%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU055+1 : TPTP v9.0.0. Released v3.2.0.
% 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 05:26:50 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
% 0.03/0.12 % Problem : SEU055+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:00:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(singleton_type, type, (
% 0.19/0.39 singleton: $i > $i)).
% 0.19/0.39 tff(apply_type, type, (
% 0.19/0.39 apply: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C_1_type, type, (
% 0.19/0.39 tptp_fun_C_1: $i > $i)).
% 0.19/0.39 tff(tptp_fun_A_14_type, type, (
% 0.19/0.39 tptp_fun_A_14: $i)).
% 0.19/0.39 tff(set_difference_type, type, (
% 0.19/0.39 set_difference: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_B_2_type, type, (
% 0.19/0.39 tptp_fun_B_2: $i > $i)).
% 0.19/0.39 tff(in_type, type, (
% 0.19/0.39 in: ( $i * $i ) > $o)).
% 0.19/0.39 tff(relation_dom_type, type, (
% 0.19/0.39 relation_dom: $i > $i)).
% 0.19/0.39 tff(one_to_one_type, type, (
% 0.19/0.39 one_to_one: $i > $o)).
% 0.19/0.39 tff(function_type, type, (
% 0.19/0.39 function: $i > $o)).
% 0.19/0.39 tff(relation_image_type, type, (
% 0.19/0.39 relation_image: ( $i * $i ) > $i)).
% 0.19/0.39 tff(relation_type, type, (
% 0.19/0.39 relation: $i > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (((~one_to_one(A!14)) & (relation(A!14) & function(A!14)) & ![B: $i, C: $i] : (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C)))) <=> ((~one_to_one(A!14)) & relation(A!14) & function(A!14) & ![B: $i, C: $i] : (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C)))))) <=> (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((~![A: $i] : ((relation(A) & function(A)) => (![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C))) => one_to_one(A)))) <=> (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C))) => one_to_one(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t124_funct_1')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_difference(B, C)) = set_difference(relation_image(A, B), relation_image(A, C)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ((~one_to_one(A!14)) & relation(A!14) & function(A!14) & ![B: $i, C: $i] : (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (function(A!14)),
% 0.19/0.39 inference(and_elim,[status(thm)],[9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (relation(A!14)),
% 0.19/0.39 inference(and_elim,[status(thm)],[9])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), trans(monotonicity(rewrite(((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) <=> ((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))), rewrite((one_to_one(A) | (~((~(in(tptp_fun_B_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))) <=> (one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)))))) <=> (((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))), rewrite((((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))))) <=> (((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))) <=> (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))))), rewrite(((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.39 tff(22,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_funct_1')).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.39 tff(25,plain,(
% 0.19/0.39 ![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))))))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))))))))) <=> (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14))))))))))) <=> ((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14))))))))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[33, 28])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[36, 27, 11, 10])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!14))) | (~in(C, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))))))) | (one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~one_to_one(A!14)),
% 0.19/0.40 inference(and_elim,[status(thm)],[9])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))) | one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))))) | (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (~((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))) | (apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (apply(A!14, tptp_fun_C_1(A!14)) = apply(A!14, tptp_fun_B_2(A!14))),
% 0.19/0.40 inference(symmetry,[status(thm)],[45])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (singleton(apply(A!14, tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (singleton(apply(A!14, tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))) | in(tptp_fun_B_2(A!14), relation_dom(A!14))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (in(tptp_fun_B_2(A!14), relation_dom(A!14))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 43])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl(((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B))) <=> ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B))) <=> ![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), (((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B)))) <=> ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | ((~relation(B)) | (~function(B))) | (~in(A, relation_dom(B)))))), rewrite(((relation_image(B, singleton(A)) = singleton(apply(B, A))) | ((~relation(B)) | (~function(B))) | (~in(A, relation_dom(B)))) <=> ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))), (((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B)))) <=> ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B)))) <=> ![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B)))) <=> ![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (relation_image(B, singleton(A)) = singleton(apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (relation_image(B, singleton(A)) = singleton(apply(B, A))))), (((relation(B) & function(B)) => (in(A, relation_dom(B)) => (relation_image(B, singleton(A)) = singleton(apply(B, A))))) <=> ((relation(B) & function(B)) => ((~in(A, relation_dom(B))) | (relation_image(B, singleton(A)) = singleton(apply(B, A))))))), rewrite(((relation(B) & function(B)) => ((~in(A, relation_dom(B))) | (relation_image(B, singleton(A)) = singleton(apply(B, A))))) <=> ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))), (((relation(B) & function(B)) => (in(A, relation_dom(B)) => (relation_image(B, singleton(A)) = singleton(apply(B, A))))) <=> ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((relation(B) & function(B)) => (in(A, relation_dom(B)) => (relation_image(B, singleton(A)) = singleton(apply(B, A))))) <=> ![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.41 tff(58,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => (in(A, relation_dom(B)) => (relation_image(B, singleton(A)) = singleton(apply(B, A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t117_funct_1')).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.41 tff(61,plain,(
% 0.19/0.41 ![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))))) <=> ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (((relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~relation(A!14)) | (~function(A!14))) <=> ((~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~relation(A!14)) | (~function(A!14)))) <=> ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~relation(A!14)) | (~function(A!14)))) <=> ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[66, 64])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~relation(A!14)) | (~function(A!14)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[69, 63, 11, 10, 50])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A)))) <=> (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A)))) <=> ![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A)))) <=> ![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(rewrite(((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B))) <=> (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))), rewrite((~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A)))) <=> (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))), (((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B))) <=> (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B))) <=> ![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.41 tff(76,axiom,(![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_zfmisc_1')).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.41 tff(79,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[78])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) <=> (set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = singleton(tptp_fun_B_2(A!14)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (~((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) <=> (set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = singleton(tptp_fun_B_2(A!14))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))) | (~(tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (~(tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 43])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) <=> (set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = singleton(tptp_fun_B_2(A!14)))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | (set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = singleton(tptp_fun_B_2(A!14)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) <=> (set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = singleton(tptp_fun_B_2(A!14)))) | (set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = singleton(tptp_fun_B_2(A!14)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = singleton(tptp_fun_B_2(A!14))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[86, 82])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (singleton(tptp_fun_B_2(A!14)) = set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[87])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = relation_image(A!14, set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (relation_image(A!14, set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))) = relation_image(A!14, singleton(tptp_fun_B_2(A!14)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (^[B: $i, C: $i] : refl((relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C))) <=> (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (![B: $i, C: $i] : (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C))) <=> ![B: $i, C: $i] : (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (![B: $i, C: $i] : (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C)))),
% 0.19/0.41 inference(and_elim,[status(thm)],[9])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (![B: $i, C: $i] : (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~![B: $i, C: $i] : (relation_image(A!14, set_difference(B, C)) = set_difference(relation_image(A!14, B), relation_image(A!14, C)))) | (relation_image(A!14, set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))) = set_difference(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (relation_image(A!14, set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))) = set_difference(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (set_difference(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14)))) = relation_image(A!14, set_difference(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[96])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (((~(apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))) | in(tptp_fun_C_1(A!14), relation_dom(A!14))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (in(tptp_fun_C_1(A!14), relation_dom(A!14))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 43])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))) <=> ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (((relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~relation(A!14)) | (~function(A!14))) <=> ((~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~relation(A!14)) | (~function(A!14)))) <=> ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~relation(A!14)) | (~function(A!14)))) <=> ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~relation(A!14)) | (~function(A!14)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (~function(A!14)) | (~relation(A!14)) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 63, 11, 10, 99])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[70, 48])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (set_difference(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14)))) = set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[107, 106])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = set_difference(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14))))),
% 0.19/0.42 inference(symmetry,[status(thm)],[108])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[109, 97, 90, 70, 48])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~(set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))) <=> ((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~(set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 ((~((apply(A!14, tptp_fun_C_1(A!14)) = apply(A!14, tptp_fun_C_1(A!14))) <=> (set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))) <=> (~(set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~((apply(A!14, tptp_fun_C_1(A!14)) = apply(A!14, tptp_fun_C_1(A!14))) <=> (set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))))) <=> ((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~(set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~((apply(A!14, tptp_fun_C_1(A!14)) = apply(A!14, tptp_fun_C_1(A!14))) <=> (set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))))) <=> ((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~(set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~((apply(A!14, tptp_fun_C_1(A!14)) = apply(A!14, tptp_fun_C_1(A!14))) <=> (set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (~((A = B) <=> (set_difference(singleton(A), singleton(B)) = singleton(A))))) | (~(set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (~(set_difference(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[116, 80])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[117, 110])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------