%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU250+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:27:23 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU250+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:30:46 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_A_8_type, type, (
% 0.21/0.39 tptp_fun_A_8: $i)).
% 0.21/0.39 tff(tptp_fun_C_0_type, type, (
% 0.21/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.39 tff(relation_field_type, type, (
% 0.21/0.39 relation_field: $i > $i)).
% 0.21/0.39 tff(relation_restriction_type, type, (
% 0.21/0.39 relation_restriction: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_B_7_type, type, (
% 0.21/0.39 tptp_fun_B_7: $i)).
% 0.21/0.39 tff(subset_type, type, (
% 0.21/0.39 subset: ( $i * $i ) > $o)).
% 0.21/0.39 tff(relation_type, type, (
% 0.21/0.39 relation: $i > $o)).
% 0.21/0.39 tff(set_union2_type, type, (
% 0.21/0.39 set_union2: ( $i * $i ) > $i)).
% 0.21/0.39 tff(relation_rng_type, type, (
% 0.21/0.39 relation_rng: $i > $i)).
% 0.21/0.39 tff(relation_dom_type, type, (
% 0.21/0.39 relation_dom: $i > $i)).
% 0.21/0.39 tff(1,assumption,(~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 ((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : (relation(B) => (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(10,axiom,(~![A: $i, B: $i] : (relation(B) => (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_wellord1')).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.21/0.39 tff(15,plain,(
% 0.21/0.39 ~((~relation(B!7)) | (subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (relation(B!7)),
% 0.21/0.39 inference(or_elim,[status(thm)],[15])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(C)) & in(A, B)) <=> (~((~in(A, relation_field(C))) | (~in(A, B))))), (((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~((~in(A, relation_field(C))) | (~in(A, B)))) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))))), rewrite(((~((~in(A, relation_field(C))) | (~in(A, B)))) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))), (((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))) <=> ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))), ((relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> (relation(C) => ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))))), rewrite((relation(C) => ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))) <=> ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))), ((relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.39 tff(24,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t19_wellord1')).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.39 tff(27,plain,(
% 0.21/0.39 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))))) <=> ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[32, 30])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[35, 29, 16, 7, 5])).
% 0.21/0.39 tff(37,plain,((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.40 tff(43,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_relat_1')).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.21/0.40 tff(46,plain,(
% 0.21/0.40 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[45])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(B!7)) | (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(B!7)) | (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(B!7)) | (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(B!7)) | (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[50, 47, 16])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (set_union2(relation_dom(B!7), relation_rng(B!7)) = relation_field(B!7)),
% 0.21/0.40 inference(symmetry,[status(thm)],[51])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) <=> subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) <=> subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.21/0.40 inference(symmetry,[status(thm)],[53])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 ((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) <=> (~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[54])).
% 0.21/0.40 tff(56,assumption,(~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))), introduced(assumption)).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[61, 59])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.40 tff(68,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.40 tff(71,plain,(
% 0.21/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[70])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, set_union2(relation_dom(B!7), relation_rng(B!7)))))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (~((~((~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, set_union2(relation_dom(B!7), relation_rng(B!7)))))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((~((~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, set_union2(relation_dom(B!7), relation_rng(B!7)))))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))))))) | (subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)) <=> in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))) <=> in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))),
% 0.21/0.40 inference(symmetry,[status(thm)],[78])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 ((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))) <=> (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.40 tff(81,assumption,(~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))), introduced(assumption)).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 (((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[85, 81])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[89, 29, 16, 86])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[92, 84])).
% 0.21/0.41 tff(94,plain,((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 ((~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))))) | subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 ((~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))))) | subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[96, 77])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[97, 57])).
% 0.21/0.41 tff(99,plain,(subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 ((~(~((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8))))) <=> ((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 ((subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8)) <=> (~((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 ((~(subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8))) <=> (~(~((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 ((~(subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8))) <=> ((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[102, 100])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (~(subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8))),
% 0.21/0.41 inference(or_elim,[status(thm)],[15])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 ((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 (~subset(relation_field(relation_restriction(B!7, A!8)), A!8)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 ((~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))))) | subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[107, 106, 37])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (((~((~subset(relation_field(relation_restriction(B!7, A!8)), A!8)) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, A!8)))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))) | (subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 ((~((~subset(relation_field(relation_restriction(B!7, A!8)), A!8)) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, A!8)))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(relation_field(relation_restriction(B!7, A!8)), A!8)) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, A!8)))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[111, 73, 110])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------