%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU053+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU053+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:58:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(empty_set_type, type, (
% 0.20/0.46 empty_set: $i)).
% 0.20/0.46 tff(set_intersection2_type, type, (
% 0.20/0.46 set_intersection2: ( $i * $i ) > $i)).
% 0.20/0.46 tff(singleton_type, type, (
% 0.20/0.46 singleton: $i > $i)).
% 0.20/0.46 tff(apply_type, type, (
% 0.20/0.46 apply: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_B_2_type, type, (
% 0.20/0.46 tptp_fun_B_2: $i > $i)).
% 0.20/0.46 tff(tptp_fun_A_14_type, type, (
% 0.20/0.46 tptp_fun_A_14: $i)).
% 0.20/0.46 tff(tptp_fun_C_1_type, type, (
% 0.20/0.46 tptp_fun_C_1: $i > $i)).
% 0.20/0.46 tff(in_type, type, (
% 0.20/0.46 in: ( $i * $i ) > $o)).
% 0.20/0.46 tff(relation_dom_type, type, (
% 0.20/0.46 relation_dom: $i > $i)).
% 0.20/0.46 tff(one_to_one_type, type, (
% 0.20/0.46 one_to_one: $i > $o)).
% 0.20/0.46 tff(function_type, type, (
% 0.20/0.46 function: $i > $o)).
% 0.20/0.46 tff(relation_image_type, type, (
% 0.20/0.46 relation_image: ( $i * $i ) > $i)).
% 0.20/0.46 tff(relation_type, type, (
% 0.20/0.46 relation: $i > $o)).
% 0.20/0.46 tff(disjoint_type, type, (
% 0.20/0.46 disjoint: ( $i * $i ) > $o)).
% 0.20/0.46 tff(disjoint_nonempty_type, type, (
% 0.20/0.46 disjoint_nonempty: ( $i * $i ) > $o)).
% 0.20/0.46 tff(empty_type, type, (
% 0.20/0.46 empty: $i > $o)).
% 0.20/0.46 tff(tptp_fun_B_6_type, type, (
% 0.20/0.46 tptp_fun_B_6: $i > $i)).
% 0.20/0.46 tff(element_type, type, (
% 0.20/0.46 element: ( $i * $i ) > $o)).
% 0.20/0.46 tff(powerset_type, type, (
% 0.20/0.46 powerset: $i > $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 ((singleton(apply(A!14, tptp_fun_C_1(A!14))) = empty_set) <=> (empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 0.20/0.46 inference(commutativity,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (((~one_to_one(A!14)) & (relation(A!14) & function(A!14)) & ![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(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_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 ((~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_intersection2(B, C)) = set_intersection2(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_intersection2(B, C)) = set_intersection2(relation_image(A, B), relation_image(A, C))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 ((~![A: $i] : ((relation(A) & function(A)) => (![B: $i, C: $i] : (relation_image(A, set_intersection2(B, C)) = set_intersection2(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_intersection2(B, C)) = set_intersection2(relation_image(A, B), relation_image(A, C))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(5,axiom,(~![A: $i] : ((relation(A) & function(A)) => (![B: $i, C: $i] : (relation_image(A, set_intersection2(B, C)) = set_intersection2(relation_image(A, B), relation_image(A, C))) => one_to_one(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t122_funct_1')).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_intersection2(B, C)) = set_intersection2(relation_image(A, B), relation_image(A, C)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_intersection2(B, C)) = set_intersection2(relation_image(A, B), relation_image(A, C)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_intersection2(B, C)) = set_intersection2(relation_image(A, B), relation_image(A, C)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~![B: $i, C: $i] : (relation_image(A, set_intersection2(B, C)) = set_intersection2(relation_image(A, B), relation_image(A, C)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 ((~one_to_one(A!14)) & relation(A!14) & function(A!14) & ![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (function(A!14)),
% 0.20/0.46 inference(and_elim,[status(thm)],[10])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (relation(A!14)),
% 0.20/0.46 inference(and_elim,[status(thm)],[10])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (^[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))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (^[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))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (^[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)))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (![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)))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.47 tff(23,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/sandbox2/benchmark/theBenchmark.p','d8_funct_1')).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.47 tff(26,plain,(
% 0.20/0.47 ![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)))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[25])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (![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)))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (![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)))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (((~![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)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (((~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)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 ((~((~((~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))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (((~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)))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (((~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)))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (((~![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))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (((~![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)))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[34, 29])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 ((~![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)))))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 ((~![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))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (~((~((~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)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[37, 28, 12, 11])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (((~((~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)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (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))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (~one_to_one(A!14)),
% 0.20/0.47 inference(and_elim,[status(thm)],[10])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 ((~(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))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((~(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))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (~((~(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)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (((~(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)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (apply(A!14, tptp_fun_C_1(A!14)) = apply(A!14, tptp_fun_B_2(A!14))),
% 0.20/0.47 inference(symmetry,[status(thm)],[46])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (singleton(apply(A!14, tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (singleton(apply(A!14, tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[48])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (^[A: $i] : refl((set_intersection2(A, A) = A) <=> (set_intersection2(A, A) = A))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (![A: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![A: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (![A: $i, B: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 0.20/0.47 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.47 tff(54,axiom,(![A: $i, B: $i] : (set_intersection2(A, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','idempotence_k3_xboole_0')).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![A: $i] : (set_intersection2(A, A) = A)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (![A: $i] : (set_intersection2(A, A) = A)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.20/0.47 tff(57,plain,(
% 0.20/0.47 ![A: $i] : (set_intersection2(A, A) = A)),
% 0.20/0.47 inference(skolemize,[status(sab)],[56])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (![A: $i] : (set_intersection2(A, A) = A)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 ((~![A: $i] : (set_intersection2(A, A) = A)) | (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[60, 49])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 ((set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set) <=> (singleton(apply(A!14, tptp_fun_C_1(A!14))) = empty_set)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 ((set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set) <=> (empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[62, 1])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 ((empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set)),
% 0.20/0.47 inference(symmetry,[status(thm)],[63])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (((~(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))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (in(tptp_fun_C_1(A!14), relation_dom(A!14))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[65, 44])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.48 tff(74,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/sandbox2/benchmark/theBenchmark.p','t117_funct_1')).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.48 tff(77,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[76])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (((~![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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (((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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (((~![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))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (((~![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)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 ((~![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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[85, 79, 12, 11, 66])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 (singleton(apply(A!14, tptp_fun_C_1(A!14))) = relation_image(A!14, singleton(tptp_fun_C_1(A!14)))),
% 0.20/0.48 inference(symmetry,[status(thm)],[86])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (singleton(apply(A!14, tptp_fun_B_2(A!14))) = relation_image(A!14, singleton(tptp_fun_C_1(A!14)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[49, 87])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (((~(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))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (in(tptp_fun_B_2(A!14), relation_dom(A!14))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[89, 44])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (((~![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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (((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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (((~![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))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (((~![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)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 ((~![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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[96, 79, 12, 11, 90])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (singleton(apply(A!14, tptp_fun_B_2(A!14))) = relation_image(A!14, singleton(tptp_fun_B_2(A!14)))),
% 0.20/0.48 inference(symmetry,[status(thm)],[97])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = set_intersection2(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[98, 88])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (set_intersection2(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14)))) = set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[99])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (^[B: $i, C: $i] : refl((relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C))) <=> (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C))) <=> ![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 (![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C)))),
% 0.20/0.48 inference(and_elim,[status(thm)],[10])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 (![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 ((~![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C)))) | (relation_image(A!14, set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))) = set_intersection2(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 (relation_image(A!14, set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))) = set_intersection2(relation_image(A!14, singleton(tptp_fun_B_2(A!14))), relation_image(A!14, singleton(tptp_fun_C_1(A!14))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(110,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_xboole_0')).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.48 tff(112,plain,(
% 0.20/0.48 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.20/0.48 inference(skolemize,[status(sab)],[111])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) <=> (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = empty_set))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) <=> (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = empty_set)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (((~(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)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (~(tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[116, 44])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl(((A = B) | disjoint(singleton(A), singleton(B))) <=> ((A = B) | disjoint(singleton(A), singleton(B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 (^[A: $i, B: $i] : rewrite(((~(A = B)) => disjoint(singleton(A), singleton(B))) <=> ((A = B) | disjoint(singleton(A), singleton(B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(A = B)) => disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.48 tff(123,axiom,(![A: $i, B: $i] : ((~(A = B)) => disjoint(singleton(A), singleton(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_zfmisc_1')).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.20/0.48 tff(126,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[125])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))) | ((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))))) <=> ((~![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))) | ((tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))) | (tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)) | disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[130, 127, 117])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 ((~(disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) <=> (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = empty_set))) | (~disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))) | (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = empty_set)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 ((~(disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) <=> (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = empty_set))) | (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = empty_set)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = empty_set),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[133, 115])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (relation_image(A!14, set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))) = relation_image(A!14, empty_set)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (relation_image(A!14, empty_set) = relation_image(A!14, set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[135])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (^[A: $i] : refl(((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ((~relation(A)) | (relation_image(A, empty_set) = empty_set)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[137])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (^[A: $i] : rewrite((relation(A) => (relation_image(A, empty_set) = empty_set)) <=> ((~relation(A)) | (relation_image(A, empty_set) = empty_set)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (![A: $i] : (relation(A) => (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.48 tff(142,axiom,(![A: $i] : (relation(A) => (relation_image(A, empty_set) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t149_relat_1')).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.20/0.48 tff(145,plain,(
% 0.20/0.48 ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.20/0.48 inference(skolemize,[status(sab)],[144])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 (((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | ((~relation(A!14)) | (relation_image(A!14, empty_set) = empty_set))) <=> ((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | (~relation(A!14)) | (relation_image(A!14, empty_set) = empty_set))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 ((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | ((~relation(A!14)) | (relation_image(A!14, empty_set) = empty_set))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 ((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | (~relation(A!14)) | (relation_image(A!14, empty_set) = empty_set)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 (relation_image(A!14, empty_set) = empty_set),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[149, 12, 146])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (empty_set = relation_image(A!14, empty_set)),
% 0.20/0.48 inference(symmetry,[status(thm)],[150])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[151, 136, 106, 100, 60, 49])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[152, 64])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[154, 113])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 (empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> empty(singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> empty(singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[156])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 ((~empty(singleton(apply(A!14, tptp_fun_C_1(A!14))))) <=> (~empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[157])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (^[A: $i] : refl((~empty(singleton(A))) <=> (~empty(singleton(A))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (![A: $i] : (~empty(singleton(A))) <=> ![A: $i] : (~empty(singleton(A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (![A: $i] : (~empty(singleton(A))) <=> ![A: $i] : (~empty(singleton(A)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(162,axiom,(![A: $i] : (~empty(singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_subset_1')).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (![A: $i] : (~empty(singleton(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.48 tff(164,plain,(
% 0.20/0.48 ![A: $i] : (~empty(singleton(A)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[163])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (![A: $i] : (~empty(singleton(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 ((~![A: $i] : (~empty(singleton(A)))) | (~empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 (~empty(singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (~empty(singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[167, 158])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl((empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 (![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> ![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[169])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(A)) & (~empty(B))) <=> (~(empty(B) | empty(A)))), ((~((~empty(A)) & (~empty(B)))) <=> (~(~(empty(B) | empty(A)))))), rewrite((~(~(empty(B) | empty(A)))) <=> (empty(B) | empty(A))), ((~((~empty(A)) & (~empty(B)))) <=> (empty(B) | empty(A)))), (((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> ((empty(B) | empty(A)) | (disjoint_nonempty(A, B) <=> disjoint(A, B))))), rewrite(((empty(B) | empty(A)) | (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))), (((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> ![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> ![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (^[A: $i, B: $i] : rewrite((((~empty(A)) & (~empty(B))) => (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (![A: $i, B: $i] : (((~empty(A)) & (~empty(B))) => (disjoint_nonempty(A, B) <=> disjoint(A, B))) <=> ![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[174])).
% 0.20/0.48 tff(176,axiom,(![A: $i, B: $i] : (((~empty(A)) & (~empty(B))) => (disjoint_nonempty(A, B) <=> disjoint(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r1_subset_1')).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.20/0.48 tff(179,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[178])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))))) <=> ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 ((empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))))) <=> (empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))))) <=> ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[183])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))))) <=> ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[184, 182])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[187, 181, 168])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14))) | one_to_one(A!14)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 ((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[189, 41])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (^[A: $i] : refl(((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A))))) <=> ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A))))) <=> ![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[191])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & empty(A) & function(A)) <=> (~((~empty(A)) | (~relation(A)) | (~function(A))))), ((~(relation(A) & empty(A) & function(A))) <=> (~(~((~empty(A)) | (~relation(A)) | (~function(A))))))), rewrite((~(~((~empty(A)) | (~relation(A)) | (~function(A))))) <=> ((~empty(A)) | (~relation(A)) | (~function(A)))), ((~(relation(A) & empty(A) & function(A))) <=> ((~empty(A)) | (~relation(A)) | (~function(A))))), rewrite((relation(A) & function(A) & one_to_one(A)) <=> (~((~relation(A)) | (~one_to_one(A)) | (~function(A))))), (((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A))) <=> (((~empty(A)) | (~relation(A)) | (~function(A))) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A))))))), rewrite((((~empty(A)) | (~relation(A)) | (~function(A))) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A))))) <=> ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))), (((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A))) <=> ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 (![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A))) <=> ![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[193])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A))) <=> ![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 (^[A: $i] : trans(monotonicity(rewrite(((relation(A) & empty(A)) & function(A)) <=> (relation(A) & empty(A) & function(A))), rewrite(((relation(A) & function(A)) & one_to_one(A)) <=> (relation(A) & function(A) & one_to_one(A))), ((((relation(A) & empty(A)) & function(A)) => ((relation(A) & function(A)) & one_to_one(A))) <=> ((relation(A) & empty(A) & function(A)) => (relation(A) & function(A) & one_to_one(A))))), rewrite(((relation(A) & empty(A) & function(A)) => (relation(A) & function(A) & one_to_one(A))) <=> ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))), ((((relation(A) & empty(A)) & function(A)) => ((relation(A) & function(A)) & one_to_one(A))) <=> ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (![A: $i] : (((relation(A) & empty(A)) & function(A)) => ((relation(A) & function(A)) & one_to_one(A))) <=> ![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.49 tff(198,axiom,(![A: $i] : (((relation(A) & empty(A)) & function(A)) => ((relation(A) & function(A)) & one_to_one(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc2_funct_1')).
% 0.20/0.49 tff(199,plain,
% 0.20/0.49 (![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 (![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.20/0.49 tff(201,plain,(
% 0.20/0.49 ![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[200])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 (![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.20/0.49 tff(203,plain,
% 0.20/0.49 (![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[202, 192])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 (((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | ((~function(A!14)) | (~relation(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14)))))) <=> ((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | (~function(A!14)) | (~relation(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(205,plain,
% 0.20/0.49 (((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(206,plain,
% 0.20/0.49 ((~((~relation(A!14)) | (~one_to_one(A!14)) | (~function(A!14)))) <=> (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(207,plain,
% 0.20/0.49 (((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~relation(A!14)) | (~one_to_one(A!14)) | (~function(A!14))))) <=> ((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[206])).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 (((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~relation(A!14)) | (~one_to_one(A!14)) | (~function(A!14))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[207, 205])).
% 0.20/0.49 tff(209,plain,
% 0.20/0.49 (((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | ((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~relation(A!14)) | (~one_to_one(A!14)) | (~function(A!14)))))) <=> ((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | ((~function(A!14)) | (~relation(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[208])).
% 0.20/0.49 tff(210,plain,
% 0.20/0.49 (((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | ((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~relation(A!14)) | (~one_to_one(A!14)) | (~function(A!14)))))) <=> ((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | (~function(A!14)) | (~relation(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[209, 204])).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 ((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | ((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~relation(A!14)) | (~one_to_one(A!14)) | (~function(A!14)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 ((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | (~function(A!14)) | (~relation(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~function(A!14)) | (~relation(A!14))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.49 tff(213,plain,
% 0.20/0.49 (~empty(A!14)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[212, 203, 12, 11, 190])).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 (^[A: $i] : refl((empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A)))))) <=> (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 (![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A)))))) <=> ![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[214])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (^[A: $i] : rewrite((empty(A) | (element(tptp_fun_B_6(A), powerset(A)) & (~empty(tptp_fun_B_6(A))))) <=> (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 (![A: $i] : (empty(A) | (element(tptp_fun_B_6(A), powerset(A)) & (~empty(tptp_fun_B_6(A))))) <=> ![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[216])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> ![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 (^[A: $i] : rewrite(((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 (![A: $i] : ((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> ![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[219])).
% 0.20/0.49 tff(221,axiom,(![A: $i] : ((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_subset_1')).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.20/0.49 tff(224,plain,(
% 0.20/0.49 ![A: $i] : (empty(A) | (element(tptp_fun_B_6(A), powerset(A)) & (~empty(tptp_fun_B_6(A)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[223])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[224, 217])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 (![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[225, 215])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | (empty(A!14) | (~(empty(tptp_fun_B_6(A!14)) | (~element(tptp_fun_B_6(A!14), powerset(A!14))))))) <=> ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | empty(A!14) | (~(empty(tptp_fun_B_6(A!14)) | (~element(tptp_fun_B_6(A!14), powerset(A!14))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | (empty(A!14) | (~(empty(tptp_fun_B_6(A!14)) | (~element(tptp_fun_B_6(A!14), powerset(A!14))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | empty(A!14) | (~(empty(tptp_fun_B_6(A!14)) | (~element(tptp_fun_B_6(A!14), powerset(A!14)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (~(empty(tptp_fun_B_6(A!14)) | (~element(tptp_fun_B_6(A!14), powerset(A!14))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[229, 226, 213])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 ((empty(tptp_fun_B_6(A!14)) | (~element(tptp_fun_B_6(A!14), powerset(A!14)))) | (~empty(tptp_fun_B_6(A!14)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 (~empty(tptp_fun_B_6(A!14))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 (((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | (empty(tptp_fun_B_6(A!14)) | (~(empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~element(tptp_fun_B_6(tptp_fun_B_6(A!14)), powerset(tptp_fun_B_6(A!14)))))))) <=> ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | empty(tptp_fun_B_6(A!14)) | (~(empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~element(tptp_fun_B_6(tptp_fun_B_6(A!14)), powerset(tptp_fun_B_6(A!14)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | (empty(tptp_fun_B_6(A!14)) | (~(empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~element(tptp_fun_B_6(tptp_fun_B_6(A!14)), powerset(tptp_fun_B_6(A!14)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | empty(tptp_fun_B_6(A!14)) | (~(empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~element(tptp_fun_B_6(tptp_fun_B_6(A!14)), powerset(tptp_fun_B_6(A!14))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 (~(empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~element(tptp_fun_B_6(tptp_fun_B_6(A!14)), powerset(tptp_fun_B_6(A!14)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[235, 226, 232])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 ((empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~element(tptp_fun_B_6(tptp_fun_B_6(A!14)), powerset(tptp_fun_B_6(A!14))))) | (~empty(tptp_fun_B_6(tptp_fun_B_6(A!14))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 (~empty(tptp_fun_B_6(tptp_fun_B_6(A!14)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 (((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | (empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~(empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~element(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14))), powerset(tptp_fun_B_6(tptp_fun_B_6(A!14))))))))) <=> ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~(empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~element(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14))), powerset(tptp_fun_B_6(tptp_fun_B_6(A!14))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | (empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~(empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~element(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14))), powerset(tptp_fun_B_6(tptp_fun_B_6(A!14))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))) | empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~(empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~element(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14))), powerset(tptp_fun_B_6(tptp_fun_B_6(A!14)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (~(empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~element(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14))), powerset(tptp_fun_B_6(tptp_fun_B_6(A!14))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[241, 226, 238])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 ((empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~element(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14))), powerset(tptp_fun_B_6(tptp_fun_B_6(A!14)))))) | (~empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 (~empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.20/0.49 tff(245,plain,
% 0.20/0.49 (^[A: $i, B: $i] : refl((empty(B) | (~disjoint_nonempty(A, A)) | empty(A)) <=> (empty(B) | (~disjoint_nonempty(A, A)) | empty(A)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 (![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A)) <=> ![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[245])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(A)) & (~empty(B))) <=> (~(empty(B) | empty(A)))), ((~((~empty(A)) & (~empty(B)))) <=> (~(~(empty(B) | empty(A)))))), rewrite((~(~(empty(B) | empty(A)))) <=> (empty(B) | empty(A))), ((~((~empty(A)) & (~empty(B)))) <=> (empty(B) | empty(A)))), (((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B))))) <=> ((~disjoint_nonempty(A, A)) | (empty(B) | empty(A))))), rewrite(((~disjoint_nonempty(A, A)) | (empty(B) | empty(A))) <=> (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))), (((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B))))) <=> (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B))))) <=> ![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[247])).
% 0.20/0.49 tff(249,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B))))) <=> ![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(250,plain,
% 0.20/0.49 (^[A: $i, B: $i] : rewrite((((~empty(A)) & (~empty(B))) => (~disjoint_nonempty(A, A))) <=> ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(251,plain,
% 0.20/0.49 (![A: $i, B: $i] : (((~empty(A)) & (~empty(B))) => (~disjoint_nonempty(A, A))) <=> ![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[250])).
% 0.20/0.49 tff(252,axiom,(![A: $i, B: $i] : (((~empty(A)) & (~empty(B))) => (~disjoint_nonempty(A, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','irreflexivity_r1_subset_1')).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.20/0.49 tff(255,plain,(
% 0.20/0.49 ![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[254])).
% 0.20/0.49 tff(256,plain,
% 0.20/0.49 (![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 (![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[256, 246])).
% 0.20/0.49 tff(258,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | (empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))))) <=> ((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(259,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | (empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(260,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | empty(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))) | empty(singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.49 tff(261,plain,
% 0.20/0.49 (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[260, 257, 244, 168])).
% 0.20/0.49 tff(262,plain,
% 0.20/0.49 ((~(disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))))) | disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (~disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(263,plain,
% 0.20/0.49 ((~(disjoint_nonempty(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))))) | (~disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.20/0.49 tff(264,plain,
% 0.20/0.49 (~disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[263, 188])).
% 0.20/0.49 tff(265,plain,
% 0.20/0.49 ((~(disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) <=> (set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set))) | disjoint(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) | (~(set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(266,plain,
% 0.20/0.49 (~(set_intersection2(singleton(apply(A!14, tptp_fun_B_2(A!14))), singleton(apply(A!14, tptp_fun_B_2(A!14)))) = empty_set)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[265, 264, 155])).
% 0.20/0.49 tff(267,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[266, 153])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------