TSTP Solution File: NUM397+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM397+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 13:09:30 EDT 2022
% Result : Theorem 3.74s 2.65s
% Output : Proof 3.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM397+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.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 10:32:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 3.74/2.65 % SZS status Theorem
% 3.74/2.65 % SZS output start Proof
% 3.74/2.65 tff(in_type, type, (
% 3.74/2.65 in: ( $i * $i ) > $o)).
% 3.74/2.65 tff(empty_set_type, type, (
% 3.74/2.65 empty_set: $i)).
% 3.74/2.65 tff(tptp_fun_D_3_type, type, (
% 3.74/2.65 tptp_fun_D_3: ( $i * $i ) > $i)).
% 3.74/2.65 tff(tptp_fun_B_0_type, type, (
% 3.74/2.65 tptp_fun_B_0: $i > $i)).
% 3.74/2.65 tff(union_type, type, (
% 3.74/2.65 union: $i > $i)).
% 3.74/2.65 tff(tptp_fun_A_19_type, type, (
% 3.74/2.65 tptp_fun_A_19: $i)).
% 3.74/2.65 tff(tptp_fun_C_4_type, type, (
% 3.74/2.65 tptp_fun_C_4: ( $i * $i ) > $i)).
% 3.74/2.65 tff(tptp_fun_D_5_type, type, (
% 3.74/2.65 tptp_fun_D_5: ( $i * $i ) > $i)).
% 3.74/2.65 tff(empty_type, type, (
% 3.74/2.65 empty: $i > $o)).
% 3.74/2.65 tff(subset_type, type, (
% 3.74/2.65 subset: ( $i * $i ) > $o)).
% 3.74/2.65 tff(epsilon_transitive_type, type, (
% 3.74/2.65 epsilon_transitive: $i > $o)).
% 3.74/2.65 tff(epsilon_connected_type, type, (
% 3.74/2.65 epsilon_connected: $i > $o)).
% 3.74/2.65 tff(tptp_fun_C_1_type, type, (
% 3.74/2.65 tptp_fun_C_1: $i > $i)).
% 3.74/2.65 tff(tptp_fun_B_2_type, type, (
% 3.74/2.65 tptp_fun_B_2: $i > $i)).
% 3.74/2.65 tff(ordinal_type, type, (
% 3.74/2.65 ordinal: $i > $o)).
% 3.74/2.65 tff(element_type, type, (
% 3.74/2.65 element: ( $i * $i ) > $o)).
% 3.74/2.65 tff(powerset_type, type, (
% 3.74/2.65 powerset: $i > $i)).
% 3.74/2.65 tff(relation_type, type, (
% 3.74/2.65 relation: $i > $o)).
% 3.74/2.65 tff(relation_empty_yielding_type, type, (
% 3.74/2.65 relation_empty_yielding: $i > $o)).
% 3.74/2.65 tff(1,plain,
% 3.74/2.65 (^[A: $i, B: $i, D_20: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 3.74/2.65 inference(bind,[status(th)],[])).
% 3.74/2.65 tff(2,plain,
% 3.74/2.65 (![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))),
% 3.74/2.65 inference(quant_intro,[status(thm)],[1])).
% 3.74/2.65 tff(3,plain,
% 3.74/2.65 (^[A: $i, B: $i, D_20: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))))),
% 3.74/2.65 inference(bind,[status(th)],[])).
% 3.74/2.65 tff(4,plain,
% 3.74/2.65 (![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 3.74/2.65 inference(quant_intro,[status(thm)],[3])).
% 3.74/2.65 tff(5,plain,
% 3.74/2.65 (![A: $i, B: $i] : ![D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 3.74/2.65 inference(pull_quant,[status(thm)],[])).
% 3.74/2.65 tff(6,plain,
% 3.74/2.65 (^[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_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))), ((~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))), ((~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))), (((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))) <=> ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))), (((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))), ((~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))), ((~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))) <=> ?[D_20: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))) <=> ?[D_20: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> (~?[D_20: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))))), pull_quant((~?[D_20: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> ![D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))))),
% 3.74/2.65 inference(bind,[status(th)],[])).
% 3.74/2.65 tff(7,plain,
% 3.74/2.65 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 3.74/2.65 inference(quant_intro,[status(thm)],[6])).
% 3.74/2.65 tff(8,plain,
% 3.74/2.65 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 3.74/2.65 inference(transitivity,[status(thm)],[7, 5])).
% 3.74/2.65 tff(9,plain,
% 3.74/2.65 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 3.74/2.65 inference(transitivity,[status(thm)],[8, 4])).
% 3.74/2.65 tff(10,plain,
% 3.74/2.65 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))))),
% 3.74/2.65 inference(bind,[status(th)],[])).
% 3.74/2.65 tff(11,plain,
% 3.74/2.65 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))),
% 3.74/2.65 inference(quant_intro,[status(thm)],[10])).
% 3.74/2.65 tff(12,plain,
% 3.74/2.65 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 3.74/2.65 inference(transitivity,[status(thm)],[11, 9])).
% 3.74/2.65 tff(13,plain,
% 3.74/2.65 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(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_3(C, A))) | (~in(tptp_fun_D_3(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_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A)) <=> (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))), ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) <=> (in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))))), rewrite((in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))) <=> (in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))), ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) <=> (in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))))), rewrite(((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))), (((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))), rewrite(((in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))) <=> (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))), (((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))))),
% 3.74/2.65 inference(bind,[status(th)],[])).
% 3.74/2.65 tff(14,plain,
% 3.74/2.65 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))),
% 3.74/2.65 inference(quant_intro,[status(thm)],[13])).
% 3.74/2.65 tff(15,plain,
% 3.74/2.65 (![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))))),
% 3.74/2.65 inference(rewrite,[status(thm)],[])).
% 3.74/2.65 tff(16,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')).
% 3.74/2.65 tff(17,plain,
% 3.74/2.65 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[16, 15])).
% 3.74/2.66 tff(18,plain,(
% 3.74/2.66 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A)))))))),
% 3.74/2.66 inference(skolemize,[status(sab)],[17])).
% 3.74/2.66 tff(19,plain,
% 3.74/2.66 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.74/2.66 tff(20,plain,
% 3.74/2.66 (![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[19, 12])).
% 3.74/2.66 tff(21,plain,
% 3.74/2.66 (![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[20, 2])).
% 3.74/2.66 tff(22,plain,
% 3.74/2.66 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))) | (~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))) | (~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))))))))))),
% 3.74/2.66 inference(rewrite,[status(thm)],[])).
% 3.74/2.66 tff(23,plain,
% 3.74/2.66 ((~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(A!19, empty_set)))))))) | (~((union(A!19) = union(empty_set)) | (~((~(in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))))) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))))))))) <=> (~((~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))) | (~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))))))))))),
% 3.74/2.66 inference(rewrite,[status(thm)],[])).
% 3.74/2.66 tff(24,plain,
% 3.74/2.66 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(A!19, empty_set)))))))) | (~((union(A!19) = union(empty_set)) | (~((~(in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))))) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))) | (~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))))))))))),
% 3.74/2.66 inference(monotonicity,[status(thm)],[23])).
% 3.74/2.66 tff(25,plain,
% 3.74/2.66 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(A!19, empty_set)))))))) | (~((union(A!19) = union(empty_set)) | (~((~(in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))))) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))) | (~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))))))))))),
% 3.74/2.66 inference(transitivity,[status(thm)],[24, 22])).
% 3.74/2.66 tff(26,plain,
% 3.74/2.66 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(A!19, empty_set)))))))) | (~((union(A!19) = union(empty_set)) | (~((~(in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))))) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19))))))))))),
% 3.74/2.66 inference(quant_inst,[status(thm)],[])).
% 3.74/2.66 tff(27,plain,
% 3.74/2.66 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))) | (~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))))))))))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[26, 25])).
% 3.74/2.66 tff(28,plain,
% 3.74/2.66 (~((~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))) | (~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))))))))),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[27, 21])).
% 3.74/2.66 tff(29,plain,
% 3.74/2.66 (((~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))) | (~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))))))))) | ((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))))))),
% 3.74/2.66 inference(tautology,[status(thm)],[])).
% 3.74/2.66 tff(30,plain,
% 3.74/2.66 ((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))))))),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[29, 28])).
% 3.74/2.66 tff(31,plain,
% 3.74/2.66 ((tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) <=> (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19)))),
% 3.74/2.66 inference(commutativity,[status(thm)],[])).
% 3.74/2.66 tff(32,plain,
% 3.74/2.66 ((tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) <=> (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))),
% 3.74/2.66 inference(symmetry,[status(thm)],[31])).
% 3.74/2.66 tff(33,plain,
% 3.74/2.66 ((~(tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19)))) <=> (~(tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))))),
% 3.74/2.66 inference(monotonicity,[status(thm)],[32])).
% 3.74/2.66 tff(34,assumption,(~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19))))), introduced(assumption)).
% 3.74/2.66 tff(35,plain,
% 3.74/2.66 ((in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))) | (~(tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))))),
% 3.74/2.66 inference(tautology,[status(thm)],[])).
% 3.74/2.66 tff(36,plain,
% 3.74/2.66 (~(tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19)))),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[35, 34])).
% 3.74/2.66 tff(37,plain,
% 3.74/2.66 (~(tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[36, 33])).
% 3.74/2.66 tff(38,plain,
% 3.74/2.66 ((in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))) | in(tptp_fun_B_2(union(A!19)), union(A!19))),
% 3.74/2.66 inference(tautology,[status(thm)],[])).
% 3.74/2.66 tff(39,plain,
% 3.74/2.66 (in(tptp_fun_B_2(union(A!19)), union(A!19))),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[38, 34])).
% 3.74/2.66 tff(40,plain,
% 3.74/2.66 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))))))),
% 3.74/2.66 inference(rewrite,[status(thm)],[])).
% 3.74/2.66 tff(41,plain,
% 3.74/2.66 ((~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set)))))))))) <=> (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))))))),
% 3.74/2.66 inference(rewrite,[status(thm)],[])).
% 3.74/2.66 tff(42,plain,
% 3.74/2.66 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))))))),
% 3.74/2.66 inference(monotonicity,[status(thm)],[41])).
% 3.74/2.66 tff(43,plain,
% 3.74/2.66 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))))))),
% 3.74/2.66 inference(transitivity,[status(thm)],[42, 40])).
% 3.74/2.66 tff(44,plain,
% 3.74/2.66 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))),
% 3.74/2.66 inference(quant_inst,[status(thm)],[])).
% 3.74/2.66 tff(45,plain,
% 3.74/2.66 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))))))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[44, 43])).
% 3.74/2.66 tff(46,plain,
% 3.74/2.66 (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))))),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[45, 21])).
% 3.74/2.66 tff(47,plain,
% 3.74/2.66 (((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))))) | ((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))),
% 3.74/2.66 inference(tautology,[status(thm)],[])).
% 3.74/2.66 tff(48,plain,
% 3.74/2.66 ((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))))),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[47, 46])).
% 3.74/2.66 tff(49,assumption,(in(tptp_fun_B_2(union(A!19)), union(A!19))), introduced(assumption)).
% 3.74/2.66 tff(50,plain,
% 3.74/2.66 ((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))))),
% 3.74/2.66 inference(tautology,[status(thm)],[])).
% 3.74/2.66 tff(51,plain,
% 3.74/2.66 ((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))))),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[50, 49])).
% 3.74/2.66 tff(52,plain,
% 3.74/2.66 (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[51, 48])).
% 3.74/2.66 tff(53,plain,
% 3.74/2.66 (((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))) | in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)),
% 3.74/2.66 inference(tautology,[status(thm)],[])).
% 3.74/2.66 tff(54,plain,
% 3.74/2.66 (in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)),
% 3.74/2.66 inference(unit_resolution,[status(thm)],[53, 52])).
% 3.74/2.66 tff(55,plain,
% 3.74/2.66 ((~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))) <=> (~![A: $i] : ((~ordinal(A)) | ordinal(union(A))))),
% 3.74/2.66 inference(rewrite,[status(thm)],[])).
% 3.74/2.66 tff(56,plain,
% 3.74/2.66 ((~![A: $i] : (ordinal(A) => ordinal(union(A)))) <=> (~![A: $i] : ((~ordinal(A)) | ordinal(union(A))))),
% 3.74/2.66 inference(rewrite,[status(thm)],[])).
% 3.74/2.66 tff(57,axiom,(~![A: $i] : (ordinal(A) => ordinal(union(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_ordinal1')).
% 3.74/2.66 tff(58,plain,
% 3.74/2.66 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[57, 56])).
% 3.74/2.66 tff(59,plain,
% 3.74/2.66 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[58, 55])).
% 3.74/2.66 tff(60,plain,
% 3.74/2.66 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[59, 55])).
% 3.74/2.66 tff(61,plain,
% 3.74/2.66 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[60, 55])).
% 3.74/2.66 tff(62,plain,
% 3.74/2.66 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[61, 55])).
% 3.74/2.66 tff(63,plain,
% 3.74/2.66 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[62, 55])).
% 3.74/2.66 tff(64,plain,
% 3.74/2.66 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 3.74/2.66 inference(modus_ponens,[status(thm)],[63, 55])).
% 3.74/2.66 tff(65,plain,(
% 3.74/2.66 ~((~ordinal(A!19)) | ordinal(union(A!19)))),
% 3.74/2.66 inference(skolemize,[status(sab)],[64])).
% 3.74/2.66 tff(66,plain,
% 3.74/2.66 (ordinal(A!19)),
% 3.74/2.66 inference(or_elim,[status(thm)],[65])).
% 3.74/2.66 tff(67,plain,
% 3.74/2.66 (^[A: $i, B: $i] : refl((ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B))))),
% 3.74/2.66 inference(bind,[status(th)],[])).
% 3.74/2.66 tff(68,plain,
% 3.74/2.66 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 3.74/2.66 inference(quant_intro,[status(thm)],[67])).
% 3.74/2.67 tff(69,plain,
% 3.74/2.67 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(70,plain,
% 3.74/2.67 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) => ordinal(A)) <=> (ordinal(A) | (~in(A, B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(B) => (ordinal(A) | (~in(A, B)))))), rewrite((ordinal(B) => (ordinal(A) | (~in(A, B)))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))))),
% 3.74/2.67 inference(bind,[status(th)],[])).
% 3.74/2.67 tff(71,plain,
% 3.74/2.67 (![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 3.74/2.67 inference(quant_intro,[status(thm)],[70])).
% 3.74/2.67 tff(72,axiom,(![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_ordinal1')).
% 3.74/2.67 tff(73,plain,
% 3.74/2.67 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[72, 71])).
% 3.74/2.67 tff(74,plain,
% 3.74/2.67 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[73, 69])).
% 3.74/2.67 tff(75,plain,(
% 3.74/2.67 ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 3.74/2.67 inference(skolemize,[status(sab)],[74])).
% 3.74/2.67 tff(76,plain,
% 3.74/2.67 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[75, 68])).
% 3.74/2.67 tff(77,plain,
% 3.74/2.67 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(78,plain,
% 3.74/2.67 ((ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | (~ordinal(A!19))) <=> ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(79,plain,
% 3.74/2.67 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))))),
% 3.74/2.67 inference(monotonicity,[status(thm)],[78])).
% 3.74/2.67 tff(80,plain,
% 3.74/2.67 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))),
% 3.74/2.67 inference(transitivity,[status(thm)],[79, 77])).
% 3.74/2.67 tff(81,plain,
% 3.74/2.67 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))),
% 3.74/2.67 inference(quant_inst,[status(thm)],[])).
% 3.74/2.67 tff(82,plain,
% 3.74/2.67 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[81, 80])).
% 3.74/2.67 tff(83,plain,
% 3.74/2.67 (ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[82, 76, 66, 54])).
% 3.74/2.67 tff(84,plain,
% 3.74/2.67 (((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))),
% 3.74/2.67 inference(tautology,[status(thm)],[])).
% 3.74/2.67 tff(85,plain,
% 3.74/2.67 (in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[84, 52])).
% 3.74/2.67 tff(86,assumption,(~ordinal(tptp_fun_B_2(union(A!19)))), introduced(assumption)).
% 3.74/2.67 tff(87,plain,
% 3.74/2.67 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(88,plain,
% 3.74/2.67 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))))),
% 3.74/2.67 inference(quant_inst,[status(thm)],[])).
% 3.74/2.67 tff(89,plain,
% 3.74/2.67 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[88, 87])).
% 3.74/2.67 tff(90,plain,
% 3.74/2.67 ($false),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[89, 76, 86, 85, 83])).
% 3.74/2.67 tff(91,plain,(ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19)))), inference(lemma,lemma(discharge,[]))).
% 3.74/2.67 tff(92,plain,
% 3.74/2.67 (ordinal(tptp_fun_B_2(union(A!19)))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[91, 39])).
% 3.74/2.67 tff(93,plain,
% 3.74/2.67 ((in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))))),
% 3.74/2.67 inference(tautology,[status(thm)],[])).
% 3.74/2.67 tff(94,plain,
% 3.74/2.67 (~in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19)))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[93, 34])).
% 3.74/2.67 tff(95,plain,
% 3.74/2.67 ((in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))),
% 3.74/2.67 inference(tautology,[status(thm)],[])).
% 3.74/2.67 tff(96,plain,
% 3.74/2.67 (~in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[95, 34])).
% 3.74/2.67 tff(97,plain,
% 3.74/2.67 ((in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))) | in(tptp_fun_C_1(union(A!19)), union(A!19))),
% 3.74/2.67 inference(tautology,[status(thm)],[])).
% 3.74/2.67 tff(98,plain,
% 3.74/2.67 (in(tptp_fun_C_1(union(A!19)), union(A!19))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[97, 34])).
% 3.74/2.67 tff(99,assumption,((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))))), introduced(assumption)).
% 3.74/2.67 tff(100,plain,
% 3.74/2.67 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(101,plain,
% 3.74/2.67 ((~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_C_1(union(A!19)), empty_set)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(empty_set, A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set)))))))))) <=> (~((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))))))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(102,plain,
% 3.74/2.67 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_C_1(union(A!19)), empty_set)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(empty_set, A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))))),
% 3.74/2.67 inference(monotonicity,[status(thm)],[101])).
% 3.74/2.67 tff(103,plain,
% 3.74/2.67 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_C_1(union(A!19)), empty_set)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(empty_set, A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))))),
% 3.74/2.67 inference(transitivity,[status(thm)],[102, 100])).
% 3.74/2.67 tff(104,plain,
% 3.74/2.67 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_C_1(union(A!19)), empty_set)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(empty_set, A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))),
% 3.74/2.67 inference(quant_inst,[status(thm)],[])).
% 3.74/2.67 tff(105,plain,
% 3.74/2.67 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))))))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[104, 103])).
% 3.74/2.67 tff(106,plain,
% 3.74/2.67 ($false),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[105, 21, 99])).
% 3.74/2.67 tff(107,plain,(~((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/2.67 tff(108,plain,
% 3.74/2.67 (((~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))))) | ((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))),
% 3.74/2.67 inference(tautology,[status(thm)],[])).
% 3.74/2.67 tff(109,plain,
% 3.74/2.67 ((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[108, 107])).
% 3.74/2.67 tff(110,plain,
% 3.74/2.67 ((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))),
% 3.74/2.67 inference(tautology,[status(thm)],[])).
% 3.74/2.67 tff(111,plain,
% 3.74/2.67 ((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[110, 109])).
% 3.74/2.67 tff(112,plain,
% 3.74/2.67 (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[111, 98])).
% 3.74/2.67 tff(113,assumption,(~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))), introduced(assumption)).
% 3.74/2.67 tff(114,plain,
% 3.74/2.67 (((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))) | in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)),
% 3.74/2.67 inference(tautology,[status(thm)],[])).
% 3.74/2.67 tff(115,plain,
% 3.74/2.67 (in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[114, 113])).
% 3.74/2.67 tff(116,plain,
% 3.74/2.67 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(117,plain,
% 3.74/2.67 ((ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~ordinal(A!19))) <=> ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(118,plain,
% 3.74/2.67 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))),
% 3.74/2.67 inference(monotonicity,[status(thm)],[117])).
% 3.74/2.67 tff(119,plain,
% 3.74/2.67 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))),
% 3.74/2.67 inference(transitivity,[status(thm)],[118, 116])).
% 3.74/2.67 tff(120,plain,
% 3.74/2.67 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))),
% 3.74/2.67 inference(quant_inst,[status(thm)],[])).
% 3.74/2.67 tff(121,plain,
% 3.74/2.67 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[120, 119])).
% 3.74/2.67 tff(122,plain,
% 3.74/2.67 (ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[121, 76, 66, 115])).
% 3.74/2.67 tff(123,plain,
% 3.74/2.67 (((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))),
% 3.74/2.67 inference(tautology,[status(thm)],[])).
% 3.74/2.67 tff(124,plain,
% 3.74/2.67 (in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[123, 113])).
% 3.74/2.67 tff(125,assumption,(~ordinal(tptp_fun_C_1(union(A!19)))), introduced(assumption)).
% 3.74/2.67 tff(126,plain,
% 3.74/2.67 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_1(union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ordinal(tptp_fun_C_1(union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(127,plain,
% 3.74/2.67 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_1(union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))),
% 3.74/2.67 inference(quant_inst,[status(thm)],[])).
% 3.74/2.67 tff(128,plain,
% 3.74/2.67 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ordinal(tptp_fun_C_1(union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[127, 126])).
% 3.74/2.67 tff(129,plain,
% 3.74/2.67 ($false),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[128, 76, 125, 124, 122])).
% 3.74/2.67 tff(130,plain,(((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))) | ordinal(tptp_fun_C_1(union(A!19)))), inference(lemma,lemma(discharge,[]))).
% 3.74/2.67 tff(131,plain,
% 3.74/2.67 (ordinal(tptp_fun_C_1(union(A!19)))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[130, 112])).
% 3.74/2.67 tff(132,assumption,(~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))), introduced(assumption)).
% 3.74/2.67 tff(133,assumption,(ordinal(tptp_fun_C_1(union(A!19)))), introduced(assumption)).
% 3.74/2.67 tff(134,plain,
% 3.74/2.67 (^[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)))))),
% 3.74/2.67 inference(bind,[status(th)],[])).
% 3.74/2.67 tff(135,plain,
% 3.74/2.67 (![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))))),
% 3.74/2.67 inference(quant_intro,[status(thm)],[134])).
% 3.74/2.67 tff(136,plain,
% 3.74/2.67 (^[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)))))),
% 3.74/2.67 inference(bind,[status(th)],[])).
% 3.74/2.67 tff(137,plain,
% 3.74/2.67 (![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))))),
% 3.74/2.67 inference(quant_intro,[status(thm)],[136])).
% 3.74/2.67 tff(138,plain,
% 3.74/2.67 (![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))))),
% 3.74/2.67 inference(transitivity,[status(thm)],[137, 135])).
% 3.74/2.67 tff(139,plain,
% 3.74/2.67 (^[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)))))),
% 3.74/2.67 inference(bind,[status(th)],[])).
% 3.74/2.67 tff(140,plain,
% 3.74/2.67 (![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))))),
% 3.74/2.67 inference(quant_intro,[status(thm)],[139])).
% 3.74/2.67 tff(141,plain,
% 3.74/2.67 (![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))))))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(142,plain,
% 3.74/2.67 (^[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))))))))),
% 3.74/2.67 inference(bind,[status(th)],[])).
% 3.74/2.67 tff(143,plain,
% 3.74/2.67 (![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))))))),
% 3.74/2.67 inference(quant_intro,[status(thm)],[142])).
% 3.74/2.67 tff(144,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')).
% 3.74/2.67 tff(145,plain,
% 3.74/2.67 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[144, 143])).
% 3.74/2.67 tff(146,plain,
% 3.74/2.67 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[145, 141])).
% 3.74/2.67 tff(147,plain,(
% 3.74/2.67 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 3.74/2.67 inference(skolemize,[status(sab)],[146])).
% 3.74/2.67 tff(148,plain,
% 3.74/2.67 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[147, 140])).
% 3.74/2.67 tff(149,plain,
% 3.74/2.67 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[148, 138])).
% 3.74/2.67 tff(150,plain,
% 3.74/2.67 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B)))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(151,plain,
% 3.74/2.67 (((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B)))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(152,plain,
% 3.74/2.67 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))))),
% 3.74/2.67 inference(monotonicity,[status(thm)],[151])).
% 3.74/2.67 tff(153,plain,
% 3.74/2.67 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B)))),
% 3.74/2.67 inference(transitivity,[status(thm)],[152, 150])).
% 3.74/2.67 tff(154,plain,
% 3.74/2.67 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B) | (~ordinal(B))))),
% 3.74/2.67 inference(quant_inst,[status(thm)],[])).
% 3.74/2.67 tff(155,plain,
% 3.74/2.67 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))),
% 3.74/2.67 inference(modus_ponens,[status(thm)],[154, 153])).
% 3.74/2.67 tff(156,plain,
% 3.74/2.67 ($false),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[155, 149, 133, 132])).
% 3.74/2.67 tff(157,plain,((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))), inference(lemma,lemma(discharge,[]))).
% 3.74/2.67 tff(158,plain,
% 3.74/2.67 (![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))),
% 3.74/2.67 inference(unit_resolution,[status(thm)],[157, 131])).
% 3.74/2.67 tff(159,assumption,(![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))), introduced(assumption)).
% 3.74/2.67 tff(160,assumption,(~(tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))), introduced(assumption)).
% 3.74/2.67 tff(161,assumption,(~in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19)))), introduced(assumption)).
% 3.74/2.67 tff(162,assumption,(~in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))), introduced(assumption)).
% 3.74/2.67 tff(163,assumption,(ordinal(tptp_fun_B_2(union(A!19)))), introduced(assumption)).
% 3.74/2.67 tff(164,plain,
% 3.74/2.67 (((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | (in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19)))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19)))))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(165,plain,
% 3.74/2.67 (((~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))) <=> (in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19)))))),
% 3.74/2.67 inference(rewrite,[status(thm)],[])).
% 3.74/2.67 tff(166,plain,
% 3.74/2.67 (((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | (in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19))))))),
% 3.74/2.67 inference(monotonicity,[status(thm)],[165])).
% 3.74/2.67 tff(167,plain,
% 3.74/2.67 (((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19)))))),
% 3.74/2.67 inference(transitivity,[status(thm)],[166, 164])).
% 3.74/2.67 tff(168,plain,
% 3.74/2.67 ((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))))),
% 3.74/2.67 inference(quant_inst,[status(thm)],[])).
% 3.74/2.67 tff(169,plain,
% 3.74/2.67 ((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[168, 167])).
% 3.74/2.68 tff(170,plain,
% 3.74/2.68 ($false),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[169, 163, 162, 161, 160, 159])).
% 3.74/2.68 tff(171,plain,((~![B: $i] : ((~ordinal(B)) | in(tptp_fun_C_1(union(A!19)), B) | in(B, tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = B))) | (~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))), inference(lemma,lemma(discharge,[]))).
% 3.74/2.68 tff(172,plain,
% 3.74/2.68 (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[171, 158, 96, 94, 92])).
% 3.74/2.68 tff(173,plain,
% 3.74/2.68 ($false),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[172, 37])).
% 3.74/2.68 tff(174,plain,(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))), inference(lemma,lemma(discharge,[]))).
% 3.74/2.68 tff(175,assumption,((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))))), introduced(assumption)).
% 3.74/2.68 tff(176,plain,
% 3.74/2.68 (^[A: $i] : refl((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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)))))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(177,plain,
% 3.74/2.68 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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))))))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[176])).
% 3.74/2.68 tff(178,plain,
% 3.74/2.68 (^[A: $i] : rewrite((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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)))))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(179,plain,
% 3.74/2.68 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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))))))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[178])).
% 3.74/2.68 tff(180,plain,
% 3.74/2.68 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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))))))))),
% 3.74/2.68 inference(transitivity,[status(thm)],[179, 177])).
% 3.74/2.68 tff(181,plain,
% 3.74/2.68 (^[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(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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))))))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(182,plain,
% 3.74/2.68 (![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(B, A)) | (~in(C, 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))))))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[181])).
% 3.74/2.68 tff(183,plain,
% 3.74/2.68 (^[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)))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(184,plain,
% 3.74/2.68 (![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))))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[183])).
% 3.74/2.68 tff(185,plain,
% 3.74/2.68 (![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)))))),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(186,plain,
% 3.74/2.68 (^[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))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(187,plain,
% 3.74/2.68 (![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)))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[186])).
% 3.74/2.68 tff(188,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')).
% 3.74/2.68 tff(189,plain,
% 3.74/2.68 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[188, 187])).
% 3.74/2.68 tff(190,plain,
% 3.74/2.68 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[189, 185])).
% 3.74/2.68 tff(191,plain,(
% 3.74/2.68 ![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))))))))),
% 3.74/2.68 inference(skolemize,[status(sab)],[190])).
% 3.74/2.68 tff(192,plain,
% 3.74/2.68 (![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))))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[191, 184])).
% 3.74/2.68 tff(193,plain,
% 3.74/2.68 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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))))))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[192, 182])).
% 3.74/2.68 tff(194,plain,
% 3.74/2.68 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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))))))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[193, 180])).
% 3.74/2.68 tff(195,plain,
% 3.74/2.68 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))))))),
% 3.74/2.68 inference(quant_inst,[status(thm)],[])).
% 3.74/2.68 tff(196,plain,
% 3.74/2.68 ($false),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[195, 194, 175])).
% 3.74/2.68 tff(197,plain,(~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19))))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/2.68 tff(198,plain,
% 3.74/2.68 (((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))))) | (epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19))))))),
% 3.74/2.68 inference(tautology,[status(thm)],[])).
% 3.74/2.68 tff(199,plain,
% 3.74/2.68 (epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[198, 197])).
% 3.74/2.68 tff(200,plain,
% 3.74/2.68 ((~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19))))))) | epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))),
% 3.74/2.68 inference(tautology,[status(thm)],[])).
% 3.74/2.68 tff(201,plain,
% 3.74/2.68 (epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[200, 199])).
% 3.74/2.68 tff(202,plain,
% 3.74/2.68 (epsilon_connected(union(A!19))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[201, 174])).
% 3.74/2.68 tff(203,plain,
% 3.74/2.68 (^[A: $i] : refl((ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(204,plain,
% 3.74/2.68 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[203])).
% 3.74/2.68 tff(205,plain,
% 3.74/2.68 (^[A: $i] : rewrite((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(206,plain,
% 3.74/2.68 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[205])).
% 3.74/2.68 tff(207,plain,
% 3.74/2.68 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(208,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_ordinal1')).
% 3.74/2.68 tff(209,plain,
% 3.74/2.68 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[208, 207])).
% 3.74/2.68 tff(210,plain,(
% 3.74/2.68 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 3.74/2.68 inference(skolemize,[status(sab)],[209])).
% 3.74/2.68 tff(211,plain,
% 3.74/2.68 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[210, 206])).
% 3.74/2.68 tff(212,plain,
% 3.74/2.68 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[211, 204])).
% 3.74/2.68 tff(213,plain,
% 3.74/2.68 ((~![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (ordinal(union(A!19)) <=> (~((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19))))))),
% 3.74/2.68 inference(quant_inst,[status(thm)],[])).
% 3.74/2.68 tff(214,plain,
% 3.74/2.68 (ordinal(union(A!19)) <=> (~((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[213, 212])).
% 3.74/2.68 tff(215,plain,
% 3.74/2.68 (~ordinal(union(A!19))),
% 3.74/2.68 inference(or_elim,[status(thm)],[65])).
% 3.74/2.68 tff(216,plain,
% 3.74/2.68 ((~(ordinal(union(A!19)) <=> (~((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19))))))) | ordinal(union(A!19)) | ((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19))))),
% 3.74/2.68 inference(tautology,[status(thm)],[])).
% 3.74/2.68 tff(217,plain,
% 3.74/2.68 ((~(ordinal(union(A!19)) <=> (~((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19))))))) | ((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19))))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[216, 215])).
% 3.74/2.68 tff(218,plain,
% 3.74/2.68 ((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[217, 214])).
% 3.74/2.68 tff(219,plain,
% 3.74/2.68 ((~((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19))))) | (~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))),
% 3.74/2.68 inference(tautology,[status(thm)],[])).
% 3.74/2.68 tff(220,plain,
% 3.74/2.68 ((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[219, 218])).
% 3.74/2.68 tff(221,plain,
% 3.74/2.68 (~epsilon_transitive(union(A!19))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[220, 202])).
% 3.74/2.68 tff(222,assumption,((~((~epsilon_transitive(union(A!19))) | ![B: $i] : ((~in(B, union(A!19))) | subset(B, union(A!19))))) | (~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))))), introduced(assumption)).
% 3.74/2.68 tff(223,plain,
% 3.74/2.68 (^[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))))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(224,plain,
% 3.74/2.68 (![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)))))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[223])).
% 3.74/2.68 tff(225,plain,
% 3.74/2.68 (^[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))))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(226,plain,
% 3.74/2.68 (![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)))))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[225])).
% 3.74/2.68 tff(227,plain,
% 3.74/2.68 (![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)))))))),
% 3.74/2.68 inference(transitivity,[status(thm)],[226, 224])).
% 3.74/2.68 tff(228,plain,
% 3.74/2.68 (^[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)))))))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(229,plain,
% 3.74/2.68 (![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)))))))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[228])).
% 3.74/2.68 tff(230,plain,
% 3.74/2.68 (![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)))),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(231,plain,
% 3.74/2.68 (^[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))))),
% 3.74/2.68 inference(bind,[status(th)],[])).
% 3.74/2.68 tff(232,plain,
% 3.74/2.68 (![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)))),
% 3.74/2.68 inference(quant_intro,[status(thm)],[231])).
% 3.74/2.68 tff(233,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_ordinal1')).
% 3.74/2.68 tff(234,plain,
% 3.74/2.68 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[233, 232])).
% 3.74/2.68 tff(235,plain,
% 3.74/2.68 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[234, 230])).
% 3.74/2.68 tff(236,plain,(
% 3.74/2.68 ![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)))))),
% 3.74/2.68 inference(skolemize,[status(sab)],[235])).
% 3.74/2.68 tff(237,plain,
% 3.74/2.68 (![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)))))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[236, 229])).
% 3.74/2.68 tff(238,plain,
% 3.74/2.68 (![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)))))))),
% 3.74/2.68 inference(modus_ponens,[status(thm)],[237, 227])).
% 3.74/2.68 tff(239,plain,
% 3.74/2.68 ((~![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!19))) | ![B: $i] : ((~in(B, union(A!19))) | subset(B, union(A!19))))) | (~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))))))),
% 3.74/2.68 inference(quant_inst,[status(thm)],[])).
% 3.74/2.68 tff(240,plain,
% 3.74/2.68 ($false),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[239, 238, 222])).
% 3.74/2.68 tff(241,plain,(~((~((~epsilon_transitive(union(A!19))) | ![B: $i] : ((~in(B, union(A!19))) | subset(B, union(A!19))))) | (~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/2.68 tff(242,plain,
% 3.74/2.68 (((~((~epsilon_transitive(union(A!19))) | ![B: $i] : ((~in(B, union(A!19))) | subset(B, union(A!19))))) | (~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))))) | (epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))))),
% 3.74/2.68 inference(tautology,[status(thm)],[])).
% 3.74/2.68 tff(243,plain,
% 3.74/2.68 (epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[242, 241])).
% 3.74/2.68 tff(244,plain,
% 3.74/2.68 ((~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))))) | epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))),
% 3.74/2.68 inference(tautology,[status(thm)],[])).
% 3.74/2.68 tff(245,plain,
% 3.74/2.68 (epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[244, 243])).
% 3.74/2.68 tff(246,plain,
% 3.74/2.68 (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[245, 221])).
% 3.74/2.68 tff(247,assumption,(~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))), introduced(assumption)).
% 3.74/2.68 tff(248,plain,
% 3.74/2.68 (((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19))),
% 3.74/2.68 inference(tautology,[status(thm)],[])).
% 3.74/2.68 tff(249,plain,
% 3.74/2.68 (in(tptp_fun_B_0(union(A!19)), union(A!19))),
% 3.74/2.68 inference(unit_resolution,[status(thm)],[248, 247])).
% 3.74/2.68 tff(250,plain,
% 3.74/2.68 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(251,plain,
% 3.74/2.68 ((~(~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))) <=> ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(252,plain,
% 3.74/2.68 (((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | $false) <=> (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(253,plain,
% 3.74/2.68 ((~$true) <=> $false),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(254,plain,
% 3.74/2.68 (($true | (~((~((~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))) | in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19))))))) <=> $true),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(255,plain,
% 3.74/2.68 ((~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))) <=> (~((~((~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))) | in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19))))))),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(256,plain,
% 3.74/2.68 ((union(A!19) = union(A!19)) <=> $true),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(257,plain,
% 3.74/2.68 (((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))) <=> ($true | (~((~((~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))) | in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)))))))),
% 3.74/2.68 inference(monotonicity,[status(thm)],[256, 255])).
% 3.74/2.68 tff(258,plain,
% 3.74/2.68 (((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))) <=> $true),
% 3.74/2.68 inference(transitivity,[status(thm)],[257, 254])).
% 3.74/2.68 tff(259,plain,
% 3.74/2.68 ((~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))))) <=> (~$true)),
% 3.74/2.68 inference(monotonicity,[status(thm)],[258])).
% 3.74/2.68 tff(260,plain,
% 3.74/2.68 ((~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))))) <=> $false),
% 3.74/2.68 inference(transitivity,[status(thm)],[259, 253])).
% 3.74/2.68 tff(261,plain,
% 3.74/2.68 ((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) <=> (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))),
% 3.74/2.68 inference(rewrite,[status(thm)],[])).
% 3.74/2.68 tff(262,plain,
% 3.74/2.68 (((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))) <=> ((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | $false)),
% 3.74/2.68 inference(monotonicity,[status(thm)],[261, 260])).
% 3.74/2.68 tff(263,plain,
% 3.74/2.68 (((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))) <=> (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))),
% 3.74/2.68 inference(transitivity,[status(thm)],[262, 252])).
% 3.74/2.68 tff(264,plain,
% 3.74/2.68 ((~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))))))) <=> (~(~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))))),
% 3.74/2.68 inference(monotonicity,[status(thm)],[263])).
% 3.74/2.68 tff(265,plain,
% 3.74/2.68 ((~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))))))) <=> ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))),
% 3.74/2.68 inference(transitivity,[status(thm)],[264, 251])).
% 3.74/2.68 tff(266,plain,
% 3.74/2.68 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))),
% 3.74/2.69 inference(monotonicity,[status(thm)],[265])).
% 3.74/2.69 tff(267,plain,
% 3.74/2.69 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))),
% 3.74/2.69 inference(transitivity,[status(thm)],[266, 250])).
% 3.74/2.69 tff(268,plain,
% 3.74/2.69 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(269,plain,
% 3.74/2.69 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[268, 267])).
% 3.74/2.69 tff(270,plain,
% 3.74/2.69 (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[269, 21, 249])).
% 3.74/2.69 tff(271,plain,
% 3.74/2.69 (((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))) | in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(272,plain,
% 3.74/2.69 (in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[271, 270])).
% 3.74/2.69 tff(273,plain,
% 3.74/2.69 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | (~(epsilon_transitive(A!19) | (~((~in(tptp_fun_B_0(A!19), A!19)) | subset(tptp_fun_B_0(A!19), A!19)))))))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(274,plain,
% 3.74/2.69 (~((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | (~(epsilon_transitive(A!19) | (~((~in(tptp_fun_B_0(A!19), A!19)) | subset(tptp_fun_B_0(A!19), A!19))))))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[273, 238])).
% 3.74/2.69 tff(275,plain,
% 3.74/2.69 (((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | (~(epsilon_transitive(A!19) | (~((~in(tptp_fun_B_0(A!19), A!19)) | subset(tptp_fun_B_0(A!19), A!19)))))) | ((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(276,plain,
% 3.74/2.69 ((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[275, 274])).
% 3.74/2.69 tff(277,plain,
% 3.74/2.69 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(278,plain,
% 3.74/2.69 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[277])).
% 3.74/2.69 tff(279,plain,
% 3.74/2.69 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(280,plain,
% 3.74/2.69 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[279])).
% 3.74/2.69 tff(281,plain,
% 3.74/2.69 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(282,plain,
% 3.74/2.69 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(283,plain,
% 3.74/2.69 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[282])).
% 3.74/2.69 tff(284,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_ordinal1')).
% 3.74/2.69 tff(285,plain,
% 3.74/2.69 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[284, 283])).
% 3.74/2.69 tff(286,plain,
% 3.74/2.69 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[285, 281])).
% 3.74/2.69 tff(287,plain,(
% 3.74/2.69 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 3.74/2.69 inference(skolemize,[status(sab)],[286])).
% 3.74/2.69 tff(288,plain,
% 3.74/2.69 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[287, 280])).
% 3.74/2.69 tff(289,plain,
% 3.74/2.69 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[288, 278])).
% 3.74/2.69 tff(290,plain,
% 3.74/2.69 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!19)) | (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!19)) | (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19)))))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(291,plain,
% 3.74/2.69 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!19)) | (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19)))))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(292,plain,
% 3.74/2.69 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!19)) | (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19))))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[291, 290])).
% 3.74/2.69 tff(293,plain,
% 3.74/2.69 (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19)))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[292, 289, 66])).
% 3.74/2.69 tff(294,plain,
% 3.74/2.69 (((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19))) | epsilon_transitive(A!19)),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(295,plain,
% 3.74/2.69 (epsilon_transitive(A!19)),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[294, 293])).
% 3.74/2.69 tff(296,plain,
% 3.74/2.69 ((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | (~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19))),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(297,plain,
% 3.74/2.69 ((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[296, 295])).
% 3.74/2.69 tff(298,plain,
% 3.74/2.69 (![B: $i] : ((~in(B, A!19)) | subset(B, A!19))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[297, 276])).
% 3.74/2.69 tff(299,plain,
% 3.74/2.69 (((~![B: $i] : ((~in(B, A!19)) | subset(B, A!19))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)) | subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))) <=> ((~![B: $i] : ((~in(B, A!19)) | subset(B, A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)) | subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(300,plain,
% 3.74/2.69 ((~![B: $i] : ((~in(B, A!19)) | subset(B, A!19))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)) | subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(301,plain,
% 3.74/2.69 ((~![B: $i] : ((~in(B, A!19)) | subset(B, A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)) | subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[300, 299])).
% 3.74/2.69 tff(302,plain,
% 3.74/2.69 (subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[301, 298, 272])).
% 3.74/2.69 tff(303,plain,
% 3.74/2.69 (((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))) | in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(304,plain,
% 3.74/2.69 (in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[303, 270])).
% 3.74/2.69 tff(305,plain,
% 3.74/2.69 (((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))) | (~subset(tptp_fun_B_0(union(A!19)), union(A!19)))),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(306,plain,
% 3.74/2.69 (~subset(tptp_fun_B_0(union(A!19)), union(A!19))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[305, 247])).
% 3.74/2.69 tff(307,plain,
% 3.74/2.69 (^[A: $i, B: $i] : refl(((~in(A, B)) | subset(A, union(B))) <=> ((~in(A, B)) | subset(A, union(B))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(308,plain,
% 3.74/2.69 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[307])).
% 3.74/2.69 tff(309,plain,
% 3.74/2.69 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(310,plain,
% 3.74/2.69 (^[A: $i, B: $i] : rewrite((in(A, B) => subset(A, union(B))) <=> ((~in(A, B)) | subset(A, union(B))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(311,plain,
% 3.74/2.69 (![A: $i, B: $i] : (in(A, B) => subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[310])).
% 3.74/2.69 tff(312,axiom,(![A: $i, B: $i] : (in(A, B) => subset(A, union(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t92_zfmisc_1')).
% 3.74/2.69 tff(313,plain,
% 3.74/2.69 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[312, 311])).
% 3.74/2.69 tff(314,plain,
% 3.74/2.69 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[313, 309])).
% 3.74/2.69 tff(315,plain,(
% 3.74/2.69 ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 3.74/2.69 inference(skolemize,[status(sab)],[314])).
% 3.74/2.69 tff(316,plain,
% 3.74/2.69 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[315, 308])).
% 3.74/2.69 tff(317,plain,
% 3.74/2.69 (((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | ((~in(tptp_fun_B_0(union(A!19)), A!19)) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | (~in(tptp_fun_B_0(union(A!19)), A!19)) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(318,plain,
% 3.74/2.69 ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | ((~in(tptp_fun_B_0(union(A!19)), A!19)) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(319,plain,
% 3.74/2.69 ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | (~in(tptp_fun_B_0(union(A!19)), A!19)) | subset(tptp_fun_B_0(union(A!19)), union(A!19))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[318, 317])).
% 3.74/2.69 tff(320,plain,
% 3.74/2.69 (~in(tptp_fun_B_0(union(A!19)), A!19)),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[319, 316, 306])).
% 3.74/2.69 tff(321,assumption,(~empty(A!19)), introduced(assumption)).
% 3.74/2.69 tff(322,plain,
% 3.74/2.69 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(323,plain,
% 3.74/2.69 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[322])).
% 3.74/2.69 tff(324,plain,
% 3.74/2.69 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(325,plain,
% 3.74/2.69 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(326,plain,
% 3.74/2.69 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[325])).
% 3.74/2.69 tff(327,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 3.74/2.69 tff(328,plain,
% 3.74/2.69 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[327, 326])).
% 3.74/2.69 tff(329,plain,
% 3.74/2.69 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[328, 324])).
% 3.74/2.69 tff(330,plain,(
% 3.74/2.69 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.74/2.69 inference(skolemize,[status(sab)],[329])).
% 3.74/2.69 tff(331,plain,
% 3.74/2.69 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[330, 323])).
% 3.74/2.69 tff(332,plain,
% 3.74/2.69 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(333,plain,
% 3.74/2.69 ((empty(A!19) | in(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19))) <=> (empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(334,plain,
% 3.74/2.69 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | in(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19)))),
% 3.74/2.69 inference(monotonicity,[status(thm)],[333])).
% 3.74/2.69 tff(335,plain,
% 3.74/2.69 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | in(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19))),
% 3.74/2.69 inference(transitivity,[status(thm)],[334, 332])).
% 3.74/2.69 tff(336,plain,
% 3.74/2.69 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | in(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(337,plain,
% 3.74/2.69 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19)),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[336, 335])).
% 3.74/2.69 tff(338,plain,
% 3.74/2.69 (~element(tptp_fun_B_0(union(A!19)), A!19)),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[337, 331, 321, 320])).
% 3.74/2.69 tff(339,plain,
% 3.74/2.69 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(340,plain,
% 3.74/2.69 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[339])).
% 3.74/2.69 tff(341,plain,
% 3.74/2.69 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(342,plain,
% 3.74/2.69 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[341])).
% 3.74/2.69 tff(343,plain,
% 3.74/2.69 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(344,plain,
% 3.74/2.69 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(345,plain,
% 3.74/2.69 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[344])).
% 3.74/2.69 tff(346,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_subset')).
% 3.74/2.69 tff(347,plain,
% 3.74/2.69 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[346, 345])).
% 3.74/2.69 tff(348,plain,
% 3.74/2.69 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[347, 343])).
% 3.74/2.69 tff(349,plain,(
% 3.74/2.69 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 3.74/2.69 inference(skolemize,[status(sab)],[348])).
% 3.74/2.69 tff(350,plain,
% 3.74/2.69 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[349, 342])).
% 3.74/2.69 tff(351,plain,
% 3.74/2.69 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[350, 340])).
% 3.74/2.69 tff(352,plain,
% 3.74/2.69 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(353,plain,
% 3.74/2.69 ((element(tptp_fun_B_0(union(A!19)), A!19) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)))) <=> (element(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(354,plain,
% 3.74/2.69 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_0(union(A!19)), A!19) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19)))))),
% 3.74/2.69 inference(monotonicity,[status(thm)],[353])).
% 3.74/2.69 tff(355,plain,
% 3.74/2.69 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_0(union(A!19)), A!19) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))))),
% 3.74/2.69 inference(transitivity,[status(thm)],[354, 352])).
% 3.74/2.69 tff(356,plain,
% 3.74/2.69 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_0(union(A!19)), A!19) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(357,plain,
% 3.74/2.69 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[356, 355])).
% 3.74/2.69 tff(358,plain,
% 3.74/2.69 (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[357, 351, 338, 304])).
% 3.74/2.69 tff(359,assumption,(~(element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) <=> subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))), introduced(assumption)).
% 3.74/2.69 tff(360,plain,
% 3.74/2.69 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(361,plain,
% 3.74/2.69 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[360])).
% 3.74/2.69 tff(362,plain,
% 3.74/2.69 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(363,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 3.74/2.69 tff(364,plain,
% 3.74/2.69 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[363, 362])).
% 3.74/2.69 tff(365,plain,(
% 3.74/2.69 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 3.74/2.69 inference(skolemize,[status(sab)],[364])).
% 3.74/2.69 tff(366,plain,
% 3.74/2.69 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[365, 361])).
% 3.74/2.69 tff(367,plain,
% 3.74/2.69 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) <=> subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(368,plain,
% 3.74/2.69 ($false),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[367, 366, 359])).
% 3.74/2.69 tff(369,plain,(element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) <=> subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)), inference(lemma,lemma(discharge,[]))).
% 3.74/2.69 tff(370,plain,
% 3.74/2.69 ((~(element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) <=> subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))) | element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) | (~subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(371,plain,
% 3.74/2.69 (element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) | (~subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[370, 369])).
% 3.74/2.69 tff(372,plain,
% 3.74/2.69 ($false),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[371, 358, 302])).
% 3.74/2.69 tff(373,plain,(((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))) | empty(A!19)), inference(lemma,lemma(discharge,[]))).
% 3.74/2.69 tff(374,plain,
% 3.74/2.69 (empty(A!19)),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[373, 246])).
% 3.74/2.69 tff(375,plain,
% 3.74/2.69 (^[A: $i, B: $i] : refl(((A = B) | (~empty(B)) | (~empty(A))) <=> ((A = B) | (~empty(B)) | (~empty(A))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(376,plain,
% 3.74/2.69 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[375])).
% 3.74/2.69 tff(377,plain,
% 3.74/2.69 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(B)) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(B)) | (~empty(A))))))), rewrite((~(~((A = B) | (~empty(B)) | (~empty(A))))) <=> ((A = B) | (~empty(B)) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(B)) | (~empty(A)))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(378,plain,
% 3.74/2.69 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[377])).
% 3.74/2.69 tff(379,plain,
% 3.74/2.69 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(380,plain,
% 3.74/2.69 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 3.74/2.69 inference(bind,[status(th)],[])).
% 3.74/2.69 tff(381,plain,
% 3.74/2.69 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.74/2.69 inference(quant_intro,[status(thm)],[380])).
% 3.74/2.69 tff(382,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 3.74/2.69 tff(383,plain,
% 3.74/2.69 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[382, 381])).
% 3.74/2.69 tff(384,plain,
% 3.74/2.69 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[383, 379])).
% 3.74/2.69 tff(385,plain,(
% 3.74/2.69 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.74/2.69 inference(skolemize,[status(sab)],[384])).
% 3.74/2.69 tff(386,plain,
% 3.74/2.69 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[385, 378])).
% 3.74/2.69 tff(387,plain,
% 3.74/2.69 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[386, 376])).
% 3.74/2.69 tff(388,plain,
% 3.74/2.69 (empty(empty_set) <=> empty(empty_set)),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(389,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_relat_1')).
% 3.74/2.69 tff(390,plain,
% 3.74/2.69 (empty(empty_set) & relation(empty_set)),
% 3.74/2.69 inference(and_elim,[status(thm)],[389])).
% 3.74/2.69 tff(391,plain,
% 3.74/2.69 (empty(empty_set)),
% 3.74/2.69 inference(and_elim,[status(thm)],[390])).
% 3.74/2.69 tff(392,plain,
% 3.74/2.69 (empty(empty_set)),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[391, 388])).
% 3.74/2.69 tff(393,plain,
% 3.74/2.69 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((~empty(empty_set)) | (~empty(A!19)) | (A!19 = empty_set))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (~empty(A!19)) | (A!19 = empty_set))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(394,plain,
% 3.74/2.69 (((A!19 = empty_set) | (~empty(empty_set)) | (~empty(A!19))) <=> ((~empty(empty_set)) | (~empty(A!19)) | (A!19 = empty_set))),
% 3.74/2.69 inference(rewrite,[status(thm)],[])).
% 3.74/2.69 tff(395,plain,
% 3.74/2.69 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!19 = empty_set) | (~empty(empty_set)) | (~empty(A!19)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((~empty(empty_set)) | (~empty(A!19)) | (A!19 = empty_set)))),
% 3.74/2.69 inference(monotonicity,[status(thm)],[394])).
% 3.74/2.69 tff(396,plain,
% 3.74/2.69 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!19 = empty_set) | (~empty(empty_set)) | (~empty(A!19)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (~empty(A!19)) | (A!19 = empty_set))),
% 3.74/2.69 inference(transitivity,[status(thm)],[395, 393])).
% 3.74/2.69 tff(397,plain,
% 3.74/2.69 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!19 = empty_set) | (~empty(empty_set)) | (~empty(A!19)))),
% 3.74/2.69 inference(quant_inst,[status(thm)],[])).
% 3.74/2.69 tff(398,plain,
% 3.74/2.69 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (~empty(A!19)) | (A!19 = empty_set)),
% 3.74/2.69 inference(modus_ponens,[status(thm)],[397, 396])).
% 3.74/2.69 tff(399,plain,
% 3.74/2.69 (A!19 = empty_set),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[398, 392, 387, 374])).
% 3.74/2.69 tff(400,plain,
% 3.74/2.69 (union(A!19) = union(empty_set)),
% 3.74/2.69 inference(monotonicity,[status(thm)],[399])).
% 3.74/2.69 tff(401,plain,
% 3.74/2.69 ((~((~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))))))) | (~(union(A!19) = union(empty_set))) | (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))))))),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(402,plain,
% 3.74/2.69 (~((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[401, 400, 30])).
% 3.74/2.69 tff(403,plain,
% 3.74/2.69 (((~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))))) | ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(404,plain,
% 3.74/2.69 ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[403, 402])).
% 3.74/2.69 tff(405,plain,
% 3.74/2.69 (in(tptp_fun_B_0(union(A!19)), union(A!19))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[248, 246])).
% 3.74/2.69 tff(406,plain,
% 3.74/2.69 ((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(407,plain,
% 3.74/2.69 ((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[406, 405])).
% 3.74/2.69 tff(408,plain,
% 3.74/2.69 (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[407, 404])).
% 3.74/2.69 tff(409,plain,
% 3.74/2.69 (((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))) | in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)),
% 3.74/2.69 inference(tautology,[status(thm)],[])).
% 3.74/2.69 tff(410,plain,
% 3.74/2.69 (in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)),
% 3.74/2.69 inference(unit_resolution,[status(thm)],[409, 408])).
% 3.74/2.69 tff(411,plain,
% 3.74/2.69 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~empty(B))) <=> ((~in(A, B)) | (~empty(B))))),
% 3.74/2.70 inference(bind,[status(th)],[])).
% 3.74/2.70 tff(412,plain,
% 3.74/2.70 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 3.74/2.70 inference(quant_intro,[status(thm)],[411])).
% 3.74/2.70 tff(413,plain,
% 3.74/2.70 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~in(A, B)) | (~empty(B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~in(A, B)) | (~empty(B))))))), rewrite((~(~((~in(A, B)) | (~empty(B))))) <=> ((~in(A, B)) | (~empty(B)))), ((~(in(A, B) & empty(B))) <=> ((~in(A, B)) | (~empty(B)))))),
% 3.74/2.70 inference(bind,[status(th)],[])).
% 3.74/2.70 tff(414,plain,
% 3.74/2.70 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 3.74/2.70 inference(quant_intro,[status(thm)],[413])).
% 3.74/2.70 tff(415,plain,
% 3.74/2.70 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 3.74/2.70 inference(rewrite,[status(thm)],[])).
% 3.74/2.70 tff(416,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_boole')).
% 3.74/2.70 tff(417,plain,
% 3.74/2.70 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 3.74/2.70 inference(modus_ponens,[status(thm)],[416, 415])).
% 3.74/2.70 tff(418,plain,(
% 3.74/2.70 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 3.74/2.70 inference(skolemize,[status(sab)],[417])).
% 3.74/2.70 tff(419,plain,
% 3.74/2.70 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 3.74/2.70 inference(modus_ponens,[status(thm)],[418, 414])).
% 3.74/2.70 tff(420,plain,
% 3.74/2.70 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 3.74/2.70 inference(modus_ponens,[status(thm)],[419, 412])).
% 3.74/2.70 tff(421,plain,
% 3.74/2.70 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))),
% 3.74/2.70 inference(rewrite,[status(thm)],[])).
% 3.74/2.70 tff(422,plain,
% 3.74/2.70 (((~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)) | (~empty(empty_set))) <=> ((~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))),
% 3.74/2.70 inference(rewrite,[status(thm)],[])).
% 3.74/2.70 tff(423,plain,
% 3.74/2.70 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)) | (~empty(empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))),
% 3.74/2.70 inference(monotonicity,[status(thm)],[422])).
% 3.74/2.70 tff(424,plain,
% 3.74/2.70 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)) | (~empty(empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))),
% 3.74/2.70 inference(transitivity,[status(thm)],[423, 421])).
% 3.74/2.70 tff(425,plain,
% 3.74/2.70 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)) | (~empty(empty_set)))),
% 3.74/2.70 inference(quant_inst,[status(thm)],[])).
% 3.74/2.70 tff(426,plain,
% 3.74/2.70 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))),
% 3.74/2.70 inference(modus_ponens,[status(thm)],[425, 424])).
% 3.74/2.70 tff(427,plain,
% 3.74/2.70 ($false),
% 3.74/2.70 inference(unit_resolution,[status(thm)],[426, 392, 420, 410])).
% 3.74/2.70 % SZS output end Proof
%------------------------------------------------------------------------------