%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM404+1 : TPTP v9.0.0. Released v3.2.0.
% 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 05:20:53 AM UTC 2025
% Result : Theorem 216.76s 217.07s
% Output : Proof 216.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM404+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.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 01:03:46 EDT 2025
% 0.11/0.33 % CPUTime :
% 216.76/217.07 % SZS status Theorem
% 216.76/217.07 % SZS output start Proof
% 216.76/217.07 tff(in_type, type, (
% 216.76/217.07 in: ( $i * $i ) > $o)).
% 216.76/217.07 tff(tptp_fun_A_18_type, type, (
% 216.76/217.07 tptp_fun_A_18: $i)).
% 216.76/217.07 tff(ordinal_type, type, (
% 216.76/217.07 ordinal: $i > $o)).
% 216.76/217.07 tff(epsilon_connected_type, type, (
% 216.76/217.07 epsilon_connected: $i > $o)).
% 216.76/217.07 tff(epsilon_transitive_type, type, (
% 216.76/217.07 epsilon_transitive: $i > $o)).
% 216.76/217.07 tff(subset_type, type, (
% 216.76/217.07 subset: ( $i * $i ) > $o)).
% 216.76/217.07 tff(tptp_fun_B_0_type, type, (
% 216.76/217.07 tptp_fun_B_0: $i > $i)).
% 216.76/217.07 tff(tptp_fun_C_3_type, type, (
% 216.76/217.07 tptp_fun_C_3: ( $i * $i ) > $i)).
% 216.76/217.07 tff(tptp_fun_C_1_type, type, (
% 216.76/217.07 tptp_fun_C_1: $i > $i)).
% 216.76/217.07 tff(tptp_fun_B_2_type, type, (
% 216.76/217.07 tptp_fun_B_2: $i > $i)).
% 216.76/217.07 tff(1,plain,
% 216.76/217.07 (^[B: $i] : refl((in(B, A!18) <=> ordinal(B)) <=> (in(B, A!18) <=> ordinal(B)))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(2,plain,
% 216.76/217.07 (![B: $i] : (in(B, A!18) <=> ordinal(B)) <=> ![B: $i] : (in(B, A!18) <=> ordinal(B))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[1])).
% 216.76/217.07 tff(3,plain,
% 216.76/217.07 ((~![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))) <=> (~![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B))))),
% 216.76/217.07 inference(rewrite,[status(thm)],[])).
% 216.76/217.07 tff(4,axiom,(~![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_ordinal1')).
% 216.76/217.07 tff(5,plain,
% 216.76/217.07 (~![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[4, 3])).
% 216.76/217.07 tff(6,plain,
% 216.76/217.07 (~![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[5, 3])).
% 216.76/217.07 tff(7,plain,
% 216.76/217.07 (~![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[6, 3])).
% 216.76/217.07 tff(8,plain,
% 216.76/217.07 (~![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[7, 3])).
% 216.76/217.07 tff(9,plain,(
% 216.76/217.07 $oeq((~(~![B: $i] : (in(B, A!18) <=> ordinal(B)))), ![B: $i] : (in(B, A!18) <=> ordinal(B)))),
% 216.76/217.07 inference(transitivity,[status(sab)],[8])).
% 216.76/217.07 tff(10,plain,
% 216.76/217.07 (![B: $i] : (in(B, A!18) <=> ordinal(B))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[9, 2])).
% 216.76/217.07 tff(11,plain,
% 216.76/217.07 ((~![B: $i] : (in(B, A!18) <=> ordinal(B))) | (in(A!18, A!18) <=> ordinal(A!18))),
% 216.76/217.07 inference(quant_inst,[status(thm)],[])).
% 216.76/217.07 tff(12,plain,
% 216.76/217.07 (in(A!18, A!18) <=> ordinal(A!18)),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[11, 10])).
% 216.76/217.07 tff(13,assumption,(~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))), introduced(assumption)).
% 216.76/217.07 tff(14,plain,
% 216.76/217.07 (((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)) | in(tptp_fun_B_0(A!18), A!18)),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(15,plain,
% 216.76/217.07 (in(tptp_fun_B_0(A!18), A!18)),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[14, 13])).
% 216.76/217.07 tff(16,assumption,(~(in(tptp_fun_B_0(A!18), A!18) <=> ordinal(tptp_fun_B_0(A!18)))), introduced(assumption)).
% 216.76/217.07 tff(17,plain,
% 216.76/217.07 ((~![B: $i] : (in(B, A!18) <=> ordinal(B))) | (in(tptp_fun_B_0(A!18), A!18) <=> ordinal(tptp_fun_B_0(A!18)))),
% 216.76/217.07 inference(quant_inst,[status(thm)],[])).
% 216.76/217.07 tff(18,plain,
% 216.76/217.07 ($false),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[17, 10, 16])).
% 216.76/217.07 tff(19,plain,(in(tptp_fun_B_0(A!18), A!18) <=> ordinal(tptp_fun_B_0(A!18))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.07 tff(20,plain,
% 216.76/217.07 ((~(in(tptp_fun_B_0(A!18), A!18) <=> ordinal(tptp_fun_B_0(A!18)))) | (~in(tptp_fun_B_0(A!18), A!18)) | ordinal(tptp_fun_B_0(A!18))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(21,plain,
% 216.76/217.07 ((~in(tptp_fun_B_0(A!18), A!18)) | ordinal(tptp_fun_B_0(A!18))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[20, 19])).
% 216.76/217.07 tff(22,plain,
% 216.76/217.07 (ordinal(tptp_fun_B_0(A!18))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[21, 15])).
% 216.76/217.07 tff(23,plain,
% 216.76/217.07 (((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)) | (~subset(tptp_fun_B_0(A!18), A!18))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(24,plain,
% 216.76/217.07 (~subset(tptp_fun_B_0(A!18), A!18)),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[23, 13])).
% 216.76/217.07 tff(25,assumption,((~((~subset(tptp_fun_B_0(A!18), A!18)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, A!18)))) | (~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))))), introduced(assumption)).
% 216.76/217.07 tff(26,plain,
% 216.76/217.07 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(27,plain,
% 216.76/217.07 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[26])).
% 216.76/217.07 tff(28,plain,
% 216.76/217.07 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(29,plain,
% 216.76/217.07 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[28])).
% 216.76/217.07 tff(30,plain,
% 216.76/217.07 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 216.76/217.07 inference(transitivity,[status(thm)],[29, 27])).
% 216.76/217.07 tff(31,plain,
% 216.76/217.07 (^[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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(32,plain,
% 216.76/217.07 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[31])).
% 216.76/217.07 tff(33,plain,
% 216.76/217.07 (![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)))),
% 216.76/217.07 inference(rewrite,[status(thm)],[])).
% 216.76/217.07 tff(34,plain,
% 216.76/217.07 (^[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))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(35,plain,
% 216.76/217.07 (![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)))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[34])).
% 216.76/217.07 tff(36,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')).
% 216.76/217.07 tff(37,plain,
% 216.76/217.07 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[36, 35])).
% 216.76/217.07 tff(38,plain,
% 216.76/217.07 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[37, 33])).
% 216.76/217.07 tff(39,plain,(
% 216.76/217.07 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))),
% 216.76/217.07 inference(skolemize,[status(sab)],[38])).
% 216.76/217.07 tff(40,plain,
% 216.76/217.07 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[39, 32])).
% 216.76/217.07 tff(41,plain,
% 216.76/217.07 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[40, 30])).
% 216.76/217.07 tff(42,plain,
% 216.76/217.07 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))) | (~((~((~subset(tptp_fun_B_0(A!18), A!18)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, A!18)))) | (~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))))))),
% 216.76/217.07 inference(quant_inst,[status(thm)],[])).
% 216.76/217.07 tff(43,plain,
% 216.76/217.07 ($false),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[42, 41, 25])).
% 216.76/217.07 tff(44,plain,(~((~((~subset(tptp_fun_B_0(A!18), A!18)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, A!18)))) | (~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))))))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.07 tff(45,plain,
% 216.76/217.07 (((~((~subset(tptp_fun_B_0(A!18), A!18)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, A!18)))) | (~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))))) | (subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(46,plain,
% 216.76/217.07 (subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[45, 44])).
% 216.76/217.07 tff(47,plain,
% 216.76/217.07 ((~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))))) | subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(48,plain,
% 216.76/217.07 (subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[47, 46])).
% 216.76/217.07 tff(49,plain,
% 216.76/217.07 (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[48, 24])).
% 216.76/217.07 tff(50,plain,
% 216.76/217.07 (((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(51,plain,
% 216.76/217.07 (in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[50, 49])).
% 216.76/217.07 tff(52,plain,
% 216.76/217.07 (((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(53,plain,
% 216.76/217.07 (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[52, 49])).
% 216.76/217.07 tff(54,assumption,(~(in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) <=> ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))), introduced(assumption)).
% 216.76/217.07 tff(55,plain,
% 216.76/217.07 ((~![B: $i] : (in(B, A!18) <=> ordinal(B))) | (in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) <=> ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 216.76/217.07 inference(quant_inst,[status(thm)],[])).
% 216.76/217.07 tff(56,plain,
% 216.76/217.07 ($false),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[55, 10, 54])).
% 216.76/217.07 tff(57,plain,(in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) <=> ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.07 tff(58,assumption,(in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) <=> ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))), introduced(assumption)).
% 216.76/217.07 tff(59,assumption,(in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))), introduced(assumption)).
% 216.76/217.07 tff(60,assumption,(ordinal(tptp_fun_B_0(A!18))), introduced(assumption)).
% 216.76/217.07 tff(61,plain,
% 216.76/217.07 (^[A: $i, B: $i] : refl(((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ((~in(A, B)) | ordinal(A) | (~ordinal(B))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(62,plain,
% 216.76/217.07 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[61])).
% 216.76/217.07 tff(63,plain,
% 216.76/217.07 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 216.76/217.07 inference(rewrite,[status(thm)],[])).
% 216.76/217.07 tff(64,plain,
% 216.76/217.07 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) => ordinal(A)) <=> ((~in(A, B)) | ordinal(A))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(B) => ((~in(A, B)) | ordinal(A))))), rewrite((ordinal(B) => ((~in(A, B)) | ordinal(A))) <=> ((~in(A, B)) | ordinal(A) | (~ordinal(B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> ((~in(A, B)) | ordinal(A) | (~ordinal(B)))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(65,plain,
% 216.76/217.07 (![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[64])).
% 216.76/217.07 tff(66,axiom,(![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_ordinal1')).
% 216.76/217.07 tff(67,plain,
% 216.76/217.07 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[66, 65])).
% 216.76/217.07 tff(68,plain,
% 216.76/217.07 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[67, 63])).
% 216.76/217.07 tff(69,plain,(
% 216.76/217.07 ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 216.76/217.07 inference(skolemize,[status(sab)],[68])).
% 216.76/217.07 tff(70,plain,
% 216.76/217.07 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[69, 62])).
% 216.76/217.07 tff(71,plain,
% 216.76/217.07 (((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~ordinal(tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~ordinal(tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 216.76/217.07 inference(rewrite,[status(thm)],[])).
% 216.76/217.07 tff(72,plain,
% 216.76/217.07 (((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~ordinal(tptp_fun_B_0(A!18)))) <=> ((~ordinal(tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 216.76/217.07 inference(rewrite,[status(thm)],[])).
% 216.76/217.07 tff(73,plain,
% 216.76/217.07 (((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~ordinal(tptp_fun_B_0(A!18))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~ordinal(tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))),
% 216.76/217.07 inference(monotonicity,[status(thm)],[72])).
% 216.76/217.07 tff(74,plain,
% 216.76/217.07 (((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~ordinal(tptp_fun_B_0(A!18))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~ordinal(tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 216.76/217.07 inference(transitivity,[status(thm)],[73, 71])).
% 216.76/217.07 tff(75,plain,
% 216.76/217.07 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~ordinal(tptp_fun_B_0(A!18))))),
% 216.76/217.07 inference(quant_inst,[status(thm)],[])).
% 216.76/217.07 tff(76,plain,
% 216.76/217.07 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~ordinal(tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[75, 74])).
% 216.76/217.07 tff(77,plain,
% 216.76/217.07 (ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[76, 70, 60, 59])).
% 216.76/217.07 tff(78,assumption,(~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)), introduced(assumption)).
% 216.76/217.07 tff(79,plain,
% 216.76/217.07 ((~(in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) <=> ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | (~ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(80,plain,
% 216.76/217.07 ((~(in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) <=> ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))) | (~ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[79, 78])).
% 216.76/217.07 tff(81,plain,
% 216.76/217.07 ($false),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[80, 77, 58])).
% 216.76/217.07 tff(82,plain,((~(in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) <=> ordinal(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | (~ordinal(tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18)))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.07 tff(83,plain,
% 216.76/217.07 (in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | (~ordinal(tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18)))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[82, 57])).
% 216.76/217.07 tff(84,plain,
% 216.76/217.07 ($false),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[83, 53, 51, 22])).
% 216.76/217.07 tff(85,plain,((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)), inference(lemma,lemma(discharge,[]))).
% 216.76/217.07 tff(86,assumption,((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))))), introduced(assumption)).
% 216.76/217.07 tff(87,plain,
% 216.76/217.07 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(88,plain,
% 216.76/217.07 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[87])).
% 216.76/217.07 tff(89,plain,
% 216.76/217.07 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(90,plain,
% 216.76/217.07 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[89])).
% 216.76/217.07 tff(91,plain,
% 216.76/217.07 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 216.76/217.07 inference(transitivity,[status(thm)],[90, 88])).
% 216.76/217.07 tff(92,plain,
% 216.76/217.07 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(93,plain,
% 216.76/217.07 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[92])).
% 216.76/217.07 tff(94,plain,
% 216.76/217.07 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 216.76/217.07 inference(rewrite,[status(thm)],[])).
% 216.76/217.07 tff(95,plain,
% 216.76/217.07 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(96,plain,
% 216.76/217.07 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[95])).
% 216.76/217.07 tff(97,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 216.76/217.07 tff(98,plain,
% 216.76/217.07 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[97, 96])).
% 216.76/217.07 tff(99,plain,
% 216.76/217.07 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[98, 94])).
% 216.76/217.07 tff(100,plain,(
% 216.76/217.07 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))),
% 216.76/217.07 inference(skolemize,[status(sab)],[99])).
% 216.76/217.07 tff(101,plain,
% 216.76/217.07 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[100, 93])).
% 216.76/217.07 tff(102,plain,
% 216.76/217.07 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[101, 91])).
% 216.76/217.07 tff(103,plain,
% 216.76/217.07 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))))))),
% 216.76/217.07 inference(quant_inst,[status(thm)],[])).
% 216.76/217.07 tff(104,plain,
% 216.76/217.07 ($false),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[103, 102, 86])).
% 216.76/217.07 tff(105,plain,(~((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))))))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.07 tff(106,plain,
% 216.76/217.07 (((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))))) | (epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(107,plain,
% 216.76/217.07 (epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[106, 105])).
% 216.76/217.07 tff(108,plain,
% 216.76/217.07 ((~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))))) | epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))),
% 216.76/217.07 inference(tautology,[status(thm)],[])).
% 216.76/217.07 tff(109,plain,
% 216.76/217.07 (epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[108, 107])).
% 216.76/217.07 tff(110,plain,
% 216.76/217.07 (epsilon_transitive(A!18)),
% 216.76/217.07 inference(unit_resolution,[status(thm)],[109, 85])).
% 216.76/217.07 tff(111,assumption,((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))), introduced(assumption)).
% 216.76/217.07 tff(112,plain,
% 216.76/217.07 (^[A: $i] : refl((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(113,plain,
% 216.76/217.07 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[112])).
% 216.76/217.07 tff(114,plain,
% 216.76/217.07 (^[A: $i] : rewrite((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(115,plain,
% 216.76/217.07 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[114])).
% 216.76/217.07 tff(116,plain,
% 216.76/217.07 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 216.76/217.07 inference(transitivity,[status(thm)],[115, 113])).
% 216.76/217.07 tff(117,plain,
% 216.76/217.07 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))), rewrite((epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))) <=> (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))), ((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> (((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A)))) & (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))), rewrite((((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A)))) & (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))), ((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(118,plain,
% 216.76/217.07 (![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[117])).
% 216.76/217.07 tff(119,plain,
% 216.76/217.07 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 216.76/217.07 inference(rewrite,[status(thm)],[])).
% 216.76/217.07 tff(120,plain,
% 216.76/217.07 (^[A: $i] : rewrite((epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))))),
% 216.76/217.07 inference(bind,[status(th)],[])).
% 216.76/217.07 tff(121,plain,
% 216.76/217.07 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 216.76/217.07 inference(quant_intro,[status(thm)],[120])).
% 216.76/217.07 tff(122,axiom,(![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_ordinal1')).
% 216.76/217.07 tff(123,plain,
% 216.76/217.07 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[122, 121])).
% 216.76/217.07 tff(124,plain,
% 216.76/217.07 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 216.76/217.07 inference(modus_ponens,[status(thm)],[123, 119])).
% 216.76/217.07 tff(125,plain,(
% 216.76/217.07 ![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))))),
% 216.76/217.07 inference(skolemize,[status(sab)],[124])).
% 216.76/217.08 tff(126,plain,
% 216.76/217.08 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[125, 118])).
% 216.76/217.08 tff(127,plain,
% 216.76/217.08 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[126, 116])).
% 216.76/217.08 tff(128,plain,
% 216.76/217.08 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))))))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(129,plain,
% 216.76/217.08 ((~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | (~in(tptp_fun_C_1(A!18), A!18)))))))) <=> (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(130,plain,
% 216.76/217.08 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | (~in(tptp_fun_C_1(A!18), A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))))))),
% 216.76/217.08 inference(monotonicity,[status(thm)],[129])).
% 216.76/217.08 tff(131,plain,
% 216.76/217.08 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | (~in(tptp_fun_C_1(A!18), A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))))))),
% 216.76/217.08 inference(transitivity,[status(thm)],[130, 128])).
% 216.76/217.08 tff(132,plain,
% 216.76/217.08 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | (~in(tptp_fun_C_1(A!18), A!18))))))))),
% 216.76/217.08 inference(quant_inst,[status(thm)],[])).
% 216.76/217.08 tff(133,plain,
% 216.76/217.08 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[132, 131])).
% 216.76/217.08 tff(134,plain,
% 216.76/217.08 ($false),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[133, 127, 111])).
% 216.76/217.08 tff(135,plain,(~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.08 tff(136,plain,
% 216.76/217.08 (((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))) | (epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(137,plain,
% 216.76/217.08 (epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[136, 135])).
% 216.76/217.08 tff(138,plain,
% 216.76/217.08 ((~![B: $i] : (in(B, A!18) <=> ordinal(B))) | (in(tptp_fun_B_2(A!18), A!18) <=> ordinal(tptp_fun_B_2(A!18)))),
% 216.76/217.08 inference(quant_inst,[status(thm)],[])).
% 216.76/217.08 tff(139,plain,
% 216.76/217.08 (in(tptp_fun_B_2(A!18), A!18) <=> ordinal(tptp_fun_B_2(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[138, 10])).
% 216.76/217.08 tff(140,assumption,(~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))), introduced(assumption)).
% 216.76/217.08 tff(141,plain,
% 216.76/217.08 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | in(tptp_fun_B_2(A!18), A!18)),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(142,plain,
% 216.76/217.08 (in(tptp_fun_B_2(A!18), A!18)),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[141, 140])).
% 216.76/217.08 tff(143,plain,
% 216.76/217.08 ((~(in(tptp_fun_B_2(A!18), A!18) <=> ordinal(tptp_fun_B_2(A!18)))) | (~in(tptp_fun_B_2(A!18), A!18)) | ordinal(tptp_fun_B_2(A!18))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(144,plain,
% 216.76/217.08 ((~(in(tptp_fun_B_2(A!18), A!18) <=> ordinal(tptp_fun_B_2(A!18)))) | ordinal(tptp_fun_B_2(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[143, 142])).
% 216.76/217.08 tff(145,plain,
% 216.76/217.08 (ordinal(tptp_fun_B_2(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[144, 139])).
% 216.76/217.08 tff(146,plain,
% 216.76/217.08 ((tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)) <=> (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18))),
% 216.76/217.08 inference(commutativity,[status(thm)],[])).
% 216.76/217.08 tff(147,plain,
% 216.76/217.08 ((tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) <=> (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18))),
% 216.76/217.08 inference(symmetry,[status(thm)],[146])).
% 216.76/217.08 tff(148,plain,
% 216.76/217.08 ((~(tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18))) <=> (~(tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)))),
% 216.76/217.08 inference(monotonicity,[status(thm)],[147])).
% 216.76/217.08 tff(149,plain,
% 216.76/217.08 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | (~(tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(150,plain,
% 216.76/217.08 (~(tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[149, 140])).
% 216.76/217.08 tff(151,plain,
% 216.76/217.08 (~(tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[150, 148])).
% 216.76/217.08 tff(152,plain,
% 216.76/217.08 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | (~in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(153,plain,
% 216.76/217.08 (~in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[152, 140])).
% 216.76/217.08 tff(154,plain,
% 216.76/217.08 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | (~in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(155,plain,
% 216.76/217.08 (~in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[154, 140])).
% 216.76/217.08 tff(156,assumption,(![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))), introduced(assumption)).
% 216.76/217.08 tff(157,assumption,(ordinal(tptp_fun_B_2(A!18))), introduced(assumption)).
% 216.76/217.08 tff(158,assumption,(~(tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18))), introduced(assumption)).
% 216.76/217.08 tff(159,assumption,(~in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))), introduced(assumption)).
% 216.76/217.08 tff(160,assumption,(~in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18))), introduced(assumption)).
% 216.76/217.08 tff(161,plain,
% 216.76/217.08 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)) | (~ordinal(tptp_fun_B_2(A!18))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)) | (~ordinal(tptp_fun_B_2(A!18))))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(162,plain,
% 216.76/217.08 (((~ordinal(tptp_fun_B_2(A!18))) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18))) <=> (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)) | (~ordinal(tptp_fun_B_2(A!18))))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(163,plain,
% 216.76/217.08 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | ((~ordinal(tptp_fun_B_2(A!18))) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)) | (~ordinal(tptp_fun_B_2(A!18)))))),
% 216.76/217.08 inference(monotonicity,[status(thm)],[162])).
% 216.76/217.08 tff(164,plain,
% 216.76/217.08 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | ((~ordinal(tptp_fun_B_2(A!18))) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)) | (~ordinal(tptp_fun_B_2(A!18))))),
% 216.76/217.08 inference(transitivity,[status(thm)],[163, 161])).
% 216.76/217.08 tff(165,plain,
% 216.76/217.08 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | ((~ordinal(tptp_fun_B_2(A!18))) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)))),
% 216.76/217.08 inference(quant_inst,[status(thm)],[])).
% 216.76/217.08 tff(166,plain,
% 216.76/217.08 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)) | (~ordinal(tptp_fun_B_2(A!18)))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[165, 164])).
% 216.76/217.08 tff(167,plain,
% 216.76/217.08 ($false),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[166, 160, 159, 158, 157, 156])).
% 216.76/217.08 tff(168,plain,((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_C_1(A!18) = tptp_fun_B_2(A!18)) | (~ordinal(tptp_fun_B_2(A!18)))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.08 tff(169,plain,
% 216.76/217.08 (~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[168, 155, 153, 151, 145])).
% 216.76/217.08 tff(170,plain,
% 216.76/217.08 ((~![B: $i] : (in(B, A!18) <=> ordinal(B))) | (in(tptp_fun_C_1(A!18), A!18) <=> ordinal(tptp_fun_C_1(A!18)))),
% 216.76/217.08 inference(quant_inst,[status(thm)],[])).
% 216.76/217.08 tff(171,plain,
% 216.76/217.08 (in(tptp_fun_C_1(A!18), A!18) <=> ordinal(tptp_fun_C_1(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[170, 10])).
% 216.76/217.08 tff(172,plain,
% 216.76/217.08 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | in(tptp_fun_C_1(A!18), A!18)),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(173,plain,
% 216.76/217.08 (in(tptp_fun_C_1(A!18), A!18)),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[172, 140])).
% 216.76/217.08 tff(174,plain,
% 216.76/217.08 ((~(in(tptp_fun_C_1(A!18), A!18) <=> ordinal(tptp_fun_C_1(A!18)))) | (~in(tptp_fun_C_1(A!18), A!18)) | ordinal(tptp_fun_C_1(A!18))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(175,plain,
% 216.76/217.08 ((~(in(tptp_fun_C_1(A!18), A!18) <=> ordinal(tptp_fun_C_1(A!18)))) | ordinal(tptp_fun_C_1(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[174, 173])).
% 216.76/217.08 tff(176,plain,
% 216.76/217.08 (ordinal(tptp_fun_C_1(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[175, 171])).
% 216.76/217.08 tff(177,plain,
% 216.76/217.08 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 216.76/217.08 inference(bind,[status(th)],[])).
% 216.76/217.08 tff(178,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 216.76/217.08 inference(quant_intro,[status(thm)],[177])).
% 216.76/217.08 tff(179,plain,
% 216.76/217.08 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 216.76/217.08 inference(bind,[status(th)],[])).
% 216.76/217.08 tff(180,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 216.76/217.08 inference(quant_intro,[status(thm)],[179])).
% 216.76/217.08 tff(181,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 216.76/217.08 inference(transitivity,[status(thm)],[180, 178])).
% 216.76/217.08 tff(182,plain,
% 216.76/217.08 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 216.76/217.08 inference(bind,[status(th)],[])).
% 216.76/217.08 tff(183,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 216.76/217.08 inference(quant_intro,[status(thm)],[182])).
% 216.76/217.08 tff(184,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(185,plain,
% 216.76/217.08 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))) <=> (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> (ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), rewrite((ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), (![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))))),
% 216.76/217.08 inference(bind,[status(th)],[])).
% 216.76/217.08 tff(186,plain,
% 216.76/217.08 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 216.76/217.08 inference(quant_intro,[status(thm)],[185])).
% 216.76/217.08 tff(187,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_ordinal1')).
% 216.76/217.08 tff(188,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[187, 186])).
% 216.76/217.08 tff(189,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[188, 184])).
% 216.76/217.08 tff(190,plain,(
% 216.76/217.08 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 216.76/217.08 inference(skolemize,[status(sab)],[189])).
% 216.76/217.08 tff(191,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[190, 183])).
% 216.76/217.08 tff(192,plain,
% 216.76/217.08 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[191, 181])).
% 216.76/217.08 tff(193,plain,
% 216.76/217.08 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B)))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(194,plain,
% 216.76/217.08 (((~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : (in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B)))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(195,plain,
% 216.76/217.08 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : (in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))))),
% 216.76/217.08 inference(monotonicity,[status(thm)],[194])).
% 216.76/217.08 tff(196,plain,
% 216.76/217.08 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : (in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B)))),
% 216.76/217.08 inference(transitivity,[status(thm)],[195, 193])).
% 216.76/217.08 tff(197,plain,
% 216.76/217.08 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : (in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B) | (~ordinal(B))))),
% 216.76/217.08 inference(quant_inst,[status(thm)],[])).
% 216.76/217.08 tff(198,plain,
% 216.76/217.08 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!18))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), B) | (tptp_fun_C_1(A!18) = B))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[197, 196])).
% 216.76/217.08 tff(199,plain,
% 216.76/217.08 ($false),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[198, 192, 176, 169])).
% 216.76/217.08 tff(200,plain,((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.08 tff(201,plain,
% 216.76/217.08 ((~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))) | epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(202,plain,
% 216.76/217.08 ((~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))) | epsilon_connected(A!18)),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[201, 200])).
% 216.76/217.08 tff(203,plain,
% 216.76/217.08 (epsilon_connected(A!18)),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[202, 137])).
% 216.76/217.08 tff(204,plain,
% 216.76/217.08 ((~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))) | (~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(205,plain,
% 216.76/217.08 ((~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))) | (~epsilon_transitive(A!18))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[204, 203])).
% 216.76/217.08 tff(206,plain,
% 216.76/217.08 (~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[205, 110])).
% 216.76/217.08 tff(207,assumption,(((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) <=> ordinal(A!18)), introduced(assumption)).
% 216.76/217.08 tff(208,plain,
% 216.76/217.08 (^[A: $i] : refl((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))),
% 216.76/217.08 inference(bind,[status(th)],[])).
% 216.76/217.08 tff(209,plain,
% 216.76/217.08 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 216.76/217.08 inference(quant_intro,[status(thm)],[208])).
% 216.76/217.08 tff(210,plain,
% 216.76/217.08 (^[A: $i] : trans(trans(monotonicity(rewrite((epsilon_transitive(A) & epsilon_connected(A)) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))), rewrite((ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))), rewrite((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))))),
% 216.76/217.08 inference(bind,[status(th)],[])).
% 216.76/217.08 tff(211,plain,
% 216.76/217.08 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 216.76/217.08 inference(quant_intro,[status(thm)],[210])).
% 216.76/217.08 tff(212,plain,
% 216.76/217.08 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(213,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_ordinal1')).
% 216.76/217.08 tff(214,plain,
% 216.76/217.08 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[213, 212])).
% 216.76/217.08 tff(215,plain,(
% 216.76/217.08 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 216.76/217.08 inference(skolemize,[status(sab)],[214])).
% 216.76/217.08 tff(216,plain,
% 216.76/217.08 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[215, 211])).
% 216.76/217.08 tff(217,plain,
% 216.76/217.08 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[216, 209])).
% 216.76/217.08 tff(218,plain,
% 216.76/217.08 ((~![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))) | (~(((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) <=> ordinal(A!18)))),
% 216.76/217.08 inference(quant_inst,[status(thm)],[])).
% 216.76/217.08 tff(219,plain,
% 216.76/217.08 ($false),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[218, 217, 207])).
% 216.76/217.08 tff(220,plain,(~(((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) <=> ordinal(A!18))), inference(lemma,lemma(discharge,[]))).
% 216.76/217.08 tff(221,plain,
% 216.76/217.08 ((((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) <=> ordinal(A!18)) | ((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) | ordinal(A!18)),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(222,plain,
% 216.76/217.08 (((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) | ordinal(A!18)),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[221, 220])).
% 216.76/217.08 tff(223,plain,
% 216.76/217.08 (ordinal(A!18)),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[222, 206])).
% 216.76/217.08 tff(224,plain,
% 216.76/217.08 ((~(in(A!18, A!18) <=> ordinal(A!18))) | in(A!18, A!18) | (~ordinal(A!18))),
% 216.76/217.08 inference(tautology,[status(thm)],[])).
% 216.76/217.08 tff(225,plain,
% 216.76/217.08 ((~(in(A!18, A!18) <=> ordinal(A!18))) | in(A!18, A!18)),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[224, 223])).
% 216.76/217.08 tff(226,plain,
% 216.76/217.08 (in(A!18, A!18)),
% 216.76/217.08 inference(unit_resolution,[status(thm)],[225, 12])).
% 216.76/217.08 tff(227,plain,
% 216.76/217.08 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 216.76/217.08 inference(bind,[status(th)],[])).
% 216.76/217.08 tff(228,plain,
% 216.76/217.08 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 216.76/217.08 inference(quant_intro,[status(thm)],[227])).
% 216.76/217.08 tff(229,plain,
% 216.76/217.08 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(230,plain,
% 216.76/217.08 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 216.76/217.08 inference(bind,[status(th)],[])).
% 216.76/217.08 tff(231,plain,
% 216.76/217.08 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 216.76/217.08 inference(quant_intro,[status(thm)],[230])).
% 216.76/217.08 tff(232,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 216.76/217.08 tff(233,plain,
% 216.76/217.08 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[232, 231])).
% 216.76/217.08 tff(234,plain,
% 216.76/217.08 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[233, 229])).
% 216.76/217.08 tff(235,plain,(
% 216.76/217.08 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 216.76/217.08 inference(skolemize,[status(sab)],[234])).
% 216.76/217.08 tff(236,plain,
% 216.76/217.08 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 216.76/217.08 inference(modus_ponens,[status(thm)],[235, 228])).
% 216.76/217.08 tff(237,plain,
% 216.76/217.08 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!18, A!18))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!18, A!18)))),
% 216.76/217.08 inference(rewrite,[status(thm)],[])).
% 216.76/217.08 tff(238,plain,
% 216.76/217.08 (((~in(A!18, A!18)) | (~in(A!18, A!18))) <=> (~in(A!18, A!18))),
% 216.83/217.14 inference(rewrite,[status(thm)],[])).
% 216.83/217.14 tff(239,plain,
% 216.83/217.14 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!18, A!18)) | (~in(A!18, A!18)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!18, A!18)))),
% 216.83/217.14 inference(monotonicity,[status(thm)],[238])).
% 216.83/217.14 tff(240,plain,
% 216.83/217.14 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!18, A!18)) | (~in(A!18, A!18)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!18, A!18)))),
% 216.83/217.14 inference(transitivity,[status(thm)],[239, 237])).
% 216.83/217.14 tff(241,plain,
% 216.83/217.14 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!18, A!18)) | (~in(A!18, A!18)))),
% 216.83/217.14 inference(quant_inst,[status(thm)],[])).
% 216.83/217.14 tff(242,plain,
% 216.83/217.14 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!18, A!18))),
% 216.83/217.14 inference(modus_ponens,[status(thm)],[241, 240])).
% 216.83/217.14 tff(243,plain,
% 216.83/217.14 ($false),
% 216.83/217.14 inference(unit_resolution,[status(thm)],[242, 236, 226])).
% 216.83/217.14 % SZS output end Proof
% 216.83/217.14 % E exiting
%------------------------------------------------------------------------------