TSTP Solution File: SEV517+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEV517+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 : Tue Sep 20 08:12:46 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV517+1 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 19:02:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(member_type, type, (
% 0.21/0.43 member: ( $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_Y_4_type, type, (
% 0.21/0.43 tptp_fun_Y_4: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_P_24_type, type, (
% 0.21/0.43 tptp_fun_P_24: $i)).
% 0.21/0.43 tff(tptp_fun_X_27_type, type, (
% 0.21/0.43 tptp_fun_X_27: $i)).
% 0.21/0.43 tff(tptp_fun_B_25_type, type, (
% 0.21/0.43 tptp_fun_B_25: $i)).
% 0.21/0.43 tff(singleton_type, type, (
% 0.21/0.43 singleton: $i > $i)).
% 0.21/0.43 tff(difference_type, type, (
% 0.21/0.43 difference: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_A_26_type, type, (
% 0.21/0.43 tptp_fun_A_26: $i)).
% 0.21/0.43 tff(subset_type, type, (
% 0.21/0.43 subset: ( $i * $i ) > $o)).
% 0.21/0.43 tff(partition_type, type, (
% 0.21/0.43 partition: ( $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_X_6_type, type, (
% 0.21/0.43 tptp_fun_X_6: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Y_7_type, type, (
% 0.21/0.43 tptp_fun_Y_7: $i > $i)).
% 0.21/0.43 tff(tptp_fun_Z_9_type, type, (
% 0.21/0.43 tptp_fun_Z_9: $i > $i)).
% 0.21/0.43 tff(tptp_fun_X_8_type, type, (
% 0.21/0.43 tptp_fun_X_8: $i > $i)).
% 0.21/0.43 tff(tptp_fun_X_5_type, type, (
% 0.21/0.43 tptp_fun_X_5: ( $i * $i ) > $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (^[X: $i, A: $i] : refl((member(X, singleton(A)) <=> (X = A)) <=> (member(X, singleton(A)) <=> (X = A)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(4,axiom,(![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','singleton')).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.43 tff(6,plain,(
% 0.21/0.43 ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.43 inference(skolemize,[status(sab)],[5])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)) <=> (tptp_fun_Y_4(X!27, P!24) = B!25))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)) <=> (tptp_fun_Y_4(X!27, P!24) = B!25)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (^[B: $i, A: $i, E: $i] : refl((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (^[B: $i, A: $i, E: $i] : rewrite((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(15,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.43 tff(17,plain,(
% 0.21/0.43 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[16])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25))) <=> (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25))) <=> (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (^[A: $i, E: $i] : rewrite((~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (^[A: $i, E: $i] : refl((~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (^[A: $i, E: $i] : rewrite((~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[27, 25])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (^[A: $i, E: $i] : trans(monotonicity(rewrite(((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) <=> ((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, A) & member(tptp_fun_X_6(E, A), Y)) <=> (~((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))), ((~(member(Y, A) & member(tptp_fun_X_6(E, A), Y))) <=> (~(~((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))), rewrite((~(~((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))) <=> ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))), ((~(member(Y, A) & member(tptp_fun_X_6(E, A), Y))) <=> ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))), (![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y))) <=> ![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))), ((member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) <=> (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))), rewrite((member(tptp_fun_X_6(E, A), E) & ![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))) <=> (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))), ((member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) <=> (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))))), rewrite(((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))) <=> (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))), ((partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))) <=> (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))), rewrite((partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))) <=> (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))), ((partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))) <=> (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))), ((((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) <=> (((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y)))))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))), rewrite((((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y)))))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))), ((((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (^[A: $i, E: $i] : rewrite((((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | ((~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | ((~(~member(tptp_fun_X_6(E, A), E))) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & (~(~(member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A)))) & (member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))) <=> (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | ((~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | ((~(~member(tptp_fun_X_6(E, A), E))) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & (~(~(member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A)))) & (member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))) <=> ![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y)))))) <=> ![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (^[A: $i, E: $i] : rewrite((partition(A, E) <=> ((![X: $i] : (member(X, A) => subset(X, E)) & ![X: $i] : (member(X, E) => ?[Y: $i] : (member(Y, A) & member(X, Y)))) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (?[Z: $i] : (member(Z, X) & member(Z, Y)) => (X = Y))))) <=> (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![A: $i, E: $i] : (partition(A, E) <=> ((![X: $i] : (member(X, A) => subset(X, E)) & ![X: $i] : (member(X, E) => ?[Y: $i] : (member(Y, A) & member(X, Y)))) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (?[Z: $i] : (member(Z, X) & member(Z, Y)) => (X = Y))))) <=> ![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.44 tff(36,axiom,(![A: $i, E: $i] : (partition(A, E) <=> ((![X: $i] : (member(X, A) => subset(X, E)) & ![X: $i] : (member(X, E) => ?[Y: $i] : (member(Y, A) & member(X, Y)))) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (?[Z: $i] : (member(Z, X) & member(Z, Y)) => (X = Y)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','partition')).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.44 tff(39,plain,(
% 0.21/0.44 ![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | ((~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | ((~(~member(tptp_fun_X_6(E, A), E))) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & (~(~(member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A)))) & (member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[38])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[41, 28])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[42, 23])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))) | (~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))))))) <=> ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))) | (~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 ((~((~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, P!24)) | (~member(Y, P!24)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))))) <=> (~((~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))) | (~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(46,plain,
% 0.21/0.45 (((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, P!24)) | (~member(Y, P!24)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y))))))))))) <=> ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))) | (~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.45 tff(47,plain,
% 0.21/0.45 (((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, P!24)) | (~member(Y, P!24)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y))))))))))) <=> ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))) | (~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[46, 44])).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, P!24)) | (~member(Y, P!24)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y))))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))) | (~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (~((~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))) | (~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[49, 43])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (((~(partition(P!24, A!26) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))))) | (~((~member(tptp_fun_X_6(A!26, P!24), A!26)) | (~![Y: $i] : ((~member(Y, P!24)) | (~member(tptp_fun_X_6(A!26, P!24), Y)))))))) | (~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))))) | ((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 ((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (((member(X!27, difference(A!26, B!25)) & partition(P!24, A!26)) & ![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S)))) <=> (member(X!27, difference(A!26, B!25)) & partition(P!24, A!26) & ![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 ((~(~(member(X!27, difference(A!26, B!25)) & partition(P!24, A!26)))) <=> (member(X!27, difference(A!26, B!25)) & partition(P!24, A!26))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (((~(~(member(X!27, difference(A!26, B!25)) & partition(P!24, A!26)))) & ![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S)))) <=> ((member(X!27, difference(A!26, B!25)) & partition(P!24, A!26)) & ![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[54])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (((~(~(member(X!27, difference(A!26, B!25)) & partition(P!24, A!26)))) & ![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S)))) <=> (member(X!27, difference(A!26, B!25)) & partition(P!24, A!26) & ![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[55, 53])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 ((~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))) <=> (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 ((~![X: $i, A: $i, B: $i, P: $i] : ((member(X, difference(A, B)) & partition(P, A)) => ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))) <=> (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(59,axiom,(~![X: $i, A: $i, B: $i, P: $i] : ((member(X, difference(A, B)) & partition(P, A)) => ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','diff_elem_in_partition')).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[62, 57])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[63, 57])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 (~![X: $i, A: $i, B: $i, P: $i] : ((~(member(X, difference(A, B)) & partition(P, A))) | ?[S: $i] : (member(S, difference(P, singleton(B))) & member(X, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[65, 57])).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 (member(X!27, difference(A!26, B!25)) & partition(P!24, A!26) & ![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.21/0.46 tff(68,plain,
% 0.21/0.46 (partition(P!24, A!26)),
% 0.21/0.46 inference(and_elim,[status(thm)],[67])).
% 0.21/0.46 tff(69,plain,
% 0.21/0.46 ((~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))))) | (~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(70,plain,
% 0.21/0.46 ((~((~partition(P!24, A!26)) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))))) | (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.46 tff(71,plain,
% 0.21/0.46 (~((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[70, 52])).
% 0.21/0.46 tff(72,plain,
% 0.21/0.46 (((~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))) | ![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(73,plain,
% 0.21/0.46 (![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(X!27, difference(A!26, B!25)) <=> (~((~member(X!27, A!26)) | member(X!27, B!25))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(75,plain,
% 0.21/0.46 (member(X!27, difference(A!26, B!25)) <=> (~((~member(X!27, A!26)) | member(X!27, B!25)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[74, 19])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 (member(X!27, difference(A!26, B!25))),
% 0.21/0.46 inference(and_elim,[status(thm)],[67])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 ((~(member(X!27, difference(A!26, B!25)) <=> (~((~member(X!27, A!26)) | member(X!27, B!25))))) | (~member(X!27, difference(A!26, B!25))) | (~((~member(X!27, A!26)) | member(X!27, B!25)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(78,plain,
% 0.21/0.46 ((~(member(X!27, difference(A!26, B!25)) <=> (~((~member(X!27, A!26)) | member(X!27, B!25))))) | (~((~member(X!27, A!26)) | member(X!27, B!25)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (~((~member(X!27, A!26)) | member(X!27, B!25))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (((~member(X!27, A!26)) | member(X!27, B!25)) | member(X!27, A!26)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 (member(X!27, A!26)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (((~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | ((~member(X!27, A!26)) | (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))))))) <=> ((~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~member(X!27, A!26)) | (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 ((~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | ((~member(X!27, A!26)) | (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 ((~![X: $i] : ((~member(X, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~member(X!27, A!26)) | (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | (~member(X!27, tptp_fun_Y_4(X!27, P!24)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[84, 81, 73])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | (~member(X!27, tptp_fun_Y_4(X!27, P!24)))) | member(X!27, tptp_fun_Y_4(X!27, P!24))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 (member(X!27, tptp_fun_Y_4(X!27, P!24))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 (^[S: $i] : refl(((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S))) <=> ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 (![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S))) <=> ![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (^[S: $i] : trans(monotonicity(rewrite((member(S, difference(P!24, singleton(B!25))) & member(X!27, S)) <=> (~((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S))))), ((~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S))) <=> (~(~((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S))))))), rewrite((~(~((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S))))) <=> ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))), ((~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S))) <=> ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S))) <=> ![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S)))),
% 0.21/0.46 inference(and_elim,[status(thm)],[67])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (((~![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))) | ((~member(X!27, tptp_fun_Y_4(X!27, P!24))) | (~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))))) <=> ((~![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))) | (~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (((~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))) | (~member(X!27, tptp_fun_Y_4(X!27, P!24)))) <=> ((~member(X!27, tptp_fun_Y_4(X!27, P!24))) | (~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (((~![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))) | ((~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))))) <=> ((~![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))) | ((~member(X!27, tptp_fun_Y_4(X!27, P!24))) | (~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (((~![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))) | ((~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))))) <=> ((~![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))) | (~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[97, 95])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 ((~![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))) | ((~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 ((~![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))) | (~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 (~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[100, 94, 87])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 ((~(member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25))) <=> (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)))))) | member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25))) | ((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 ((~(member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25))) <=> (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)))))) | ((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 ((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[103, 21])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | (~member(X!27, tptp_fun_Y_4(X!27, P!24)))) | member(tptp_fun_Y_4(X!27, P!24), P!24)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (member(tptp_fun_Y_4(X!27, P!24), P!24)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[105, 85])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 ((~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)))) | (~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 ((~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)))) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (member(tptp_fun_Y_4(X!27, P!24), singleton(B!25))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[108, 104])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 ((~(member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)) <=> (tptp_fun_Y_4(X!27, P!24) = B!25))) | (~member(tptp_fun_Y_4(X!27, P!24), singleton(B!25))) | (tptp_fun_Y_4(X!27, P!24) = B!25)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 ((~(member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)) <=> (tptp_fun_Y_4(X!27, P!24) = B!25))) | (tptp_fun_Y_4(X!27, P!24) = B!25)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (tptp_fun_Y_4(X!27, P!24) = B!25),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[111, 9])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 (member(X!27, tptp_fun_Y_4(X!27, P!24)) <=> member(X!27, B!25)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 (member(X!27, B!25) <=> member(X!27, tptp_fun_Y_4(X!27, P!24))),
% 0.21/0.46 inference(symmetry,[status(thm)],[113])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 ((~member(X!27, B!25)) <=> (~member(X!27, tptp_fun_Y_4(X!27, P!24)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (((~member(X!27, A!26)) | member(X!27, B!25)) | (~member(X!27, B!25))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 (~member(X!27, B!25)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[116, 79])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (~member(X!27, tptp_fun_Y_4(X!27, P!24))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[117, 115])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[87, 118])).
% 0.21/0.47 % SZS output end Proof
%------------------------------------------------------------------------------