%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU198+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:27:13 AM UTC 2025
% Result : Theorem 0.22s 0.49s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU198+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.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 06:15:56 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 % SZS output start Proof
% 0.22/0.49 tff(in_type, type, (
% 0.22/0.49 in: ( $i * $i ) > $o)).
% 0.22/0.49 tff(relation_rng_type, type, (
% 0.22/0.49 relation_rng: $i > $i)).
% 0.22/0.49 tff(relation_rng_restriction_type, type, (
% 0.22/0.49 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.22/0.49 tff(tptp_fun_B_52_type, type, (
% 0.22/0.49 tptp_fun_B_52: $i)).
% 0.22/0.49 tff(tptp_fun_A_53_type, type, (
% 0.22/0.49 tptp_fun_A_53: $i)).
% 0.22/0.49 tff(tptp_fun_C_26_type, type, (
% 0.22/0.49 tptp_fun_C_26: ( $i * $i ) > $i)).
% 0.22/0.49 tff(subset_type, type, (
% 0.22/0.49 subset: ( $i * $i ) > $o)).
% 0.22/0.49 tff(relation_type, type, (
% 0.22/0.49 relation: $i > $o)).
% 0.22/0.49 tff(1,plain,
% 0.22/0.49 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(2,plain,
% 0.22/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(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_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.49 tff(3,plain,
% 0.22/0.49 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(4,plain,
% 0.22/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(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_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.49 tff(5,plain,
% 0.22/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(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_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))),
% 0.22/0.49 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.49 tff(6,plain,
% 0.22/0.49 (^[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_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(7,plain,
% 0.22/0.49 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(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_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.49 tff(8,plain,
% 0.22/0.49 (![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)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(9,plain,
% 0.22/0.49 (^[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))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(10,plain,
% 0.22/0.49 (![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)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[9])).
% 0.22/0.49 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.22/0.49 tff(12,plain,
% 0.22/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.49 tff(13,plain,
% 0.22/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.49 tff(14,plain,(
% 0.22/0.49 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))),
% 0.22/0.49 inference(skolemize,[status(sab)],[13])).
% 0.22/0.49 tff(15,plain,
% 0.22/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.22/0.49 tff(16,plain,
% 0.22/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.49 tff(17,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_26(B, A), A)) | in(tptp_fun_C_26(B, A), B)))))))) | (~((~((~subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53)) | ![C: $i] : ((~in(C, relation_rng(relation_rng_restriction(A!53, B!52)))) | in(C, A!53)))) | (~(subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(18,plain,
% 0.22/0.49 (~((~((~subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53)) | ![C: $i] : ((~in(C, relation_rng(relation_rng_restriction(A!53, B!52)))) | in(C, A!53)))) | (~(subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53))))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.49 tff(19,plain,
% 0.22/0.49 (((~((~subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53)) | ![C: $i] : ((~in(C, relation_rng(relation_rng_restriction(A!53, B!52)))) | in(C, A!53)))) | (~(subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)))))) | (subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(20,plain,
% 0.22/0.49 (subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.49 tff(21,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(22,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_rng_restriction(A, B)), A))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(23,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_rng_restriction(A, B)), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t116_relat_1')).
% 0.22/0.49 tff(24,plain,
% 0.22/0.49 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.22/0.49 tff(25,plain,
% 0.22/0.49 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.22/0.49 tff(26,plain,
% 0.22/0.49 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.22/0.49 tff(27,plain,
% 0.22/0.49 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.22/0.49 tff(28,plain,(
% 0.22/0.49 ~((~relation(B!52)) | subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53))),
% 0.22/0.49 inference(skolemize,[status(sab)],[27])).
% 0.22/0.49 tff(29,plain,
% 0.22/0.49 (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53)),
% 0.22/0.49 inference(or_elim,[status(thm)],[28])).
% 0.22/0.49 tff(30,plain,
% 0.22/0.49 ((~(subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53))))) | subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(31,plain,
% 0.22/0.49 ((~(subset(relation_rng(relation_rng_restriction(A!53, B!52)), A!53) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53))))) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.22/0.49 tff(32,plain,
% 0.22/0.49 (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.22/0.49 tff(33,plain,
% 0.22/0.49 (((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(34,plain,
% 0.22/0.49 (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.22/0.49 tff(35,plain,
% 0.22/0.49 (((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(36,plain,
% 0.22/0.49 ((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.22/0.49 tff(37,plain,
% 0.22/0.49 (((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(38,plain,
% 0.22/0.49 (in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[37, 32])).
% 0.22/0.49 tff(39,plain,
% 0.22/0.49 ((((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52)))) <=> in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))) | (~((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52))))) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(40,plain,
% 0.22/0.49 (((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52)))) <=> in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[39, 38, 36])).
% 0.22/0.49 tff(41,plain,
% 0.22/0.49 (relation(B!52)),
% 0.22/0.49 inference(or_elim,[status(thm)],[28])).
% 0.22/0.49 tff(42,plain,
% 0.22/0.49 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C)))))) <=> ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C)))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(43,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.49 tff(44,plain,
% 0.22/0.49 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C)))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(45,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.49 tff(46,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(47,plain,
% 0.22/0.49 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(48,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[47])).
% 0.22/0.49 tff(49,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t115_relat_1')).
% 0.22/0.49 tff(50,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.22/0.49 tff(51,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.22/0.49 tff(52,plain,(
% 0.22/0.49 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.22/0.49 inference(skolemize,[status(sab)],[51])).
% 0.22/0.49 tff(53,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.22/0.49 tff(54,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.22/0.49 tff(55,plain,
% 0.22/0.49 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C))))))) | ((~relation(B!52)) | (~(((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52)))) <=> in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C))))))) | (~relation(B!52)) | (~(((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52)))) <=> in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(56,plain,
% 0.22/0.49 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C))))))) | ((~relation(B!52)) | (~(((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52)))) <=> in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(57,plain,
% 0.22/0.49 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_rng(C)))) <=> in(A, relation_rng(relation_rng_restriction(B, C))))))) | (~relation(B!52)) | (~(((~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), A!53)) | (~in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(B!52)))) <=> in(tptp_fun_C_26(A!53, relation_rng(relation_rng_restriction(A!53, B!52))), relation_rng(relation_rng_restriction(A!53, B!52)))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.22/0.49 tff(58,plain,
% 0.22/0.49 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[57, 54, 41, 40])).
% 0.22/0.50 % SZS output end Proof
% 0.22/0.50 % E exiting
%------------------------------------------------------------------------------