%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU265+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:26 AM UTC 2025
% Result : Theorem 1.91s 2.09s
% Output : Proof 1.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU265+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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 06:32:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.91/2.09 % SZS status Theorem
% 1.91/2.09 % SZS output start Proof
% 1.91/2.09 tff(in_type, type, (
% 1.91/2.09 in: ( $i * $i ) > $o)).
% 1.91/2.09 tff(tptp_fun_C_8_type, type, (
% 1.91/2.09 tptp_fun_C_8: $i)).
% 1.91/2.09 tff(ordered_pair_type, type, (
% 1.91/2.09 ordered_pair: ( $i * $i ) > $i)).
% 1.91/2.09 tff(tptp_fun_E_11_type, type, (
% 1.91/2.09 tptp_fun_E_11: $i > $i)).
% 1.91/2.09 tff(tptp_fun_C_1_type, type, (
% 1.91/2.09 tptp_fun_C_1: ( $i * $i ) > $i)).
% 1.91/2.09 tff(tptp_fun_B_9_type, type, (
% 1.91/2.09 tptp_fun_B_9: $i)).
% 1.91/2.09 tff(tptp_fun_D_2_type, type, (
% 1.91/2.09 tptp_fun_D_2: ( $i * $i ) > $i)).
% 1.91/2.09 tff(relation_dom_type, type, (
% 1.91/2.09 relation_dom: $i > $i)).
% 1.91/2.09 tff(tptp_fun_D_0_type, type, (
% 1.91/2.09 tptp_fun_D_0: ( $i * $i ) > $i)).
% 1.91/2.09 tff(tptp_fun_D_12_type, type, (
% 1.91/2.09 tptp_fun_D_12: $i)).
% 1.91/2.09 tff(relation_type, type, (
% 1.91/2.09 relation: $i > $o)).
% 1.91/2.09 tff(element_type, type, (
% 1.91/2.09 element: ( $i * $i ) > $o)).
% 1.91/2.09 tff(powerset_type, type, (
% 1.91/2.09 powerset: $i > $i)).
% 1.91/2.09 tff(cartesian_product2_type, type, (
% 1.91/2.09 cartesian_product2: ( $i * $i ) > $i)).
% 1.91/2.09 tff(tptp_fun_A_10_type, type, (
% 1.91/2.09 tptp_fun_A_10: $i)).
% 1.91/2.09 tff(relation_of2_as_subset_type, type, (
% 1.91/2.09 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 1.91/2.09 tff(relation_dom_as_subset_type, type, (
% 1.91/2.09 relation_dom_as_subset: ( $i * $i * $i ) > $i)).
% 1.91/2.09 tff(relation_of2_type, type, (
% 1.91/2.09 relation_of2: ( $i * $i * $i ) > $o)).
% 1.91/2.09 tff(empty_set_type, type, (
% 1.91/2.09 empty_set: $i)).
% 1.91/2.09 tff(empty_type, type, (
% 1.91/2.09 empty: $i > $o)).
% 1.91/2.09 tff(relation_rng_type, type, (
% 1.91/2.09 relation_rng: $i > $i)).
% 1.91/2.09 tff(1,assumption,(B!9 = relation_dom(C!8)), introduced(assumption)).
% 1.91/2.09 tff(2,plain,
% 1.91/2.09 ((relation_of2_as_subset(C!8, B!9, A!10) & (((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))))) <=> (relation_of2_as_subset(C!8, B!9, A!10) & ((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(3,plain,
% 1.91/2.09 (((![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8)) | (relation_dom_as_subset(B!9, A!10, C!8) = B!9)) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)))) <=> (((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(4,plain,
% 1.91/2.09 ((relation_of2_as_subset(C!8, B!9, A!10) & ((![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8)) | (relation_dom_as_subset(B!9, A!10, C!8) = B!9)) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))))) <=> (relation_of2_as_subset(C!8, B!9, A!10) & (((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)))))),
% 1.91/2.09 inference(monotonicity,[status(thm)],[3])).
% 1.91/2.09 tff(5,plain,
% 1.91/2.09 ((relation_of2_as_subset(C!8, B!9, A!10) & ((![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8)) | (relation_dom_as_subset(B!9, A!10, C!8) = B!9)) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))))) <=> (relation_of2_as_subset(C!8, B!9, A!10) & ((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))))),
% 1.91/2.09 inference(transitivity,[status(thm)],[4, 2])).
% 1.91/2.09 tff(6,plain,
% 1.91/2.09 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, B, A)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B)))) <=> (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, B, A)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(7,plain,
% 1.91/2.09 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, B, A) => (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B)))) <=> (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, B, A)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(8,axiom,(~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, B, A) => (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t22_relset_1')).
% 1.91/2.09 tff(9,plain,
% 1.91/2.09 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, B, A)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B)))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.91/2.09 tff(10,plain,
% 1.91/2.09 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, B, A)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B)))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[9, 6])).
% 1.91/2.09 tff(11,plain,
% 1.91/2.09 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, B, A)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B)))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[10, 6])).
% 1.91/2.09 tff(12,plain,
% 1.91/2.09 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, B, A)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(D, E), C)))) <=> (relation_dom_as_subset(B, A, C) = B)))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[11, 6])).
% 1.91/2.09 tff(13,plain,
% 1.91/2.09 (relation_of2_as_subset(C!8, B!9, A!10) & ((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[12, 5])).
% 1.91/2.09 tff(14,plain,
% 1.91/2.09 (relation_of2_as_subset(C!8, B!9, A!10)),
% 1.91/2.09 inference(and_elim,[status(thm)],[13])).
% 1.91/2.09 tff(15,plain,
% 1.91/2.09 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(16,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[15])).
% 1.91/2.09 tff(17,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(18,plain,
% 1.91/2.09 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(19,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[18])).
% 1.91/2.09 tff(20,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 1.91/2.09 tff(21,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.91/2.09 tff(22,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[21, 17])).
% 1.91/2.09 tff(23,plain,(
% 1.91/2.09 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.91/2.09 inference(skolemize,[status(sab)],[22])).
% 1.91/2.09 tff(24,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[23, 16])).
% 1.91/2.09 tff(25,plain,
% 1.91/2.09 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(C!8, B!9, A!10)) | element(C!8, powerset(cartesian_product2(B!9, A!10))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(C!8, B!9, A!10)) | element(C!8, powerset(cartesian_product2(B!9, A!10))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(26,plain,
% 1.91/2.09 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(C!8, B!9, A!10)) | element(C!8, powerset(cartesian_product2(B!9, A!10))))),
% 1.91/2.09 inference(quant_inst,[status(thm)],[])).
% 1.91/2.09 tff(27,plain,
% 1.91/2.09 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(C!8, B!9, A!10)) | element(C!8, powerset(cartesian_product2(B!9, A!10)))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.91/2.09 tff(28,plain,
% 1.91/2.09 (element(C!8, powerset(cartesian_product2(B!9, A!10)))),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 1.91/2.09 tff(29,plain,
% 1.91/2.09 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(30,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[29])).
% 1.91/2.09 tff(31,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(32,plain,
% 1.91/2.09 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(33,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[32])).
% 1.91/2.09 tff(34,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 1.91/2.09 tff(35,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[34, 33])).
% 1.91/2.09 tff(36,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[35, 31])).
% 1.91/2.09 tff(37,plain,(
% 1.91/2.09 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(skolemize,[status(sab)],[36])).
% 1.91/2.09 tff(38,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[37, 30])).
% 1.91/2.09 tff(39,plain,
% 1.91/2.09 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(C!8) | (~element(C!8, powerset(cartesian_product2(B!9, A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(C!8) | (~element(C!8, powerset(cartesian_product2(B!9, A!10)))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(40,plain,
% 1.91/2.09 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(C!8) | (~element(C!8, powerset(cartesian_product2(B!9, A!10)))))),
% 1.91/2.09 inference(quant_inst,[status(thm)],[])).
% 1.91/2.09 tff(41,plain,
% 1.91/2.09 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(C!8) | (~element(C!8, powerset(cartesian_product2(B!9, A!10))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.91/2.09 tff(42,plain,
% 1.91/2.09 (relation(C!8)),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 1.91/2.09 tff(43,plain,
% 1.91/2.09 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(44,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[43])).
% 1.91/2.09 tff(45,plain,
% 1.91/2.09 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(46,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[45])).
% 1.91/2.09 tff(47,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 1.91/2.09 inference(transitivity,[status(thm)],[46, 44])).
% 1.91/2.09 tff(48,plain,
% 1.91/2.09 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(49,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[48])).
% 1.91/2.09 tff(50,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(51,plain,
% 1.91/2.09 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(52,plain,
% 1.91/2.09 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[51])).
% 1.91/2.09 tff(53,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_relat_1')).
% 1.91/2.09 tff(54,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.91/2.09 tff(55,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.91/2.09 tff(56,plain,(
% 1.91/2.09 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))),
% 1.91/2.09 inference(skolemize,[status(sab)],[55])).
% 1.91/2.09 tff(57,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[56, 49])).
% 1.91/2.09 tff(58,plain,
% 1.91/2.09 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[57, 47])).
% 1.91/2.09 tff(59,plain,
% 1.91/2.09 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))) | (B = relation_dom(C!8)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))) | (B = relation_dom(C!8)))))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(60,plain,
% 1.91/2.09 (((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((B = relation_dom(C!8)) | (~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8))))))))))) <=> ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))) | (B = relation_dom(C!8)))))))),
% 1.91/2.09 inference(rewrite,[status(thm)],[])).
% 1.91/2.09 tff(61,plain,
% 1.91/2.09 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((B = relation_dom(C!8)) | (~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))) | (B = relation_dom(C!8))))))))),
% 1.91/2.09 inference(monotonicity,[status(thm)],[60])).
% 1.91/2.09 tff(62,plain,
% 1.91/2.09 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((B = relation_dom(C!8)) | (~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))) | (B = relation_dom(C!8)))))))),
% 1.91/2.09 inference(transitivity,[status(thm)],[61, 59])).
% 1.91/2.09 tff(63,plain,
% 1.91/2.09 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((B = relation_dom(C!8)) | (~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))))))))),
% 1.91/2.09 inference(quant_inst,[status(thm)],[])).
% 1.91/2.09 tff(64,plain,
% 1.91/2.09 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))) | (B = relation_dom(C!8))))))),
% 1.91/2.09 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.91/2.09 tff(65,plain,
% 1.91/2.09 (![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))) | (B = relation_dom(C!8))))))),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[64, 58, 42])).
% 1.91/2.09 tff(66,plain,
% 1.91/2.09 ((~![B: $i] : (~((~((~(B = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_C_1(B, C!8), tptp_fun_D_2(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!8), D), C!8)))))) | (B = relation_dom(C!8))))))) | (~((~((~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8))))))),
% 1.91/2.09 inference(quant_inst,[status(thm)],[])).
% 1.91/2.09 tff(67,plain,
% 1.91/2.09 (~((~((~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8)))))),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[66, 65])).
% 1.91/2.09 tff(68,plain,
% 1.91/2.09 (((~((~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8))))) | ((~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))),
% 1.91/2.09 inference(tautology,[status(thm)],[])).
% 1.91/2.09 tff(69,plain,
% 1.91/2.09 ((~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8))))))),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[68, 67])).
% 1.91/2.09 tff(70,plain,
% 1.91/2.09 ((~((~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8))))))),
% 1.91/2.09 inference(tautology,[status(thm)],[])).
% 1.91/2.09 tff(71,plain,
% 1.91/2.09 ((~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8))))))),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.91/2.09 tff(72,plain,
% 1.91/2.09 (![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8))))))),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[71, 1])).
% 1.91/2.09 tff(73,plain,
% 1.91/2.09 ((~![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8))))))) | (~((~((~in(D!12, B!9)) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8))) | (~(in(D!12, B!9) | ![D: $i] : (~in(ordered_pair(D!12, D), C!8))))))),
% 1.91/2.09 inference(quant_inst,[status(thm)],[])).
% 1.91/2.09 tff(74,plain,
% 1.91/2.09 (~((~((~in(D!12, B!9)) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8))) | (~(in(D!12, B!9) | ![D: $i] : (~in(ordered_pair(D!12, D), C!8)))))),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[73, 72])).
% 1.91/2.09 tff(75,plain,
% 1.91/2.09 (((~((~in(D!12, B!9)) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8))) | (~(in(D!12, B!9) | ![D: $i] : (~in(ordered_pair(D!12, D), C!8))))) | ((~in(D!12, B!9)) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8))),
% 1.91/2.09 inference(tautology,[status(thm)],[])).
% 1.91/2.09 tff(76,plain,
% 1.91/2.09 ((~in(D!12, B!9)) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8)),
% 1.91/2.09 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.91/2.09 tff(77,plain,
% 1.91/2.09 ((B!9 = relation_dom_as_subset(B!9, A!10, C!8)) <=> (relation_dom_as_subset(B!9, A!10, C!8) = B!9)),
% 1.91/2.09 inference(commutativity,[status(thm)],[])).
% 1.91/2.09 tff(78,plain,
% 1.91/2.09 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 1.91/2.09 inference(bind,[status(th)],[])).
% 1.91/2.09 tff(79,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.91/2.09 inference(quant_intro,[status(thm)],[78])).
% 1.91/2.09 tff(80,plain,
% 1.91/2.09 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(81,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 1.91/2.10 tff(82,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.91/2.10 tff(83,plain,(
% 1.91/2.10 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.91/2.10 inference(skolemize,[status(sab)],[82])).
% 1.91/2.10 tff(84,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.91/2.10 tff(85,plain,
% 1.91/2.10 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(C!8, B!9, A!10) <=> relation_of2(C!8, B!9, A!10))),
% 1.91/2.10 inference(quant_inst,[status(thm)],[])).
% 1.91/2.10 tff(86,plain,
% 1.91/2.10 (relation_of2_as_subset(C!8, B!9, A!10) <=> relation_of2(C!8, B!9, A!10)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[85, 84])).
% 1.91/2.10 tff(87,plain,
% 1.91/2.10 ((~(relation_of2_as_subset(C!8, B!9, A!10) <=> relation_of2(C!8, B!9, A!10))) | (~relation_of2_as_subset(C!8, B!9, A!10)) | relation_of2(C!8, B!9, A!10)),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(88,plain,
% 1.91/2.10 ((~(relation_of2_as_subset(C!8, B!9, A!10) <=> relation_of2(C!8, B!9, A!10))) | relation_of2(C!8, B!9, A!10)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[87, 14])).
% 1.91/2.10 tff(89,plain,
% 1.91/2.10 (relation_of2(C!8, B!9, A!10)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[88, 86])).
% 1.91/2.10 tff(90,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(91,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[90])).
% 1.91/2.10 tff(92,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(93,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2(C, A, B) => (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(94,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[93])).
% 1.91/2.10 tff(95,axiom,(![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => (relation_dom_as_subset(A, B, C) = relation_dom(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_relset_1')).
% 1.91/2.10 tff(96,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.91/2.10 tff(97,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[96, 92])).
% 1.91/2.10 tff(98,plain,(
% 1.91/2.10 ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.91/2.10 inference(skolemize,[status(sab)],[97])).
% 1.91/2.10 tff(99,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[98, 91])).
% 1.91/2.10 tff(100,plain,
% 1.91/2.10 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(C!8, B!9, A!10)) | (relation_dom_as_subset(B!9, A!10, C!8) = relation_dom(C!8)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(C!8, B!9, A!10)) | (relation_dom_as_subset(B!9, A!10, C!8) = relation_dom(C!8)))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(101,plain,
% 1.91/2.10 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(C!8, B!9, A!10)) | (relation_dom_as_subset(B!9, A!10, C!8) = relation_dom(C!8)))),
% 1.91/2.10 inference(quant_inst,[status(thm)],[])).
% 1.91/2.10 tff(102,plain,
% 1.91/2.10 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(C!8, B!9, A!10)) | (relation_dom_as_subset(B!9, A!10, C!8) = relation_dom(C!8))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.91/2.10 tff(103,plain,
% 1.91/2.10 (relation_dom_as_subset(B!9, A!10, C!8) = relation_dom(C!8)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[102, 99, 89])).
% 1.91/2.10 tff(104,plain,
% 1.91/2.10 (relation_dom(C!8) = relation_dom_as_subset(B!9, A!10, C!8)),
% 1.91/2.10 inference(symmetry,[status(thm)],[103])).
% 1.91/2.10 tff(105,plain,
% 1.91/2.10 ((B!9 = relation_dom(C!8)) <=> (B!9 = relation_dom_as_subset(B!9, A!10, C!8))),
% 1.91/2.10 inference(monotonicity,[status(thm)],[104])).
% 1.91/2.10 tff(106,plain,
% 1.91/2.10 ((B!9 = relation_dom(C!8)) <=> (relation_dom_as_subset(B!9, A!10, C!8) = B!9)),
% 1.91/2.10 inference(transitivity,[status(thm)],[105, 77])).
% 1.91/2.10 tff(107,plain,
% 1.91/2.10 (relation_dom_as_subset(B!9, A!10, C!8) = B!9),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[1, 106])).
% 1.91/2.10 tff(108,plain,
% 1.91/2.10 (((~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8)))))) <=> ((~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8))))))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(109,plain,
% 1.91/2.10 (((~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8))))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))) <=> ((~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8))))))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(110,plain,
% 1.91/2.10 ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) <=> (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8)))))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(111,plain,
% 1.91/2.10 (((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))) <=> ((~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8))))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)))),
% 1.91/2.10 inference(monotonicity,[status(thm)],[110])).
% 1.91/2.10 tff(112,plain,
% 1.91/2.10 (((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))) <=> ((~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8))))))),
% 1.91/2.10 inference(transitivity,[status(thm)],[111, 109])).
% 1.91/2.10 tff(113,plain,
% 1.91/2.10 ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))),
% 1.91/2.10 inference(and_elim,[status(thm)],[13])).
% 1.91/2.10 tff(114,plain,
% 1.91/2.10 ((~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8)))))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.91/2.10 tff(115,plain,
% 1.91/2.10 ((~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8)))))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[114, 108])).
% 1.91/2.10 tff(116,plain,
% 1.91/2.10 (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8))))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[115, 107])).
% 1.91/2.10 tff(117,plain,
% 1.91/2.10 (((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8)))) | in(D!12, B!9)),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(118,plain,
% 1.91/2.10 (in(D!12, B!9)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[117, 116])).
% 1.91/2.10 tff(119,plain,
% 1.91/2.10 ((~((~in(D!12, B!9)) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8))) | (~in(D!12, B!9)) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8)),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(120,plain,
% 1.91/2.10 ((~((~in(D!12, B!9)) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8))) | in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[119, 118])).
% 1.91/2.10 tff(121,plain,
% 1.91/2.10 (in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[120, 76])).
% 1.91/2.10 tff(122,plain,
% 1.91/2.10 (((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(D!12, E), C!8)))) | ![E: $i] : (~in(ordered_pair(D!12, E), C!8))),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(123,plain,
% 1.91/2.10 (![E: $i] : (~in(ordered_pair(D!12, E), C!8))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[122, 116])).
% 1.91/2.10 tff(124,plain,
% 1.91/2.10 ((~![E: $i] : (~in(ordered_pair(D!12, E), C!8))) | (~in(ordered_pair(D!12, tptp_fun_D_0(D!12, C!8)), C!8))),
% 1.91/2.10 inference(quant_inst,[status(thm)],[])).
% 1.91/2.10 tff(125,plain,
% 1.91/2.10 ($false),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[124, 123, 121])).
% 1.91/2.10 tff(126,plain,(~(B!9 = relation_dom(C!8))), inference(lemma,lemma(discharge,[]))).
% 1.91/2.10 tff(127,plain,
% 1.91/2.10 (((~((~(B!9 = relation_dom(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(C, tptp_fun_D_0(C, C!8)), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(C, D), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8))))) | ((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8)))),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(128,plain,
% 1.91/2.10 ((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[127, 67])).
% 1.91/2.10 tff(129,plain,
% 1.91/2.10 ((~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8)))) | (~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8))),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(130,plain,
% 1.91/2.10 ((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))) | (B!9 = relation_dom(C!8))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[129, 128])).
% 1.91/2.10 tff(131,plain,
% 1.91/2.10 (~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[130, 126])).
% 1.91/2.10 tff(132,plain,
% 1.91/2.10 (((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8))))) | ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(133,plain,
% 1.91/2.10 ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[132, 131])).
% 1.91/2.10 tff(134,plain,
% 1.91/2.10 (((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8))))) | (in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(135,plain,
% 1.91/2.10 (in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[134, 131])).
% 1.91/2.10 tff(136,assumption,(~in(tptp_fun_C_1(B!9, C!8), B!9)), introduced(assumption)).
% 1.91/2.10 tff(137,assumption,(~empty(B!9)), introduced(assumption)).
% 1.91/2.10 tff(138,plain,
% 1.91/2.10 (^[A: $i, B: $i] : refl((in(A, B) | empty(B) | (~element(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(139,plain,
% 1.91/2.10 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[138])).
% 1.91/2.10 tff(140,plain,
% 1.91/2.10 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(141,plain,
% 1.91/2.10 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(142,plain,
% 1.91/2.10 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[141])).
% 1.91/2.10 tff(143,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 1.91/2.10 tff(144,plain,
% 1.91/2.10 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.91/2.10 tff(145,plain,
% 1.91/2.10 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[144, 140])).
% 1.91/2.10 tff(146,plain,(
% 1.91/2.10 ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.91/2.10 inference(skolemize,[status(sab)],[145])).
% 1.91/2.10 tff(147,plain,
% 1.91/2.10 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[146, 139])).
% 1.91/2.10 tff(148,plain,
% 1.91/2.10 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(149,plain,
% 1.91/2.10 ((in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9))) <=> (empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(150,plain,
% 1.91/2.10 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9))))),
% 1.91/2.10 inference(monotonicity,[status(thm)],[149])).
% 1.91/2.10 tff(151,plain,
% 1.91/2.10 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 1.91/2.10 inference(transitivity,[status(thm)],[150, 148])).
% 1.91/2.10 tff(152,plain,
% 1.91/2.10 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 1.91/2.10 inference(quant_inst,[status(thm)],[])).
% 1.91/2.10 tff(153,plain,
% 1.91/2.10 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.91/2.10 tff(154,plain,
% 1.91/2.10 (~element(tptp_fun_C_1(B!9, C!8), B!9)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[153, 147, 137, 136])).
% 1.91/2.10 tff(155,assumption,(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)), introduced(assumption)).
% 1.91/2.10 tff(156,plain,
% 1.91/2.10 ((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8))) | in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(157,plain,
% 1.91/2.10 (in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[156, 136, 155])).
% 1.91/2.10 tff(158,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C)))))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C)))))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(159,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[158])).
% 1.91/2.10 tff(160,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(B, relation_rng(C))) <=> (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C)))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))), rewrite(((~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(161,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[160])).
% 1.91/2.10 tff(162,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(163,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))) <=> ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> (relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))))), rewrite((relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(164,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[163])).
% 1.91/2.10 tff(165,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_relat_1')).
% 1.91/2.10 tff(166,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.91/2.10 tff(167,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[166, 162])).
% 1.91/2.10 tff(168,plain,(
% 1.91/2.10 ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.91/2.10 inference(skolemize,[status(sab)],[167])).
% 1.91/2.10 tff(169,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[168, 161])).
% 1.91/2.10 tff(170,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[169, 159])).
% 1.91/2.10 tff(171,plain,
% 1.91/2.10 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))) | ((~relation(C!8)) | (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)) | (~((~in(tptp_fun_D_2(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))) | (~relation(C!8)) | (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)) | (~((~in(tptp_fun_D_2(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(172,plain,
% 1.91/2.10 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))) | ((~relation(C!8)) | (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)) | (~((~in(tptp_fun_D_2(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))))),
% 1.91/2.10 inference(quant_inst,[status(thm)],[])).
% 1.91/2.10 tff(173,plain,
% 1.91/2.10 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))) | (~relation(C!8)) | (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)) | (~((~in(tptp_fun_D_2(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8)))))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.91/2.10 tff(174,plain,
% 1.91/2.10 (~((~in(tptp_fun_D_2(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[173, 170, 42, 157])).
% 1.91/2.10 tff(175,plain,
% 1.91/2.10 (((~in(tptp_fun_D_2(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8)))) | in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))),
% 1.91/2.10 inference(tautology,[status(thm)],[])).
% 1.91/2.10 tff(176,plain,
% 1.91/2.10 (in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[175, 174])).
% 1.91/2.10 tff(177,plain,
% 1.91/2.10 (element(relation_dom(C!8), powerset(B!9)) <=> element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9))),
% 1.91/2.10 inference(monotonicity,[status(thm)],[104])).
% 1.91/2.10 tff(178,plain,
% 1.91/2.10 (element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9)) <=> element(relation_dom(C!8), powerset(B!9))),
% 1.91/2.10 inference(symmetry,[status(thm)],[177])).
% 1.91/2.10 tff(179,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A))) <=> ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(180,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[179])).
% 1.91/2.10 tff(181,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(182,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2(C, A, B) => element(relation_dom_as_subset(A, B, C), powerset(A))) <=> ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(183,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => element(relation_dom_as_subset(A, B, C), powerset(A))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[182])).
% 1.91/2.10 tff(184,axiom,(![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => element(relation_dom_as_subset(A, B, C), powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_relset_1')).
% 1.91/2.10 tff(185,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.91/2.10 tff(186,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[185, 181])).
% 1.91/2.10 tff(187,plain,(
% 1.91/2.10 ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))),
% 1.91/2.10 inference(skolemize,[status(sab)],[186])).
% 1.91/2.10 tff(188,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[187, 180])).
% 1.91/2.10 tff(189,plain,
% 1.91/2.10 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))) | ((~relation_of2(C!8, B!9, A!10)) | element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))) | (~relation_of2(C!8, B!9, A!10)) | element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9)))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(190,plain,
% 1.91/2.10 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))) | ((~relation_of2(C!8, B!9, A!10)) | element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9)))),
% 1.91/2.10 inference(quant_inst,[status(thm)],[])).
% 1.91/2.10 tff(191,plain,
% 1.91/2.10 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_dom_as_subset(A, B, C), powerset(A)))) | (~relation_of2(C!8, B!9, A!10)) | element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.91/2.10 tff(192,plain,
% 1.91/2.10 (element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9))),
% 1.91/2.10 inference(unit_resolution,[status(thm)],[191, 188, 89])).
% 1.91/2.10 tff(193,plain,
% 1.91/2.10 (element(relation_dom(C!8), powerset(B!9))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[192, 178])).
% 1.91/2.10 tff(194,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(195,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[194])).
% 1.91/2.10 tff(196,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(197,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[196])).
% 1.91/2.10 tff(198,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(199,plain,
% 1.91/2.10 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 1.91/2.10 inference(bind,[status(th)],[])).
% 1.91/2.10 tff(200,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.91/2.10 inference(quant_intro,[status(thm)],[199])).
% 1.91/2.10 tff(201,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 1.91/2.10 tff(202,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.91/2.10 tff(203,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[202, 198])).
% 1.91/2.10 tff(204,plain,(
% 1.91/2.10 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.91/2.10 inference(skolemize,[status(sab)],[203])).
% 1.91/2.10 tff(205,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[204, 197])).
% 1.91/2.10 tff(206,plain,
% 1.91/2.10 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.91/2.10 inference(modus_ponens,[status(thm)],[205, 195])).
% 1.91/2.10 tff(207,plain,
% 1.91/2.10 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_dom(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(208,plain,
% 1.91/2.10 ((element(tptp_fun_C_1(B!9, C!8), B!9) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | (~element(relation_dom(C!8), powerset(B!9)))) <=> ((~element(relation_dom(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9))),
% 1.91/2.10 inference(rewrite,[status(thm)],[])).
% 1.91/2.10 tff(209,plain,
% 1.91/2.10 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_1(B!9, C!8), B!9) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | (~element(relation_dom(C!8), powerset(B!9))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_dom(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 1.91/2.10 inference(monotonicity,[status(thm)],[208])).
% 1.91/2.10 tff(210,plain,
% 1.91/2.10 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_1(B!9, C!8), B!9) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | (~element(relation_dom(C!8), powerset(B!9))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9))),
% 1.91/2.11 inference(transitivity,[status(thm)],[209, 207])).
% 1.91/2.11 tff(211,plain,
% 1.91/2.11 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_1(B!9, C!8), B!9) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | (~element(relation_dom(C!8), powerset(B!9))))),
% 1.91/2.11 inference(quant_inst,[status(thm)],[])).
% 1.91/2.11 tff(212,plain,
% 1.91/2.11 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9)),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[211, 210])).
% 1.91/2.11 tff(213,plain,
% 1.91/2.11 ($false),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[212, 206, 193, 176, 154])).
% 1.91/2.11 tff(214,plain,(in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)))), inference(lemma,lemma(discharge,[]))).
% 1.91/2.11 tff(215,plain,
% 1.91/2.11 (empty(B!9)),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[214, 136, 135])).
% 1.91/2.11 tff(216,plain,
% 1.91/2.11 (^[A: $i, B: $i] : refl(((A = B) | (~empty(B)) | (~empty(A))) <=> ((A = B) | (~empty(B)) | (~empty(A))))),
% 1.91/2.11 inference(bind,[status(th)],[])).
% 1.91/2.11 tff(217,plain,
% 1.91/2.11 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 1.91/2.11 inference(quant_intro,[status(thm)],[216])).
% 1.91/2.11 tff(218,plain,
% 1.91/2.11 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(B)) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(B)) | (~empty(A))))))), rewrite((~(~((A = B) | (~empty(B)) | (~empty(A))))) <=> ((A = B) | (~empty(B)) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(B)) | (~empty(A)))))),
% 1.91/2.11 inference(bind,[status(th)],[])).
% 1.91/2.11 tff(219,plain,
% 1.91/2.11 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 1.91/2.11 inference(quant_intro,[status(thm)],[218])).
% 1.91/2.11 tff(220,plain,
% 1.91/2.11 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(221,plain,
% 1.91/2.11 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 1.91/2.11 inference(bind,[status(th)],[])).
% 1.91/2.11 tff(222,plain,
% 1.91/2.11 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.91/2.11 inference(quant_intro,[status(thm)],[221])).
% 1.91/2.11 tff(223,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 1.91/2.11 tff(224,plain,
% 1.91/2.11 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.91/2.11 tff(225,plain,
% 1.91/2.11 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[224, 220])).
% 1.91/2.11 tff(226,plain,(
% 1.91/2.11 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.91/2.11 inference(skolemize,[status(sab)],[225])).
% 1.91/2.11 tff(227,plain,
% 1.91/2.11 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[226, 219])).
% 1.91/2.11 tff(228,plain,
% 1.91/2.11 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[227, 217])).
% 1.91/2.11 tff(229,plain,
% 1.91/2.11 (empty(empty_set) <=> empty(empty_set)),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(230,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 1.91/2.11 tff(231,plain,
% 1.91/2.11 (empty(empty_set)),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.91/2.11 tff(232,plain,
% 1.91/2.11 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((~empty(empty_set)) | (~empty(B!9)) | (B!9 = empty_set))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (~empty(B!9)) | (B!9 = empty_set))),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(233,plain,
% 1.91/2.11 (((B!9 = empty_set) | (~empty(empty_set)) | (~empty(B!9))) <=> ((~empty(empty_set)) | (~empty(B!9)) | (B!9 = empty_set))),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(234,plain,
% 1.91/2.11 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((B!9 = empty_set) | (~empty(empty_set)) | (~empty(B!9)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((~empty(empty_set)) | (~empty(B!9)) | (B!9 = empty_set)))),
% 1.91/2.11 inference(monotonicity,[status(thm)],[233])).
% 1.91/2.11 tff(235,plain,
% 1.91/2.11 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((B!9 = empty_set) | (~empty(empty_set)) | (~empty(B!9)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (~empty(B!9)) | (B!9 = empty_set))),
% 1.91/2.11 inference(transitivity,[status(thm)],[234, 232])).
% 1.91/2.11 tff(236,plain,
% 1.91/2.11 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((B!9 = empty_set) | (~empty(empty_set)) | (~empty(B!9)))),
% 1.91/2.11 inference(quant_inst,[status(thm)],[])).
% 1.91/2.11 tff(237,plain,
% 1.91/2.11 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (~empty(B!9)) | (B!9 = empty_set)),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.91/2.11 tff(238,plain,
% 1.91/2.11 (B!9 = empty_set),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[237, 231, 228, 215])).
% 1.91/2.11 tff(239,plain,
% 1.91/2.11 (powerset(B!9) = powerset(empty_set)),
% 1.91/2.11 inference(monotonicity,[status(thm)],[238])).
% 1.91/2.11 tff(240,plain,
% 1.91/2.11 (powerset(empty_set) = powerset(B!9)),
% 1.91/2.11 inference(symmetry,[status(thm)],[239])).
% 1.91/2.11 tff(241,plain,
% 1.91/2.11 (element(relation_dom(C!8), powerset(empty_set)) <=> element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9))),
% 1.91/2.11 inference(monotonicity,[status(thm)],[104, 240])).
% 1.91/2.11 tff(242,plain,
% 1.91/2.11 (element(relation_dom_as_subset(B!9, A!10, C!8), powerset(B!9)) <=> element(relation_dom(C!8), powerset(empty_set))),
% 1.91/2.11 inference(symmetry,[status(thm)],[241])).
% 1.91/2.11 tff(243,plain,
% 1.91/2.11 (element(relation_dom(C!8), powerset(empty_set))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[192, 242])).
% 1.91/2.11 tff(244,plain,
% 1.91/2.11 (in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_D_2(B!9, C!8)), C!8)),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[156, 136, 135])).
% 1.91/2.11 tff(245,plain,
% 1.91/2.11 (~((~in(tptp_fun_D_2(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[173, 170, 42, 244])).
% 1.91/2.11 tff(246,plain,
% 1.91/2.11 (in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[175, 245])).
% 1.91/2.11 tff(247,plain,
% 1.91/2.11 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 1.91/2.11 inference(bind,[status(th)],[])).
% 1.91/2.11 tff(248,plain,
% 1.91/2.11 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.91/2.11 inference(quant_intro,[status(thm)],[247])).
% 1.91/2.11 tff(249,plain,
% 1.91/2.11 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 1.91/2.11 inference(bind,[status(th)],[])).
% 1.91/2.11 tff(250,plain,
% 1.91/2.11 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.91/2.11 inference(quant_intro,[status(thm)],[249])).
% 1.91/2.11 tff(251,plain,
% 1.91/2.11 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(252,plain,
% 1.91/2.11 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 1.91/2.11 inference(bind,[status(th)],[])).
% 1.91/2.11 tff(253,plain,
% 1.91/2.11 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.91/2.11 inference(quant_intro,[status(thm)],[252])).
% 1.91/2.11 tff(254,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 1.91/2.11 tff(255,plain,
% 1.91/2.11 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[254, 253])).
% 1.91/2.11 tff(256,plain,
% 1.91/2.11 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[255, 251])).
% 1.91/2.11 tff(257,plain,(
% 1.91/2.11 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.91/2.11 inference(skolemize,[status(sab)],[256])).
% 1.91/2.11 tff(258,plain,
% 1.91/2.11 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[257, 250])).
% 1.91/2.11 tff(259,plain,
% 1.91/2.11 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[258, 248])).
% 1.91/2.11 tff(260,plain,
% 1.91/2.11 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(empty_set)) | (~element(relation_dom(C!8), powerset(empty_set))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(empty_set)) | (~element(relation_dom(C!8), powerset(empty_set))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(261,plain,
% 1.91/2.11 (((~empty(empty_set)) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | (~element(relation_dom(C!8), powerset(empty_set)))) <=> ((~empty(empty_set)) | (~element(relation_dom(C!8), powerset(empty_set))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(262,plain,
% 1.91/2.11 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(empty_set)) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | (~element(relation_dom(C!8), powerset(empty_set))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(empty_set)) | (~element(relation_dom(C!8), powerset(empty_set))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8)))))),
% 1.91/2.11 inference(monotonicity,[status(thm)],[261])).
% 1.91/2.11 tff(263,plain,
% 1.91/2.11 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(empty_set)) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | (~element(relation_dom(C!8), powerset(empty_set))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(empty_set)) | (~element(relation_dom(C!8), powerset(empty_set))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))))),
% 1.91/2.11 inference(transitivity,[status(thm)],[262, 260])).
% 1.91/2.11 tff(264,plain,
% 1.91/2.11 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(empty_set)) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8))) | (~element(relation_dom(C!8), powerset(empty_set))))),
% 1.91/2.11 inference(quant_inst,[status(thm)],[])).
% 1.91/2.11 tff(265,plain,
% 1.91/2.11 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(empty_set)) | (~element(relation_dom(C!8), powerset(empty_set))) | (~in(tptp_fun_C_1(B!9, C!8), relation_dom(C!8)))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.91/2.11 tff(266,plain,
% 1.91/2.11 (~element(relation_dom(C!8), powerset(empty_set))),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[265, 231, 259, 246])).
% 1.91/2.11 tff(267,plain,
% 1.91/2.11 ($false),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[266, 243])).
% 1.91/2.11 tff(268,plain,(in(tptp_fun_C_1(B!9, C!8), B!9)), inference(lemma,lemma(discharge,[]))).
% 1.91/2.11 tff(269,plain,
% 1.91/2.11 ((~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8)))) | (~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8))),
% 1.91/2.11 inference(tautology,[status(thm)],[])).
% 1.91/2.11 tff(270,plain,
% 1.91/2.11 (![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8))),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[269, 268, 133])).
% 1.91/2.11 tff(271,plain,
% 1.91/2.11 ((~![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), D), C!8))) | (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_E_11(tptp_fun_C_1(B!9, C!8))), C!8))),
% 1.91/2.11 inference(quant_inst,[status(thm)],[])).
% 1.91/2.11 tff(272,plain,
% 1.91/2.11 (~in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_E_11(tptp_fun_C_1(B!9, C!8))), C!8)),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[271, 270])).
% 1.91/2.11 tff(273,plain,
% 1.91/2.11 ((~(B!9 = relation_dom(C!8))) <=> (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9))),
% 1.91/2.11 inference(monotonicity,[status(thm)],[106])).
% 1.91/2.11 tff(274,plain,
% 1.91/2.11 (~(relation_dom_as_subset(B!9, A!10, C!8) = B!9)),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[126, 273])).
% 1.91/2.11 tff(275,plain,
% 1.91/2.11 (((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) <=> ((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8)))),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(276,plain,
% 1.91/2.11 ((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))),
% 1.91/2.11 inference(and_elim,[status(thm)],[13])).
% 1.91/2.11 tff(277,plain,
% 1.91/2.11 ((relation_dom_as_subset(B!9, A!10, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.91/2.11 tff(278,plain,
% 1.91/2.11 (![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[277, 274])).
% 1.91/2.11 tff(279,plain,
% 1.91/2.11 (((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) | ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_E_11(tptp_fun_C_1(B!9, C!8))), C!8))) <=> ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) | (~in(tptp_fun_C_1(B!9, C!8), B!9)) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_E_11(tptp_fun_C_1(B!9, C!8))), C!8))),
% 1.91/2.11 inference(rewrite,[status(thm)],[])).
% 1.91/2.11 tff(280,plain,
% 1.91/2.11 ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) | ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_E_11(tptp_fun_C_1(B!9, C!8))), C!8))),
% 1.91/2.11 inference(quant_inst,[status(thm)],[])).
% 1.91/2.11 tff(281,plain,
% 1.91/2.11 ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(D, tptp_fun_E_11(D)), C!8))) | (~in(tptp_fun_C_1(B!9, C!8), B!9)) | in(ordered_pair(tptp_fun_C_1(B!9, C!8), tptp_fun_E_11(tptp_fun_C_1(B!9, C!8))), C!8)),
% 1.91/2.11 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.91/2.11 tff(282,plain,
% 1.91/2.11 ($false),
% 1.91/2.11 inference(unit_resolution,[status(thm)],[281, 278, 268, 272])).
% 1.91/2.11 % SZS output end Proof
% 1.96/2.11 % E exiting
%------------------------------------------------------------------------------