TSTP Solution File: NUM402+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM402+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 : Sun Sep 18 13:09:31 EDT 2022
% Result : Theorem 0.77s 0.75s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : NUM402+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 10:03:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.77/0.75 % SZS status Theorem
% 0.77/0.75 % SZS output start Proof
% 0.77/0.75 tff(in_type, type, (
% 0.77/0.75 in: ( $i * $i ) > $o)).
% 0.77/0.75 tff(tptp_fun_D_4_type, type, (
% 0.77/0.75 tptp_fun_D_4: ( $i * $i ) > $i)).
% 0.77/0.75 tff(tptp_fun_A_21_type, type, (
% 0.77/0.75 tptp_fun_A_21: $i)).
% 0.77/0.75 tff(tptp_fun_B_0_type, type, (
% 0.77/0.75 tptp_fun_B_0: $i > $i)).
% 0.77/0.75 tff(union_type, type, (
% 0.77/0.75 union: $i > $i)).
% 0.77/0.75 tff(tptp_fun_C_3_type, type, (
% 0.77/0.75 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.77/0.75 tff(subset_type, type, (
% 0.77/0.75 subset: ( $i * $i ) > $o)).
% 0.77/0.75 tff(epsilon_transitive_type, type, (
% 0.77/0.75 epsilon_transitive: $i > $o)).
% 0.77/0.75 tff(epsilon_connected_type, type, (
% 0.77/0.75 epsilon_connected: $i > $o)).
% 0.77/0.75 tff(ordinal_type, type, (
% 0.77/0.75 ordinal: $i > $o)).
% 0.77/0.75 tff(tptp_fun_C_1_type, type, (
% 0.77/0.75 tptp_fun_C_1: $i > $i)).
% 0.77/0.75 tff(tptp_fun_B_2_type, type, (
% 0.77/0.75 tptp_fun_B_2: $i > $i)).
% 0.77/0.75 tff(tptp_fun_C_5_type, type, (
% 0.77/0.75 tptp_fun_C_5: ( $i * $i ) > $i)).
% 0.77/0.75 tff(tptp_fun_D_6_type, type, (
% 0.77/0.75 tptp_fun_D_6: ( $i * $i ) > $i)).
% 0.77/0.75 tff(1,plain,
% 0.77/0.75 (^[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))))))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(2,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[1])).
% 0.77/0.75 tff(3,plain,
% 0.77/0.75 (^[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))))))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(4,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[3])).
% 0.77/0.75 tff(5,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(transitivity,[status(thm)],[4, 2])).
% 0.77/0.75 tff(6,plain,
% 0.77/0.75 (^[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)))))))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(7,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[6])).
% 0.77/0.75 tff(8,plain,
% 0.77/0.75 (![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)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(9,plain,
% 0.77/0.75 (^[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))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(10,plain,
% 0.77/0.75 (![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)))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[9])).
% 0.77/0.75 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')).
% 0.77/0.75 tff(12,plain,
% 0.77/0.75 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.77/0.75 tff(13,plain,
% 0.77/0.75 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.77/0.75 tff(14,plain,(
% 0.77/0.75 ![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)))))),
% 0.77/0.75 inference(skolemize,[status(sab)],[13])).
% 0.77/0.75 tff(15,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.77/0.75 tff(16,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.77/0.75 tff(17,plain,
% 0.77/0.75 ((~![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(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(18,plain,
% 0.77/0.75 (~((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.77/0.75 tff(19,plain,
% 0.77/0.75 (((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))) | ((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(20,plain,
% 0.77/0.75 ((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.77/0.75 tff(21,plain,
% 0.77/0.75 (^[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))))))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(22,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[21])).
% 0.77/0.75 tff(23,plain,
% 0.77/0.75 (^[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))))))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(24,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[23])).
% 0.77/0.75 tff(25,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(transitivity,[status(thm)],[24, 22])).
% 0.77/0.75 tff(26,plain,
% 0.77/0.75 (^[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)))))))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(27,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[26])).
% 0.77/0.75 tff(28,plain,
% 0.77/0.75 (![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)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(29,plain,
% 0.77/0.75 (^[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))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(30,plain,
% 0.77/0.75 (![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)))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[29])).
% 0.77/0.75 tff(31,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.77/0.75 tff(32,plain,
% 0.77/0.75 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.77/0.75 tff(33,plain,
% 0.77/0.75 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.77/0.75 tff(34,plain,(
% 0.77/0.75 ![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)))))),
% 0.77/0.75 inference(skolemize,[status(sab)],[33])).
% 0.77/0.75 tff(35,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.77/0.75 tff(36,plain,
% 0.77/0.75 (![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)))))))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.77/0.75 tff(37,plain,
% 0.77/0.75 ((~![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(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(38,plain,
% 0.77/0.75 (~((~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.77/0.75 tff(39,plain,
% 0.77/0.75 (((~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))) | ((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.77/0.76 inference(tautology,[status(thm)],[])).
% 0.77/0.76 tff(40,plain,
% 0.77/0.76 ((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.77/0.76 tff(41,plain,
% 0.77/0.76 ((~![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(union(A!21))) | ![B: $i] : ((~in(B, union(A!21))) | subset(B, union(A!21))))) | (~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))))))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(42,plain,
% 0.77/0.76 (~((~((~epsilon_transitive(union(A!21))) | ![B: $i] : ((~in(B, union(A!21))) | subset(B, union(A!21))))) | (~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[41, 36])).
% 0.77/0.76 tff(43,plain,
% 0.77/0.76 (((~((~epsilon_transitive(union(A!21))) | ![B: $i] : ((~in(B, union(A!21))) | subset(B, union(A!21))))) | (~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))))) | (epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))))),
% 0.77/0.76 inference(tautology,[status(thm)],[])).
% 0.77/0.76 tff(44,plain,
% 0.77/0.76 (epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.77/0.76 tff(45,assumption,((~((~epsilon_connected(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))))))), introduced(assumption)).
% 0.77/0.76 tff(46,plain,
% 0.77/0.76 (^[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)))))))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(47,plain,
% 0.77/0.76 (![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))))))))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[46])).
% 0.77/0.76 tff(48,plain,
% 0.77/0.76 (^[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)))))))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(49,plain,
% 0.77/0.76 (![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))))))))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[48])).
% 0.77/0.76 tff(50,plain,
% 0.77/0.76 (![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))))))))),
% 0.77/0.76 inference(transitivity,[status(thm)],[49, 47])).
% 0.77/0.76 tff(51,plain,
% 0.77/0.76 (^[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))))))))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(52,plain,
% 0.77/0.76 (![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))))))))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[51])).
% 0.77/0.76 tff(53,plain,
% 0.77/0.76 (^[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) | (~(~(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(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)))))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(54,plain,
% 0.77/0.76 (![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(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))))))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[53])).
% 0.77/0.76 tff(55,plain,
% 0.77/0.76 (![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)))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(56,plain,
% 0.77/0.76 (^[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))))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(57,plain,
% 0.77/0.76 (![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)))))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[56])).
% 0.77/0.76 tff(58,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/sandbox2/benchmark/theBenchmark.p','d3_ordinal1')).
% 0.77/0.76 tff(59,plain,
% 0.77/0.76 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.77/0.76 tff(60,plain,
% 0.77/0.76 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.77/0.76 tff(61,plain,(
% 0.77/0.76 ![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))))))))),
% 0.77/0.76 inference(skolemize,[status(sab)],[60])).
% 0.77/0.76 tff(62,plain,
% 0.77/0.76 (![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))))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.77/0.76 tff(63,plain,
% 0.77/0.76 (![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))))))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.77/0.76 tff(64,plain,
% 0.77/0.76 (![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))))))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[63, 50])).
% 0.77/0.76 tff(65,plain,
% 0.77/0.76 ((~![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(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))))))))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(66,plain,
% 0.77/0.76 ($false),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[65, 64, 45])).
% 0.77/0.76 tff(67,plain,(~((~((~epsilon_connected(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))))))))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.76 tff(68,plain,
% 0.77/0.76 (((~((~epsilon_connected(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))))))) | (epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))))))),
% 0.77/0.76 inference(tautology,[status(thm)],[])).
% 0.77/0.76 tff(69,plain,
% 0.77/0.76 (epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.77/0.76 tff(70,assumption,(~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))))), introduced(assumption)).
% 0.77/0.76 tff(71,plain,
% 0.77/0.76 ((in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))) | in(tptp_fun_B_2(union(A!21)), union(A!21))),
% 0.77/0.76 inference(tautology,[status(thm)],[])).
% 0.77/0.76 tff(72,plain,
% 0.77/0.76 (in(tptp_fun_B_2(union(A!21)), union(A!21))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.77/0.76 tff(73,plain,
% 0.77/0.76 (^[A: $i, B: $i, D_22: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(74,plain,
% 0.77/0.76 (![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[73])).
% 0.77/0.76 tff(75,plain,
% 0.77/0.76 (^[A: $i, B: $i, D_22: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(76,plain,
% 0.77/0.76 (![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[75])).
% 0.77/0.76 tff(77,plain,
% 0.77/0.76 (![A: $i, B: $i] : ![D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.77/0.76 inference(pull_quant,[status(thm)],[])).
% 0.77/0.76 tff(78,plain,
% 0.77/0.76 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))) <=> ![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> (~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))))), pull_quant((~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant(![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), pull_quant(((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> (~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), pull_quant((~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))), ((~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))), ((~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))), (((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))) <=> ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))), (((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))), ((~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))), ((~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))) <=> ?[D_22: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))) <=> ?[D_22: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> (~?[D_22: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))))), pull_quant((~?[D_22: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> ![D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(79,plain,
% 0.77/0.76 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[78])).
% 0.77/0.76 tff(80,plain,
% 0.77/0.76 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.77/0.77 inference(transitivity,[status(thm)],[79, 77])).
% 0.77/0.77 tff(81,plain,
% 0.77/0.77 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.77/0.77 inference(transitivity,[status(thm)],[80, 76])).
% 0.77/0.77 tff(82,plain,
% 0.77/0.77 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))))),
% 0.77/0.77 inference(bind,[status(th)],[])).
% 0.77/0.77 tff(83,plain,
% 0.77/0.77 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))),
% 0.77/0.77 inference(quant_intro,[status(thm)],[82])).
% 0.77/0.77 tff(84,plain,
% 0.77/0.77 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.77/0.77 inference(transitivity,[status(thm)],[83, 81])).
% 0.77/0.77 tff(85,plain,
% 0.77/0.77 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) <=> ((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A)) <=> (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))), ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) <=> (in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))))), rewrite((in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))) <=> (in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))), ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) <=> (in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))))), rewrite(((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))), (((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))), rewrite(((in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))) <=> (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))), (((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))))),
% 0.77/0.77 inference(bind,[status(th)],[])).
% 0.77/0.77 tff(86,plain,
% 0.77/0.77 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))),
% 0.77/0.77 inference(quant_intro,[status(thm)],[85])).
% 0.77/0.77 tff(87,plain,
% 0.77/0.77 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A)))) <=> ![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(88,axiom,(![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_tarski')).
% 0.77/0.77 tff(89,plain,
% 0.77/0.77 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.77/0.77 tff(90,plain,(
% 0.77/0.77 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A)))))))),
% 0.77/0.77 inference(skolemize,[status(sab)],[89])).
% 0.77/0.77 tff(91,plain,
% 0.77/0.77 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.77/0.77 tff(92,plain,
% 0.77/0.77 (![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.77/0.77 tff(93,plain,
% 0.77/0.77 (![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[92, 74])).
% 0.77/0.77 tff(94,plain,
% 0.77/0.77 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(95,plain,
% 0.77/0.77 ((~(~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))) <=> ((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(96,plain,
% 0.77/0.77 (((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | $false) <=> (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(97,plain,
% 0.84/0.77 ((~$true) <=> $false),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(98,plain,
% 0.84/0.77 (($true | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))) <=> $true),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(99,plain,
% 0.84/0.77 ((~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))) <=> (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(100,plain,
% 0.84/0.77 ((union(A!21) = union(A!21)) <=> $true),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(101,plain,
% 0.84/0.77 (((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))) <=> ($true | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))),
% 0.84/0.77 inference(monotonicity,[status(thm)],[100, 99])).
% 0.84/0.77 tff(102,plain,
% 0.84/0.77 (((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))) <=> $true),
% 0.84/0.77 inference(transitivity,[status(thm)],[101, 98])).
% 0.84/0.77 tff(103,plain,
% 0.84/0.77 ((~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))) <=> (~$true)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[102])).
% 0.84/0.77 tff(104,plain,
% 0.84/0.77 ((~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))) <=> $false),
% 0.84/0.77 inference(transitivity,[status(thm)],[103, 97])).
% 0.84/0.77 tff(105,plain,
% 0.84/0.77 ((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) <=> (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(106,plain,
% 0.84/0.77 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> ((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | $false)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[105, 104])).
% 0.84/0.77 tff(107,plain,
% 0.84/0.77 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))),
% 0.84/0.77 inference(transitivity,[status(thm)],[106, 96])).
% 0.84/0.77 tff(108,plain,
% 0.84/0.77 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> (~(~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))))),
% 0.84/0.77 inference(monotonicity,[status(thm)],[107])).
% 0.84/0.77 tff(109,plain,
% 0.84/0.77 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> ((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))),
% 0.84/0.78 inference(transitivity,[status(thm)],[108, 95])).
% 0.84/0.78 tff(110,plain,
% 0.84/0.78 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[109])).
% 0.84/0.78 tff(111,plain,
% 0.84/0.78 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))),
% 0.84/0.78 inference(transitivity,[status(thm)],[110, 94])).
% 0.84/0.78 tff(112,plain,
% 0.84/0.78 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(113,plain,
% 0.84/0.78 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.84/0.78 tff(114,plain,
% 0.84/0.78 (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[113, 93, 72])).
% 0.84/0.78 tff(115,plain,
% 0.84/0.78 (((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))) | in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(116,plain,
% 0.84/0.78 (in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.84/0.78 tff(117,plain,
% 0.84/0.78 (^[B: $i] : refl((ordinal(B) | (~in(B, A!21))) <=> (ordinal(B) | (~in(B, A!21))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(118,plain,
% 0.84/0.78 (![B: $i] : (ordinal(B) | (~in(B, A!21))) <=> ![B: $i] : (ordinal(B) | (~in(B, A!21)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[117])).
% 0.84/0.78 tff(119,plain,
% 0.84/0.78 (((~ordinal(union(A!21))) & ![B: $i] : ((~in(B, A!21)) | ordinal(B))) <=> ((~ordinal(union(A!21))) & ![B: $i] : (ordinal(B) | (~in(B, A!21))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(120,plain,
% 0.84/0.78 ((~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))) <=> (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B)))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(121,plain,
% 0.84/0.78 ((~![A: $i] : (![B: $i] : (in(B, A) => ordinal(B)) => ordinal(union(A)))) <=> (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B)))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(122,axiom,(~![A: $i] : (![B: $i] : (in(B, A) => ordinal(B)) => ordinal(union(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_ordinal1')).
% 0.84/0.78 tff(123,plain,
% 0.84/0.78 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.84/0.78 tff(124,plain,
% 0.84/0.78 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[123, 120])).
% 0.84/0.78 tff(125,plain,
% 0.84/0.78 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.84/0.78 tff(126,plain,
% 0.84/0.78 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[125, 120])).
% 0.84/0.78 tff(127,plain,
% 0.84/0.78 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[126, 120])).
% 0.84/0.78 tff(128,plain,
% 0.84/0.78 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.84/0.78 tff(129,plain,
% 0.84/0.78 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[128, 120])).
% 0.84/0.78 tff(130,plain,
% 0.84/0.78 ((~ordinal(union(A!21))) & ![B: $i] : (ordinal(B) | (~in(B, A!21)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.84/0.78 tff(131,plain,
% 0.84/0.78 (![B: $i] : (ordinal(B) | (~in(B, A!21)))),
% 0.84/0.78 inference(and_elim,[status(thm)],[130])).
% 0.84/0.78 tff(132,plain,
% 0.84/0.78 (![B: $i] : (ordinal(B) | (~in(B, A!21)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[131, 118])).
% 0.84/0.78 tff(133,plain,
% 0.84/0.78 (((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))) <=> ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(134,plain,
% 0.84/0.78 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(135,plain,
% 0.84/0.78 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.84/0.78 tff(136,plain,
% 0.84/0.78 (ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[135, 132, 116])).
% 0.84/0.78 tff(137,plain,
% 0.84/0.78 (((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(138,plain,
% 0.84/0.78 (in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[137, 114])).
% 0.84/0.78 tff(139,plain,
% 0.84/0.78 (^[A: $i, B: $i] : refl(((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ((~in(A, B)) | ordinal(A) | (~ordinal(B))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(140,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[139])).
% 0.84/0.78 tff(141,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(142,plain,
% 0.84/0.78 (^[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)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(143,plain,
% 0.84/0.78 (![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[142])).
% 0.84/0.78 tff(144,axiom,(![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_ordinal1')).
% 0.84/0.78 tff(145,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.84/0.78 tff(146,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.84/0.78 tff(147,plain,(
% 0.84/0.78 ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.84/0.78 inference(skolemize,[status(sab)],[146])).
% 0.84/0.78 tff(148,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.84/0.78 tff(149,plain,
% 0.84/0.78 (((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | ordinal(tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | ordinal(tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(150,plain,
% 0.84/0.78 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | ordinal(tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(151,plain,
% 0.84/0.78 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | ordinal(tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.84/0.78 tff(152,plain,
% 0.84/0.78 (ordinal(tptp_fun_B_2(union(A!21)))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[151, 148, 138, 136])).
% 0.84/0.78 tff(153,plain,
% 0.84/0.78 (^[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)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(154,plain,
% 0.84/0.78 (![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))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[153])).
% 0.84/0.78 tff(155,plain,
% 0.84/0.78 (^[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)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(156,plain,
% 0.84/0.78 (![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))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[155])).
% 0.84/0.78 tff(157,plain,
% 0.84/0.78 (![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))))),
% 0.84/0.78 inference(transitivity,[status(thm)],[156, 154])).
% 0.84/0.78 tff(158,plain,
% 0.84/0.78 (^[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)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(159,plain,
% 0.84/0.78 (![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))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[158])).
% 0.84/0.78 tff(160,plain,
% 0.84/0.78 (![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))))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(161,plain,
% 0.84/0.78 (^[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))))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(162,plain,
% 0.84/0.78 (![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))))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[161])).
% 0.84/0.78 tff(163,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_ordinal1')).
% 0.84/0.78 tff(164,plain,
% 0.84/0.78 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.84/0.78 tff(165,plain,
% 0.84/0.78 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.84/0.78 tff(166,plain,(
% 0.84/0.78 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.84/0.78 inference(skolemize,[status(sab)],[165])).
% 0.84/0.78 tff(167,plain,
% 0.84/0.78 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.84/0.78 tff(168,plain,
% 0.84/0.78 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.84/0.78 tff(169,plain,
% 0.84/0.78 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(170,plain,
% 0.84/0.78 (((~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : (in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(171,plain,
% 0.84/0.78 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : (in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[170])).
% 0.84/0.78 tff(172,plain,
% 0.84/0.78 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : (in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B)))),
% 0.84/0.78 inference(transitivity,[status(thm)],[171, 169])).
% 0.84/0.78 tff(173,plain,
% 0.84/0.78 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : (in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B) | (~ordinal(B))))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(174,plain,
% 0.84/0.78 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_B_2(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.84/0.78 tff(175,plain,
% 0.84/0.78 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[174, 168, 152])).
% 0.84/0.78 tff(176,plain,
% 0.84/0.78 ((in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))) | in(tptp_fun_C_1(union(A!21)), union(A!21))),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(177,plain,
% 0.84/0.78 (in(tptp_fun_C_1(union(A!21)), union(A!21))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[176, 70])).
% 0.84/0.78 tff(178,plain,
% 0.84/0.78 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(179,plain,
% 0.84/0.78 ((~(~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))) <=> ((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(180,plain,
% 0.84/0.78 (((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | $false) <=> (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(181,plain,
% 0.84/0.78 ((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) <=> (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(182,plain,
% 0.84/0.78 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> ((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | $false)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[181, 104])).
% 0.84/0.78 tff(183,plain,
% 0.84/0.78 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))),
% 0.84/0.78 inference(transitivity,[status(thm)],[182, 180])).
% 0.84/0.78 tff(184,plain,
% 0.84/0.78 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> (~(~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[183])).
% 0.84/0.78 tff(185,plain,
% 0.84/0.78 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> ((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))),
% 0.84/0.79 inference(transitivity,[status(thm)],[184, 179])).
% 0.84/0.79 tff(186,plain,
% 0.84/0.79 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[185])).
% 0.84/0.79 tff(187,plain,
% 0.84/0.79 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))),
% 0.84/0.79 inference(transitivity,[status(thm)],[186, 178])).
% 0.84/0.79 tff(188,plain,
% 0.84/0.79 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(189,plain,
% 0.84/0.79 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.84/0.79 tff(190,plain,
% 0.84/0.79 (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[189, 93, 177])).
% 0.84/0.79 tff(191,plain,
% 0.84/0.79 (((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))) | in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(192,plain,
% 0.84/0.79 (in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.84/0.79 tff(193,plain,
% 0.84/0.79 (((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))) <=> ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(194,plain,
% 0.84/0.79 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(195,plain,
% 0.84/0.79 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.84/0.79 tff(196,plain,
% 0.84/0.79 (ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[195, 132, 192])).
% 0.84/0.79 tff(197,plain,
% 0.84/0.79 (((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(198,plain,
% 0.84/0.79 (in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[197, 190])).
% 0.84/0.79 tff(199,plain,
% 0.84/0.79 (((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | ordinal(tptp_fun_C_1(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | ordinal(tptp_fun_C_1(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(200,plain,
% 0.84/0.79 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | ordinal(tptp_fun_C_1(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(201,plain,
% 0.84/0.79 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | ordinal(tptp_fun_C_1(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.84/0.79 tff(202,plain,
% 0.84/0.79 (ordinal(tptp_fun_C_1(union(A!21)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[201, 148, 198, 196])).
% 0.84/0.79 tff(203,plain,
% 0.84/0.79 ((in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))) | (~in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(204,plain,
% 0.84/0.79 (~in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[203, 70])).
% 0.84/0.79 tff(205,plain,
% 0.84/0.79 ((in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))) | (~(tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(206,plain,
% 0.84/0.79 (~(tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[205, 70])).
% 0.84/0.79 tff(207,plain,
% 0.84/0.79 ((in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))) | (~in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(208,plain,
% 0.84/0.79 (~in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[207, 70])).
% 0.84/0.79 tff(209,plain,
% 0.84/0.79 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))) | (~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(210,plain,
% 0.84/0.79 (((~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21)))) <=> ((~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(211,plain,
% 0.84/0.79 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21)))))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[210])).
% 0.84/0.79 tff(212,plain,
% 0.84/0.79 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))) | (~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))))),
% 0.84/0.79 inference(transitivity,[status(thm)],[211, 209])).
% 0.84/0.79 tff(213,plain,
% 0.84/0.79 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(214,plain,
% 0.84/0.79 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), B) | (tptp_fun_B_2(union(A!21)) = B))) | (~ordinal(tptp_fun_C_1(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.84/0.79 tff(215,plain,
% 0.84/0.79 ($false),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[214, 208, 206, 204, 202, 175])).
% 0.84/0.79 tff(216,plain,(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))), inference(lemma,lemma(discharge,[]))).
% 0.84/0.79 tff(217,plain,
% 0.84/0.79 ((~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))))))) | epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(218,plain,
% 0.84/0.79 ((~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))))))) | epsilon_connected(union(A!21))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.84/0.79 tff(219,plain,
% 0.84/0.79 (epsilon_connected(union(A!21))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[218, 69])).
% 0.84/0.79 tff(220,plain,
% 0.84/0.79 (^[A: $i] : refl((ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(221,plain,
% 0.84/0.79 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[220])).
% 0.84/0.79 tff(222,plain,
% 0.84/0.79 (^[A: $i] : rewrite((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(223,plain,
% 0.84/0.79 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[222])).
% 0.84/0.79 tff(224,plain,
% 0.84/0.79 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(225,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_ordinal1')).
% 0.84/0.79 tff(226,plain,
% 0.84/0.79 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.84/0.79 tff(227,plain,(
% 0.84/0.79 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.84/0.79 inference(skolemize,[status(sab)],[226])).
% 0.84/0.79 tff(228,plain,
% 0.84/0.79 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.84/0.79 tff(229,plain,
% 0.84/0.79 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.84/0.79 tff(230,plain,
% 0.84/0.79 ((~![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (ordinal(union(A!21)) <=> (~((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21))))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(231,plain,
% 0.84/0.79 (ordinal(union(A!21)) <=> (~((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.84/0.79 tff(232,plain,
% 0.84/0.79 (~ordinal(union(A!21))),
% 0.84/0.79 inference(and_elim,[status(thm)],[130])).
% 0.84/0.79 tff(233,plain,
% 0.84/0.79 ((~(ordinal(union(A!21)) <=> (~((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21))))))) | ordinal(union(A!21)) | ((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21))))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(234,plain,
% 0.84/0.79 ((~(ordinal(union(A!21)) <=> (~((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21))))))) | ((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21))))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.84/0.79 tff(235,plain,
% 0.84/0.79 ((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[234, 231])).
% 0.84/0.79 tff(236,plain,
% 0.84/0.79 ((~((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21))))) | (~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(237,plain,
% 0.84/0.79 ((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.84/0.79 tff(238,plain,
% 0.84/0.79 (~epsilon_transitive(union(A!21))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[237, 219])).
% 0.84/0.79 tff(239,plain,
% 0.84/0.79 ((~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))))) | epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(240,plain,
% 0.84/0.79 ((~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.84/0.79 tff(241,plain,
% 0.84/0.79 (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[240, 44])).
% 0.84/0.79 tff(242,plain,
% 0.84/0.79 (((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(243,plain,
% 0.84/0.79 (in(tptp_fun_B_0(union(A!21)), union(A!21))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.84/0.79 tff(244,plain,
% 0.84/0.79 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(245,plain,
% 0.84/0.79 ((~(~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))) <=> ((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(246,plain,
% 0.84/0.79 (((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | $false) <=> (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(247,plain,
% 0.84/0.79 ((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) <=> (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(248,plain,
% 0.84/0.79 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> ((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | $false)),
% 0.84/0.80 inference(monotonicity,[status(thm)],[247, 104])).
% 0.84/0.80 tff(249,plain,
% 0.84/0.80 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))),
% 0.84/0.80 inference(transitivity,[status(thm)],[248, 246])).
% 0.84/0.80 tff(250,plain,
% 0.84/0.80 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> (~(~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[249])).
% 0.84/0.80 tff(251,plain,
% 0.84/0.80 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> ((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))),
% 0.84/0.80 inference(transitivity,[status(thm)],[250, 245])).
% 0.84/0.80 tff(252,plain,
% 0.84/0.80 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[251])).
% 0.84/0.80 tff(253,plain,
% 0.84/0.80 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))),
% 0.84/0.80 inference(transitivity,[status(thm)],[252, 244])).
% 0.84/0.80 tff(254,plain,
% 0.84/0.80 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(255,plain,
% 0.84/0.80 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.84/0.80 tff(256,plain,
% 0.84/0.80 (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[255, 93, 243])).
% 0.84/0.80 tff(257,plain,
% 0.84/0.80 (((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))) | in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(258,plain,
% 0.84/0.80 (in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[257, 256])).
% 0.84/0.80 tff(259,plain,
% 0.84/0.80 (((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))) <=> ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(260,plain,
% 0.84/0.80 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(261,plain,
% 0.84/0.80 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.84/0.80 tff(262,plain,
% 0.84/0.80 (ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[261, 132, 258])).
% 0.84/0.80 tff(263,plain,
% 0.84/0.80 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(264,plain,
% 0.84/0.80 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[263])).
% 0.84/0.80 tff(265,plain,
% 0.84/0.80 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(266,plain,
% 0.84/0.80 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[265])).
% 0.84/0.80 tff(267,plain,
% 0.84/0.80 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(268,plain,
% 0.84/0.80 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(269,plain,
% 0.84/0.80 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[268])).
% 0.84/0.80 tff(270,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.84/0.80 tff(271,plain,
% 0.84/0.80 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.84/0.80 tff(272,plain,
% 0.84/0.80 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.84/0.80 tff(273,plain,(
% 0.84/0.80 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.84/0.80 inference(skolemize,[status(sab)],[272])).
% 0.84/0.80 tff(274,plain,
% 0.84/0.80 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.84/0.80 tff(275,plain,
% 0.84/0.80 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[274, 264])).
% 0.84/0.80 tff(276,plain,
% 0.84/0.80 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(277,plain,
% 0.84/0.80 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(278,plain,
% 0.84/0.80 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.84/0.80 tff(279,plain,
% 0.84/0.80 (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[278, 275, 262])).
% 0.84/0.80 tff(280,plain,
% 0.84/0.80 (((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(281,plain,
% 0.84/0.80 (epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[280, 279])).
% 0.84/0.80 tff(282,plain,
% 0.84/0.80 ((~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(283,plain,
% 0.84/0.80 ((~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.84/0.80 tff(284,plain,
% 0.84/0.80 (![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[283, 40])).
% 0.84/0.80 tff(285,plain,
% 0.84/0.80 (((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))) | in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(286,plain,
% 0.84/0.80 (in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[285, 256])).
% 0.84/0.80 tff(287,plain,
% 0.84/0.80 (((~![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | ((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) <=> ((~![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | (~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(288,plain,
% 0.84/0.80 ((~![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | ((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(289,plain,
% 0.84/0.80 ((~![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | (~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.84/0.80 tff(290,plain,
% 0.84/0.80 (subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[289, 286, 284])).
% 0.84/0.80 tff(291,plain,
% 0.84/0.80 ((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(292,plain,
% 0.84/0.80 ((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.84/0.80 tff(293,plain,
% 0.84/0.80 (![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[292, 20])).
% 0.84/0.80 tff(294,plain,
% 0.84/0.80 ((~![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(union(A!21)), union(A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, union(A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))))))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(295,plain,
% 0.84/0.80 (~((~((~subset(tptp_fun_B_0(union(A!21)), union(A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, union(A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))))))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[294, 16])).
% 0.84/0.80 tff(296,plain,
% 0.84/0.80 (((~((~subset(tptp_fun_B_0(union(A!21)), union(A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, union(A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))))) | (subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(297,plain,
% 0.84/0.80 (subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.84/0.80 tff(298,plain,
% 0.84/0.80 (((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))) | (~subset(tptp_fun_B_0(union(A!21)), union(A!21)))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(299,plain,
% 0.84/0.80 (~subset(tptp_fun_B_0(union(A!21)), union(A!21))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[298, 241])).
% 0.84/0.80 tff(300,plain,
% 0.84/0.80 ((~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(301,plain,
% 0.84/0.80 ((~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[300, 299])).
% 0.84/0.80 tff(302,plain,
% 0.84/0.80 (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[301, 297])).
% 0.84/0.80 tff(303,plain,
% 0.84/0.80 (((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(304,plain,
% 0.84/0.80 (in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[303, 302])).
% 0.84/0.80 tff(305,plain,
% 0.84/0.80 (((~![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | ((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) <=> ((~![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(306,plain,
% 0.84/0.80 ((~![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | ((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(307,plain,
% 0.84/0.80 ((~![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.84/0.80 tff(308,plain,
% 0.84/0.80 (in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[307, 304, 293])).
% 0.84/0.80 tff(309,plain,
% 0.84/0.80 (((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(310,plain,
% 0.84/0.80 (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[309, 302])).
% 0.84/0.80 tff(311,plain,
% 0.84/0.80 ((~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(312,plain,
% 0.84/0.80 (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[311, 310, 258, 308])).
% 0.84/0.80 tff(313,plain,
% 0.84/0.80 (((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))) | (in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(314,plain,
% 0.84/0.80 ((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.84/0.80 tff(315,plain,
% 0.84/0.80 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(316,plain,
% 0.84/0.81 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(317,plain,
% 0.84/0.81 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.84/0.81 inference(monotonicity,[status(thm)],[316])).
% 0.84/0.81 tff(318,plain,
% 0.84/0.81 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.84/0.81 inference(transitivity,[status(thm)],[317, 315])).
% 0.84/0.81 tff(319,plain,
% 0.84/0.81 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))),
% 0.84/0.81 inference(quant_inst,[status(thm)],[])).
% 0.84/0.81 tff(320,plain,
% 0.84/0.81 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.84/0.81 tff(321,plain,
% 0.84/0.81 ($false),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[320, 93, 314])).
% 0.84/0.81 % SZS output end Proof
%------------------------------------------------------------------------------