%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV517+1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:21 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV517+1 : TPTP v9.0.0. Released v7.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 07:42:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y_4_type, type, (
% 0.19/0.39 tptp_fun_Y_4: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_P_24_type, type, (
% 0.19/0.39 tptp_fun_P_24: $i)).
% 0.19/0.39 tff(tptp_fun_X_27_type, type, (
% 0.19/0.39 tptp_fun_X_27: $i)).
% 0.19/0.39 tff(tptp_fun_B_25_type, type, (
% 0.19/0.39 tptp_fun_B_25: $i)).
% 0.19/0.39 tff(singleton_type, type, (
% 0.19/0.39 singleton: $i > $i)).
% 0.19/0.39 tff(difference_type, type, (
% 0.19/0.39 difference: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_A_26_type, type, (
% 0.19/0.39 tptp_fun_A_26: $i)).
% 0.19/0.39 tff(subset_type, type, (
% 0.19/0.39 subset: ( $i * $i ) > $o)).
% 0.19/0.39 tff(partition_type, type, (
% 0.19/0.39 partition: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y_7_type, type, (
% 0.19/0.39 tptp_fun_Y_7: $i > $i)).
% 0.19/0.39 tff(tptp_fun_X_8_type, type, (
% 0.19/0.39 tptp_fun_X_8: $i > $i)).
% 0.19/0.39 tff(tptp_fun_Z_9_type, type, (
% 0.19/0.39 tptp_fun_Z_9: $i > $i)).
% 0.19/0.39 tff(tptp_fun_X_5_type, type, (
% 0.19/0.39 tptp_fun_X_5: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X_6_type, type, (
% 0.19/0.39 tptp_fun_X_6: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[X: $i, A: $i] : refl((member(X, singleton(A)) <=> (X = A)) <=> (member(X, singleton(A)) <=> (X = A)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','singleton')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![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))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (member(tptp_fun_Y_4(X!27, P!24), singleton(B!25)) <=> (tptp_fun_Y_4(X!27, P!24) = B!25)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (^[B: $i, A: $i, E: $i] : refl((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (^[B: $i, A: $i, E: $i] : trans(trans(monotonicity(rewrite((member(B, E) & (~member(B, A))) <=> (~((~member(B, E)) | member(B, A)))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))), rewrite((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))), rewrite((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![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, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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')).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.39 tff(17,plain,(
% 0.19/0.39 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~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)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~(((~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))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[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)))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![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))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[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))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![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)))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[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))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![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)))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![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)))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[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)))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![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)))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.40 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')).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.40 tff(39,plain,(
% 0.19/0.40 ![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)))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[38])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![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)))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![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)))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 28])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![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))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 23])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (((~![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, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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) | (~((~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)))))) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (tptp_fun_X_8(P!24) = tptp_fun_Y_7(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)) | (~((~![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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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) | (~((~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)))))) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 ((~((~((~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)) | (~((~![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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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) | (~((~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)))))) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (((~![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)) | (~((~![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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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) | (~((~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)))))) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (((~![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)) | (~((~![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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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) | (~((~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)))))) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 ((~![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))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~![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, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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) | (~((~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)))))) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (~((~((~partition(P!24, 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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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) | (~((~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)))))) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24)))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 43])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (((~((~partition(P!24, 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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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) | (~((~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)))))) | (~((~member(tptp_fun_X_5(A!26, P!24), P!24)) | subset(tptp_fun_X_5(A!26, P!24), A!26))) | (~((~member(tptp_fun_Z_9(P!24), tptp_fun_Y_7(P!24))) | (~member(tptp_fun_Z_9(P!24), tptp_fun_X_8(P!24))) | (~member(tptp_fun_Y_7(P!24), P!24)) | (~member(tptp_fun_X_8(P!24), P!24)) | (tptp_fun_X_8(P!24) = tptp_fun_Y_7(P!24))))))) | ((~partition(P!24, 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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 ((~partition(P!24, 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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (((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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 ((~![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((~![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,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')).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (~![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (~![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (~![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (~![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[59, 54])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (partition(P!24, A!26)),
% 0.19/0.42 inference(and_elim,[status(thm)],[61])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((~((~partition(P!24, 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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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, A!26)) | (~((~member(tptp_fun_Y_4(X, P!24), P!24)) | (~member(X, tptp_fun_Y_4(X, P!24))))))) | (~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 ((~((~partition(P!24, 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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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))))))) | (~![X: $i] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (~((~![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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![X: $i, Y: $i] : ((X = Y) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(Y, P!24)) | (~member(X, P!24)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[64, 52])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (((~![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] : ((~member(X, P!24)) | subset(X, A!26))) | (~![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))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![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))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(X!27, A!26)) | member(X!27, B!25)) <=> member(X!27, difference(A!26, B!25))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (~(((~member(X!27, A!26)) | member(X!27, B!25)) <=> member(X!27, difference(A!26, B!25)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[68, 19])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (member(X!27, difference(A!26, B!25))),
% 0.19/0.42 inference(and_elim,[status(thm)],[61])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ((((~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))) | (~member(X!27, difference(A!26, B!25)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((((~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)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (~((~member(X!27, A!26)) | member(X!27, B!25))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (((~member(X!27, A!26)) | member(X!27, B!25)) | member(X!27, A!26)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (member(X!27, A!26)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (((~![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))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~![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))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![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)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (~((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | (~member(X!27, tptp_fun_Y_4(X!27, P!24))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 75, 67])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~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))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (member(X!27, tptp_fun_Y_4(X!27, P!24))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![S: $i] : (~(member(S, difference(P!24, singleton(B!25))) & member(X!27, S)))),
% 0.19/0.42 inference(and_elim,[status(thm)],[61])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![S: $i] : ((~member(S, difference(P!24, singleton(B!25)))) | (~member(X!27, S)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~![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)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((~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)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~![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))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (((~![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)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[91, 89])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~![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))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((~![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (~member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[94, 88, 81])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((((~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))) | member(tptp_fun_Y_4(X!27, P!24), difference(P!24, singleton(B!25)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((((~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)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 ((~member(tptp_fun_Y_4(X!27, P!24), P!24)) | member(tptp_fun_Y_4(X!27, P!24), singleton(B!25))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[97, 21])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (((~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)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (member(tptp_fun_Y_4(X!27, P!24), P!24)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 79])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 ((~((~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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 ((~((~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))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (member(tptp_fun_Y_4(X!27, P!24), singleton(B!25))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[102, 98])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 ((~(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)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 ((~(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)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (tptp_fun_Y_4(X!27, P!24) = B!25),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 9])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (member(X!27, tptp_fun_Y_4(X!27, P!24)) <=> member(X!27, B!25)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (member(X!27, B!25) <=> member(X!27, tptp_fun_Y_4(X!27, P!24))),
% 0.19/0.43 inference(symmetry,[status(thm)],[107])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 ((~member(X!27, B!25)) <=> (~member(X!27, tptp_fun_Y_4(X!27, P!24)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (((~member(X!27, A!26)) | member(X!27, B!25)) | (~member(X!27, B!25))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (~member(X!27, B!25)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[110, 73])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (~member(X!27, tptp_fun_Y_4(X!27, P!24))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[111, 109])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[81, 112])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------