X92, X91))) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))))) <=> (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))), (((~(occurrence_of(X92, X91) & (~atomic(X91)))) | (root(tptp_fun_X93_13(X92, X91), X91) & subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))) <=> (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))))),
% 34.22/34.41 inference(bind,[status(th)],[])).
% 34.22/34.41 tff(243,plain,
% 34.22/34.41 (![X91: $i, X92: $i] : ((~(occurrence_of(X92, X91) & (~atomic(X91)))) | (root(tptp_fun_X93_13(X92, X91), X91) & subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92))) <=> ![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))),
% 34.22/34.41 inference(quant_intro,[status(thm)],[242])).
% 34.22/34.41 tff(244,plain,
% 34.22/34.41 (![X91: $i, X92: $i] : ((~(occurrence_of(X92, X91) & (~atomic(X91)))) | ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92))) <=> ![X91: $i, X92: $i] : ((~(occurrence_of(X92, X91) & (~atomic(X91)))) | ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92)))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(245,plain,
% 34.22/34.41 (^[X91: $i, X92: $i] : rewrite(((occurrence_of(X92, X91) & (~atomic(X91))) => ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92))) <=> ((~(occurrence_of(X92, X91) & (~atomic(X91)))) | ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92))))),
% 34.22/34.41 inference(bind,[status(th)],[])).
% 34.22/34.41 tff(246,plain,
% 34.22/34.41 (![X91: $i, X92: $i] : ((occurrence_of(X92, X91) & (~atomic(X91))) => ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92))) <=> ![X91: $i, X92: $i] : ((~(occurrence_of(X92, X91) & (~atomic(X91)))) | ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92)))),
% 34.22/34.41 inference(quant_intro,[status(thm)],[245])).
% 34.22/34.41 tff(247,axiom,(![X91: $i, X92: $i] : ((occurrence_of(X92, X91) & (~atomic(X91))) => ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_30')).
% 34.22/34.41 tff(248,plain,
% 34.22/34.41 (![X91: $i, X92: $i] : ((~(occurrence_of(X92, X91) & (~atomic(X91)))) | ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92)))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[247, 246])).
% 34.22/34.41 tff(249,plain,
% 34.22/34.41 (![X91: $i, X92: $i] : ((~(occurrence_of(X92, X91) & (~atomic(X91)))) | ?[X93: $i] : (root(X93, X91) & subactivity_occurrence(X93, X92)))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[248, 244])).
% 34.22/34.41 tff(250,plain,(
% 34.22/34.41 ![X91: $i, X92: $i] : ((~(occurrence_of(X92, X91) & (~atomic(X91)))) | (root(tptp_fun_X93_13(X92, X91), X91) & subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))),
% 34.22/34.41 inference(skolemize,[status(sab)],[249])).
% 34.22/34.41 tff(251,plain,
% 34.22/34.41 (![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[250, 243])).
% 34.22/34.41 tff(252,plain,
% 34.22/34.41 (![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[251, 241])).
% 34.22/34.41 tff(253,plain,
% 34.22/34.41 (((~![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))) | (atomic(tptp0) | (~occurrence_of(X99!17, tptp0)) | (~((~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)))))) <=> ((~![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))) | atomic(tptp0) | (~occurrence_of(X99!17, tptp0)) | (~((~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)))))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(254,plain,
% 34.22/34.41 ((~![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))) | (atomic(tptp0) | (~occurrence_of(X99!17, tptp0)) | (~((~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)))))),
% 34.22/34.41 inference(quant_inst,[status(thm)],[])).
% 34.22/34.41 tff(255,plain,
% 34.22/34.41 ((~![X91: $i, X92: $i] : (atomic(X91) | (~occurrence_of(X92, X91)) | (~((~root(tptp_fun_X93_13(X92, X91), X91)) | (~subactivity_occurrence(tptp_fun_X93_13(X92, X91), X92)))))) | atomic(tptp0) | (~occurrence_of(X99!17, tptp0)) | (~((~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17))))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[254, 253])).
% 34.22/34.41 tff(256,plain,
% 34.22/34.41 (~((~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)))),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[255, 252, 239, 10])).
% 34.22/34.41 tff(257,plain,
% 34.22/34.41 (((~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17))) | subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)),
% 34.22/34.41 inference(tautology,[status(thm)],[])).
% 34.22/34.41 tff(258,plain,
% 34.22/34.41 (subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[257, 256])).
% 34.22/34.41 tff(259,plain,
% 34.22/34.41 (((~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17))) | root(tptp_fun_X93_13(X99!17, tptp0), tptp0)),
% 34.22/34.41 inference(tautology,[status(thm)],[])).
% 34.22/34.41 tff(260,plain,
% 34.22/34.41 (root(tptp_fun_X93_13(X99!17, tptp0), tptp0)),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[259, 256])).
% 34.22/34.41 tff(261,plain,
% 34.22/34.41 (((~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))) | ((~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)))) <=> ((~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))) | (~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(262,plain,
% 34.22/34.41 (((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0))) <=> ((~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(263,plain,
% 34.22/34.41 (((~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))) | ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)))) <=> ((~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))) | ((~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17))))),
% 34.22/34.41 inference(monotonicity,[status(thm)],[262])).
% 34.22/34.41 tff(264,plain,
% 34.22/34.41 (((~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))) | ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)))) <=> ((~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))) | (~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)))),
% 34.22/34.41 inference(transitivity,[status(thm)],[263, 261])).
% 34.22/34.41 tff(265,plain,
% 34.22/34.41 ((~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))) | ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)))),
% 34.22/34.41 inference(quant_inst,[status(thm)],[])).
% 34.22/34.41 tff(266,plain,
% 34.22/34.41 ((~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))) | (~occurrence_of(X99!17, tptp0)) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp0)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[265, 264])).
% 34.22/34.41 tff(267,plain,
% 34.22/34.41 ($false),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[266, 10, 260, 258, 236])).
% 34.22/34.41 tff(268,plain,(~![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))), inference(lemma,lemma(discharge,[]))).
% 34.22/34.41 tff(269,plain,
% 34.22/34.41 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34))))))))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(270,plain,
% 34.22/34.41 ((~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34))))))) <=> (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))))))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(271,plain,
% 34.22/34.41 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34))))))))),
% 34.22/34.41 inference(monotonicity,[status(thm)],[270])).
% 34.22/34.41 tff(272,plain,
% 34.22/34.41 (((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))))))) <=> ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34))))))))),
% 34.22/34.41 inference(transitivity,[status(thm)],[271, 269])).
% 34.22/34.41 tff(273,plain,
% 34.22/34.41 ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~occurrence_of(X99!17, X34)) | (~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))))))),
% 34.22/34.41 inference(quant_inst,[status(thm)],[])).
% 34.22/34.41 tff(274,plain,
% 34.22/34.41 ((~![X32: $i, X33: $i] : (~((~((~root_occ(X32, X33)) | (~((~subactivity_occurrence(X32, X33)) | (~occurrence_of(X33, tptp_fun_X34_1(X33, X32))) | (~root(X32, tptp_fun_X34_1(X33, X32))))))) | (~(root_occ(X32, X33) | ![X34: $i] : ((~occurrence_of(X33, X34)) | (~subactivity_occurrence(X32, X33)) | (~root(X32, X34)))))))) | (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))))))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[273, 272])).
% 34.22/34.41 tff(275,plain,
% 34.22/34.41 (~((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34))))))),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[274, 64])).
% 34.22/34.41 tff(276,plain,
% 34.22/34.41 (((~((~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))) | (~root(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X34_1(X99!17, tptp_fun_X93_13(X99!17, tptp0)))))))) | (~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))))) | (root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34))))),
% 34.22/34.41 inference(tautology,[status(thm)],[])).
% 34.22/34.41 tff(277,plain,
% 34.22/34.41 (root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[276, 275])).
% 34.22/34.41 tff(278,plain,
% 34.22/34.41 ((~(root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34))))) | root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))),
% 34.22/34.41 inference(tautology,[status(thm)],[])).
% 34.22/34.41 tff(279,plain,
% 34.22/34.41 (root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17) | ![X34: $i] : ((~subactivity_occurrence(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(X99!17, X34)) | (~root(tptp_fun_X93_13(X99!17, tptp0), X34)))),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[278, 277])).
% 34.22/34.41 tff(280,plain,
% 34.22/34.41 (root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[279, 268])).
% 34.22/34.41 tff(281,plain,
% 34.22/34.41 (((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)) | (tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))) <=> ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | (~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)) | (tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(282,plain,
% 34.22/34.41 (((tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17))) <=> ((~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)) | (tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.41 inference(rewrite,[status(thm)],[])).
% 34.22/34.41 tff(283,plain,
% 34.22/34.41 (((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)))) <=> ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)) | (tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))))),
% 34.22/34.41 inference(monotonicity,[status(thm)],[282])).
% 34.22/34.41 tff(284,plain,
% 34.22/34.41 (((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)))) <=> ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | (~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)) | (tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))))),
% 34.22/34.41 inference(transitivity,[status(thm)],[283, 281])).
% 34.22/34.41 tff(285,plain,
% 34.22/34.41 ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | ((tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)))),
% 34.22/34.41 inference(quant_inst,[status(thm)],[])).
% 34.22/34.41 tff(286,plain,
% 34.22/34.41 ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((X7 = X8) | (~occurrence_of(X9, X10)) | (~root_occ(X7, X9)) | (~root_occ(X8, X9)))) | (~occurrence_of(X99!17, tptp0)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), X99!17)) | (tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[285, 284])).
% 34.22/34.41 tff(287,plain,
% 34.22/34.41 (tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[286, 225, 10, 280, 235])).
% 34.22/34.41 tff(288,plain,
% 34.22/34.41 (tptp_fun_X93_13(X99!17, tptp0) = tptp_fun_X96_16(X99!17)),
% 34.22/34.41 inference(transitivity,[status(thm)],[287, 233])).
% 34.22/34.41 tff(289,plain,
% 34.22/34.41 (min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0) <=> min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)),
% 34.22/34.41 inference(monotonicity,[status(thm)],[288])).
% 34.22/34.41 tff(290,plain,
% 34.22/34.41 (min_precedes(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0) <=> min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)),
% 34.22/34.41 inference(symmetry,[status(thm)],[289])).
% 34.22/34.41 tff(291,plain,
% 34.22/34.41 (min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[165, 290])).
% 34.22/34.41 tff(292,plain,
% 34.22/34.41 (occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3) <=> occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)),
% 34.22/34.41 inference(monotonicity,[status(thm)],[287])).
% 34.22/34.41 tff(293,plain,
% 34.22/34.41 (occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3) <=> occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)),
% 34.22/34.41 inference(symmetry,[status(thm)],[292])).
% 34.22/34.41 tff(294,plain,
% 34.22/34.41 (((~occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)) | (~root_occ(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0))) | (~occurrence_of(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp4)) | (~next_subocc(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp1) | occurrence_of(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp2))) | (~next_subocc(tptp_fun_X97_15(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp0)) | (~leaf_occ(tptp_fun_X98_14(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)))) | occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)),
% 34.22/34.41 inference(tautology,[status(thm)],[])).
% 34.22/34.41 tff(295,plain,
% 34.22/34.41 (occurrence_of(tptp_fun_X96_16(tptp_fun_X73_8(tptp_fun_X97_15(X99!17), tptp_fun_X96_16(X99!17), tptp0)), tptp3)),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[294, 210])).
% 34.22/34.41 tff(296,plain,
% 34.22/34.41 (occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)),
% 34.22/34.41 inference(modus_ponens,[status(thm)],[295, 293])).
% 34.22/34.41 tff(297,assumption,(min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)), introduced(assumption)).
% 34.22/34.41 tff(298,plain,
% 34.22/34.41 (((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17))) | leaf_occ(tptp_fun_X98_14(X99!17), X99!17)),
% 34.22/34.41 inference(tautology,[status(thm)],[])).
% 34.22/34.41 tff(299,plain,
% 34.22/34.41 (leaf_occ(tptp_fun_X98_14(X99!17), X99!17)),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[298, 90])).
% 34.22/34.41 tff(300,plain,
% 34.22/34.41 (((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17))) | (occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))),
% 34.22/34.41 inference(tautology,[status(thm)],[])).
% 34.22/34.41 tff(301,plain,
% 34.22/34.41 (occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2)),
% 34.22/34.41 inference(unit_resolution,[status(thm)],[300, 90])).
% 34.22/34.41 tff(302,plain,
% 34.22/34.41 (^[X100: $i, X101: $i] : refl(((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17))) <=> ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17))))),
% 34.22/34.41 inference(bind,[status(th)],[])).
% 34.22/34.41 tff(303,plain,
% 34.22/34.41 (![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17))) <=> ![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))),
% 34.22/34.41 inference(quant_intro,[status(thm)],[302])).
% 34.22/34.41 tff(304,plain,
% 34.22/34.41 (^[X100: $i, X101: $i] : trans(monotonicity(rewrite((occurrence_of(X100, tptp3) & root_occ(X100, X99!17) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99!17)) <=> (~((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17))))), ((~(occurrence_of(X100, tptp3) & root_occ(X100, X99!17) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99!17))) <=> (~(~((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17))))))), rewrite((~(~((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17))))) <=> ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))), ((~(occurrence_of(X100, tptp3) & root_occ(X100, X99!17) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99!17))) <=> ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))))),
% 34.22/34.41 inference(bind,[status(th)],[])).
% 34.22/34.41 tff(305,plain,
% 34.22/34.41 (![X100: $i, X101: $i] : (~(occurrence_of(X100, tptp3) & root_occ(X100, X99!17) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99!17))) <=> ![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))),
% 34.22/34.42 inference(quant_intro,[status(thm)],[304])).
% 34.22/34.42 tff(306,plain,
% 34.22/34.42 (![X100: $i, X101: $i] : (~(occurrence_of(X100, tptp3) & root_occ(X100, X99!17) & (occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2)) & min_precedes(X100, X101, tptp0) & leaf_occ(X101, X99!17)))),
% 34.22/34.42 inference(and_elim,[status(thm)],[9])).
% 34.22/34.42 tff(307,plain,
% 34.22/34.42 (![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))),
% 34.22/34.42 inference(modus_ponens,[status(thm)],[306, 305])).
% 34.22/34.42 tff(308,plain,
% 34.22/34.42 (![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))),
% 34.22/34.42 inference(modus_ponens,[status(thm)],[307, 303])).
% 34.22/34.42 tff(309,plain,
% 34.22/34.42 (((~![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))) | ((~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)))) <=> ((~![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)))),
% 34.22/34.42 inference(rewrite,[status(thm)],[])).
% 34.22/34.42 tff(310,plain,
% 34.22/34.42 (((~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17))) <=> ((~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)))),
% 34.22/34.42 inference(rewrite,[status(thm)],[])).
% 34.22/34.42 tff(311,plain,
% 34.22/34.42 (((~![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))) | ((~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)))) <=> ((~![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))) | ((~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0))))),
% 34.22/34.42 inference(monotonicity,[status(thm)],[310])).
% 34.22/34.42 tff(312,plain,
% 34.22/34.42 (((~![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))) | ((~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)))) <=> ((~![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)))),
% 34.22/34.42 inference(transitivity,[status(thm)],[311, 309])).
% 34.22/34.42 tff(313,plain,
% 34.22/34.42 ((~![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))) | ((~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)))),
% 34.22/34.42 inference(quant_inst,[status(thm)],[])).
% 34.22/34.42 tff(314,plain,
% 34.22/34.42 ((~![X100: $i, X101: $i] : ((~occurrence_of(X100, tptp3)) | (~root_occ(X100, X99!17)) | (~(occurrence_of(X101, tptp1) | occurrence_of(X101, tptp2))) | (~min_precedes(X100, X101, tptp0)) | (~leaf_occ(X101, X99!17)))) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17)) | (~root_occ(tptp_fun_X93_13(X99!17, tptp0), X99!17)) | (~occurrence_of(tptp_fun_X93_13(X99!17, tptp0), tptp3)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0))),
% 34.22/34.42 inference(modus_ponens,[status(thm)],[313, 312])).
% 34.22/34.42 tff(315,plain,
% 34.22/34.42 ($false),
% 34.22/34.42 inference(unit_resolution,[status(thm)],[314, 308, 301, 299, 280, 297, 296])).
% 34.22/34.42 tff(316,plain,(~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0)), inference(lemma,lemma(discharge,[]))).
% 34.22/34.42 tff(317,plain,
% 34.22/34.42 ((~![X15: $i, X16: $i, X17: $i] : (~((~(next_subocc(X15, X16, X17) | (~min_precedes(X15, X16, X17)) | (~((~min_precedes(X15, tptp_fun_X18_0(X17, X16, X15), X17)) | (~min_precedes(tptp_fun_X18_0(X17, X16, X15), X16, X17)))))) | (~((~next_subocc(X15, X16, X17)) | (~((~min_precedes(X15, X16, X17)) | (~![X18: $i] : ((~min_precedes(X18, X16, X17)) | (~min_precedes(X15, X18, X17))))))))))) | (~((~(next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X18_0(tptp0, tptp_fun_X98_14(X99!17), tptp_fun_X97_15(X99!17)), tptp0)) | (~min_precedes(tptp_fun_X18_0(tptp0, tptp_fun_X98_14(X99!17), tptp_fun_X97_15(X99!17)), tptp_fun_X98_14(X99!17), tptp0)))))) | (~((~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0))))))))))),
% 34.22/34.42 inference(quant_inst,[status(thm)],[])).
% 34.22/34.42 tff(318,plain,
% 34.22/34.42 (~((~(next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X18_0(tptp0, tptp_fun_X98_14(X99!17), tptp_fun_X97_15(X99!17)), tptp0)) | (~min_precedes(tptp_fun_X18_0(tptp0, tptp_fun_X98_14(X99!17), tptp_fun_X97_15(X99!17)), tptp_fun_X98_14(X99!17), tptp0)))))) | (~((~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0)))))))))),
% 34.22/34.42 inference(unit_resolution,[status(thm)],[317, 154])).
% 34.22/34.42 tff(319,plain,
% 34.22/34.42 (((~(next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X18_0(tptp0, tptp_fun_X98_14(X99!17), tptp_fun_X97_15(X99!17)), tptp0)) | (~min_precedes(tptp_fun_X18_0(tptp0, tptp_fun_X98_14(X99!17), tptp_fun_X97_15(X99!17)), tptp_fun_X98_14(X99!17), tptp0)))))) | (~((~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0))))))))) | ((~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0)))))))),
% 34.22/34.42 inference(tautology,[status(thm)],[])).
% 34.22/34.42 tff(320,plain,
% 34.22/34.42 ((~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0))))))),
% 34.22/34.42 inference(unit_resolution,[status(thm)],[319, 318])).
% 34.22/34.42 tff(321,plain,
% 34.22/34.42 (((~occurrence_of(tptp_fun_X96_16(X99!17), tptp3)) | (~root_occ(tptp_fun_X96_16(X99!17), X99!17)) | (~occurrence_of(tptp_fun_X97_15(X99!17), tptp4)) | (~next_subocc(tptp_fun_X96_16(X99!17), tptp_fun_X97_15(X99!17), tptp0)) | (~(occurrence_of(tptp_fun_X98_14(X99!17), tptp1) | occurrence_of(tptp_fun_X98_14(X99!17), tptp2))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~leaf_occ(tptp_fun_X98_14(X99!17), X99!17))) | next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)),
% 34.22/34.42 inference(tautology,[status(thm)],[])).
% 34.22/34.42 tff(322,plain,
% 34.22/34.42 (next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)),
% 34.22/34.42 inference(unit_resolution,[status(thm)],[321, 90])).
% 34.22/34.42 tff(323,plain,
% 34.22/34.42 ((~((~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0)))))))) | (~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0))))))),
% 34.22/34.42 inference(tautology,[status(thm)],[])).
% 34.22/34.42 tff(324,plain,
% 34.22/34.42 ((~((~next_subocc(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0)))))))) | (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0))))))),
% 34.22/34.42 inference(unit_resolution,[status(thm)],[323, 322])).
% 34.22/34.42 tff(325,plain,
% 34.22/34.42 (~((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0)))))),
% 34.22/34.42 inference(unit_resolution,[status(thm)],[324, 320])).
% 34.22/34.42 tff(326,plain,
% 34.22/34.42 (((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~![X18: $i] : ((~min_precedes(X18, tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X97_15(X99!17), X18, tptp0))))) | min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)),
% 34.22/34.42 inference(tautology,[status(thm)],[])).
% 34.22/34.42 tff(327,plain,
% 34.22/34.42 (min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)),
% 34.22/34.42 inference(unit_resolution,[status(thm)],[326, 325])).
% 34.22/34.42 tff(328,plain,
% 34.22/34.42 (^[X0: $i, X1: $i, X2: $i, X3: $i] : refl((min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))) <=> (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))))),
% 34.22/34.42 inference(bind,[status(th)],[])).
% 34.22/34.42 tff(329,plain,
% 34.22/34.42 (![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))) <=> ![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))),
% 34.22/34.42 inference(quant_intro,[status(thm)],[328])).
% 34.22/34.42 tff(330,plain,
% 34.22/34.42 (^[X0: $i, X1: $i, X2: $i, X3: $i] : trans(monotonicity(trans(monotonicity(rewrite((min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3)) <=> (~((~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))))), ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) <=> (~(~((~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))))))), rewrite((~(~((~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))))) <=> ((~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))), ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) <=> ((~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))))), (((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3)) <=> (((~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))) | min_precedes(X0, X2, X3)))), rewrite((((~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3))) | min_precedes(X0, X2, X3)) <=> (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))), (((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3)) <=> (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))))),
% 34.22/34.42 inference(bind,[status(th)],[])).
% 34.22/34.42 tff(331,plain,
% 34.22/34.42 (![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3)) <=> ![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))),
% 34.22/34.42 inference(quant_intro,[status(thm)],[330])).
% 34.22/34.42 tff(332,plain,
% 34.22/34.42 (![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3)) <=> ![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3))),
% 34.22/34.42 inference(rewrite,[status(thm)],[])).
% 34.22/34.42 tff(333,plain,
% 34.22/34.42 (^[X0: $i, X1: $i, X2: $i, X3: $i] : rewrite(((min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3)) => min_precedes(X0, X2, X3)) <=> ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3)))),
% 34.22/34.42 inference(bind,[status(th)],[])).
% 34.22/34.42 tff(334,plain,
% 34.22/34.42 (![X0: $i, X1: $i, X2: $i, X3: $i] : ((min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3)) => min_precedes(X0, X2, X3)) <=> ![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3))),
% 34.22/34.42 inference(quant_intro,[status(thm)],[333])).
% 34.22/34.42 tff(335,axiom,(![X0: $i, X1: $i, X2: $i, X3: $i] : ((min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3)) => min_precedes(X0, X2, X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos')).
% 34.22/34.42 tff(336,plain,
% 34.22/34.42 (![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3))),
% 34.22/34.42 inference(modus_ponens,[status(thm)],[335, 334])).
% 34.22/34.42 tff(337,plain,
% 34.22/34.42 (![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3))),
% 34.22/34.42 inference(modus_ponens,[status(thm)],[336, 332])).
% 34.22/34.42 tff(338,plain,(
% 34.22/34.42 ![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(min_precedes(X0, X1, X3) & min_precedes(X1, X2, X3))) | min_precedes(X0, X2, X3))),
% 34.22/34.42 inference(skolemize,[status(sab)],[337])).
% 34.22/34.42 tff(339,plain,
% 34.22/34.42 (![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))),
% 34.22/34.42 inference(modus_ponens,[status(thm)],[338, 331])).
% 34.22/34.42 tff(340,plain,
% 34.22/34.42 (![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))),
% 34.22/34.42 inference(modus_ponens,[status(thm)],[339, 329])).
% 34.22/34.42 tff(341,plain,
% 34.22/34.42 (((~![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))) | ((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)))) <=> ((~![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)))),
% 34.22/34.42 inference(rewrite,[status(thm)],[])).
% 34.22/34.42 tff(342,plain,
% 34.22/34.42 ((min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0))) <=> ((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)))),
% 34.22/34.42 inference(rewrite,[status(thm)],[])).
% 34.22/34.42 tff(343,plain,
% 34.22/34.42 (((~![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))) | (min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)))) <=> ((~![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))) | ((~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0))))),
% 34.22/34.42 inference(monotonicity,[status(thm)],[342])).
% 34.22/34.42 tff(344,plain,
% 34.22/34.42 (((~![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))) | (min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)))) <=> ((~![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)))),
% 34.22/34.42 inference(transitivity,[status(thm)],[343, 341])).
% 34.22/34.42 tff(345,plain,
% 34.22/34.42 ((~![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))) | (min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)))),
% 34.22/34.43 inference(quant_inst,[status(thm)],[])).
% 34.22/34.43 tff(346,plain,
% 34.22/34.43 ((~![X0: $i, X1: $i, X2: $i, X3: $i] : (min_precedes(X0, X2, X3) | (~min_precedes(X1, X2, X3)) | (~min_precedes(X0, X1, X3)))) | (~min_precedes(tptp_fun_X97_15(X99!17), tptp_fun_X98_14(X99!17), tptp0)) | min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X98_14(X99!17), tptp0) | (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0))),
% 34.22/34.43 inference(modus_ponens,[status(thm)],[345, 344])).
% 34.22/34.43 tff(347,plain,
% 34.22/34.43 (~min_precedes(tptp_fun_X93_13(X99!17, tptp0), tptp_fun_X97_15(X99!17), tptp0)),
% 34.22/34.43 inference(unit_resolution,[status(thm)],[346, 340, 327, 316])).
% 34.22/34.43 tff(348,plain,
% 34.22/34.43 ($false),
% 34.22/34.43 inference(unit_resolution,[status(thm)],[347, 291])).
% 34.22/34.43 % SZS output end Proof
% 34.22/34.43 % E exiting
%------------------------------------------------------------------------------