TSTP Solution File: SEU053+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU053+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:24 EDT 2022
% Result : Theorem 1.44s 1.16s
% Output : Proof 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SEU053+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.36 % Computer : n023.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat Sep 3 09:29:48 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.16/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.37 Usage: tptp [options] [-file:]file
% 0.16/0.37 -h, -? prints this message.
% 0.16/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.37 -m, -model generate model.
% 0.16/0.37 -p, -proof generate proof.
% 0.16/0.37 -c, -core generate unsat core of named formulas.
% 0.16/0.37 -st, -statistics display statistics.
% 0.16/0.37 -t:timeout set timeout (in second).
% 0.16/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.37 -<param>:<value> configuration parameter and value.
% 0.16/0.37 -o:<output-file> file to place output in.
% 1.44/1.16 % SZS status Theorem
% 1.44/1.16 % SZS output start Proof
% 1.44/1.16 tff(singleton_type, type, (
% 1.44/1.16 singleton: $i > $i)).
% 1.44/1.16 tff(apply_type, type, (
% 1.44/1.16 apply: ( $i * $i ) > $i)).
% 1.44/1.16 tff(tptp_fun_C_1_type, type, (
% 1.44/1.16 tptp_fun_C_1: $i > $i)).
% 1.44/1.16 tff(tptp_fun_A_14_type, type, (
% 1.44/1.16 tptp_fun_A_14: $i)).
% 1.44/1.16 tff(empty_set_type, type, (
% 1.44/1.16 empty_set: $i)).
% 1.44/1.16 tff(set_intersection2_type, type, (
% 1.44/1.16 set_intersection2: ( $i * $i ) > $i)).
% 1.44/1.16 tff(relation_image_type, type, (
% 1.44/1.16 relation_image: ( $i * $i ) > $i)).
% 1.44/1.16 tff(tptp_fun_B_2_type, type, (
% 1.44/1.16 tptp_fun_B_2: $i > $i)).
% 1.44/1.16 tff(function_type, type, (
% 1.44/1.16 function: $i > $o)).
% 1.44/1.16 tff(relation_type, type, (
% 1.44/1.16 relation: $i > $o)).
% 1.44/1.16 tff(one_to_one_type, type, (
% 1.44/1.16 one_to_one: $i > $o)).
% 1.44/1.16 tff(in_type, type, (
% 1.44/1.16 in: ( $i * $i ) > $o)).
% 1.44/1.16 tff(relation_dom_type, type, (
% 1.44/1.16 relation_dom: $i > $i)).
% 1.44/1.16 tff(disjoint_type, type, (
% 1.44/1.16 disjoint: ( $i * $i ) > $o)).
% 1.44/1.16 tff(disjoint_nonempty_type, type, (
% 1.44/1.16 disjoint_nonempty: ( $i * $i ) > $o)).
% 1.44/1.16 tff(empty_type, type, (
% 1.44/1.16 empty: $i > $o)).
% 1.44/1.16 tff(tptp_fun_B_6_type, type, (
% 1.44/1.16 tptp_fun_B_6: $i > $i)).
% 1.44/1.16 tff(element_type, type, (
% 1.44/1.16 element: ( $i * $i ) > $o)).
% 1.44/1.16 tff(powerset_type, type, (
% 1.44/1.16 powerset: $i > $i)).
% 1.44/1.16 tff(1,plain,
% 1.44/1.16 (^[A: $i] : refl((set_intersection2(A, A) = A) <=> (set_intersection2(A, A) = A))),
% 1.44/1.16 inference(bind,[status(th)],[])).
% 1.44/1.16 tff(2,plain,
% 1.44/1.16 (![A: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 1.44/1.16 inference(quant_intro,[status(thm)],[1])).
% 1.44/1.16 tff(3,plain,
% 1.44/1.16 (![A: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(4,plain,
% 1.44/1.16 (![A: $i, B: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 1.44/1.16 inference(elim_unused_vars,[status(thm)],[])).
% 1.44/1.16 tff(5,axiom,(![A: $i, B: $i] : (set_intersection2(A, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','idempotence_k3_xboole_0')).
% 1.44/1.16 tff(6,plain,
% 1.44/1.16 (![A: $i] : (set_intersection2(A, A) = A)),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.44/1.16 tff(7,plain,
% 1.44/1.16 (![A: $i] : (set_intersection2(A, A) = A)),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[6, 3])).
% 1.44/1.16 tff(8,plain,(
% 1.44/1.16 ![A: $i] : (set_intersection2(A, A) = A)),
% 1.44/1.16 inference(skolemize,[status(sab)],[7])).
% 1.44/1.16 tff(9,plain,
% 1.44/1.16 (![A: $i] : (set_intersection2(A, A) = A)),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[8, 2])).
% 1.44/1.16 tff(10,plain,
% 1.44/1.16 ((~![A: $i] : (set_intersection2(A, A) = A)) | (set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.16 inference(quant_inst,[status(thm)],[])).
% 1.44/1.16 tff(11,plain,
% 1.44/1.16 (set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 1.44/1.16 inference(unit_resolution,[status(thm)],[10, 9])).
% 1.44/1.16 tff(12,plain,
% 1.44/1.16 (^[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))))),
% 1.44/1.16 inference(bind,[status(th)],[])).
% 1.44/1.16 tff(13,plain,
% 1.44/1.16 (![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)))),
% 1.44/1.16 inference(quant_intro,[status(thm)],[12])).
% 1.44/1.16 tff(14,plain,
% 1.44/1.16 (((~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))))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(15,plain,
% 1.44/1.16 ((~(~(relation(A!14) & function(A!14)))) <=> (relation(A!14) & function(A!14))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(16,plain,
% 1.44/1.16 (((~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))))),
% 1.44/1.16 inference(monotonicity,[status(thm)],[15])).
% 1.44/1.16 tff(17,plain,
% 1.44/1.16 (((~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))))),
% 1.44/1.16 inference(transitivity,[status(thm)],[16, 14])).
% 1.44/1.16 tff(18,plain,
% 1.44/1.16 ((~![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))))))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(19,plain,
% 1.44/1.16 ((~![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))))))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(20,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')).
% 1.44/1.16 tff(21,plain,
% 1.44/1.16 (~![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)))))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.44/1.16 tff(22,plain,
% 1.44/1.16 (~![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)))))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[21, 18])).
% 1.44/1.16 tff(23,plain,
% 1.44/1.16 (~![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)))))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[22, 18])).
% 1.44/1.16 tff(24,plain,
% 1.44/1.16 (~![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)))))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[23, 18])).
% 1.44/1.16 tff(25,plain,
% 1.44/1.16 (~![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)))))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[24, 18])).
% 1.44/1.16 tff(26,plain,
% 1.44/1.16 (~![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)))))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[25, 18])).
% 1.44/1.16 tff(27,plain,
% 1.44/1.16 (~![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)))))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[26, 18])).
% 1.44/1.16 tff(28,plain,
% 1.44/1.16 ((~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)))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[27, 17])).
% 1.44/1.16 tff(29,plain,
% 1.44/1.16 (![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C)))),
% 1.44/1.16 inference(and_elim,[status(thm)],[28])).
% 1.44/1.16 tff(30,plain,
% 1.44/1.16 (![B: $i, C: $i] : (relation_image(A!14, set_intersection2(B, C)) = set_intersection2(relation_image(A!14, B), relation_image(A!14, C)))),
% 1.44/1.16 inference(modus_ponens,[status(thm)],[29, 13])).
% 1.44/1.16 tff(31,plain,
% 1.44/1.16 ((~![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_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))) = set_intersection2(relation_image(A!14, singleton(tptp_fun_C_1(A!14))), relation_image(A!14, singleton(tptp_fun_B_2(A!14)))))),
% 1.44/1.16 inference(quant_inst,[status(thm)],[])).
% 1.44/1.16 tff(32,plain,
% 1.44/1.16 (relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))) = set_intersection2(relation_image(A!14, singleton(tptp_fun_C_1(A!14))), relation_image(A!14, singleton(tptp_fun_B_2(A!14))))),
% 1.44/1.16 inference(unit_resolution,[status(thm)],[31, 30])).
% 1.44/1.16 tff(33,plain,
% 1.44/1.16 (set_intersection2(relation_image(A!14, singleton(tptp_fun_C_1(A!14))), relation_image(A!14, singleton(tptp_fun_B_2(A!14)))) = relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))),
% 1.44/1.16 inference(symmetry,[status(thm)],[32])).
% 1.44/1.16 tff(34,plain,
% 1.44/1.16 (function(A!14)),
% 1.44/1.16 inference(and_elim,[status(thm)],[28])).
% 1.44/1.16 tff(35,plain,
% 1.44/1.16 (relation(A!14)),
% 1.44/1.16 inference(and_elim,[status(thm)],[28])).
% 1.44/1.16 tff(36,plain,
% 1.44/1.16 (^[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))))))))))))),
% 1.44/1.16 inference(bind,[status(th)],[])).
% 1.44/1.16 tff(37,plain,
% 1.44/1.16 (![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)))))))))))),
% 1.44/1.16 inference(quant_intro,[status(thm)],[36])).
% 1.44/1.16 tff(38,plain,
% 1.44/1.16 (^[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))))))))))))),
% 1.44/1.16 inference(bind,[status(th)],[])).
% 1.44/1.16 tff(39,plain,
% 1.44/1.16 (![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)))))))))))),
% 1.44/1.16 inference(quant_intro,[status(thm)],[38])).
% 1.44/1.16 tff(40,plain,
% 1.44/1.16 (![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)))))))))))),
% 1.44/1.16 inference(transitivity,[status(thm)],[39, 37])).
% 1.44/1.16 tff(41,plain,
% 1.44/1.16 (^[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)))))))))))))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(42,plain,
% 1.44/1.17 (![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)))))))))))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[41])).
% 1.44/1.17 tff(43,plain,
% 1.44/1.17 (![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))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(44,plain,
% 1.44/1.17 (^[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))))))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(45,plain,
% 1.44/1.17 (![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))))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[44])).
% 1.44/1.17 tff(46,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')).
% 1.44/1.17 tff(47,plain,
% 1.44/1.17 (![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))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.44/1.17 tff(48,plain,
% 1.44/1.17 (![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))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[47, 43])).
% 1.44/1.17 tff(49,plain,(
% 1.44/1.17 ![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)))))))),
% 1.44/1.17 inference(skolemize,[status(sab)],[48])).
% 1.44/1.17 tff(50,plain,
% 1.44/1.17 (![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)))))))))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[49, 42])).
% 1.44/1.17 tff(51,plain,
% 1.44/1.17 (![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)))))))))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[50, 40])).
% 1.44/1.17 tff(52,plain,
% 1.44/1.17 (((~![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)))))))))))) | (~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)))))))))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(53,plain,
% 1.44/1.17 ((~![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)))))))))))),
% 1.44/1.17 inference(quant_inst,[status(thm)],[])).
% 1.44/1.17 tff(54,plain,
% 1.44/1.17 ((~![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))))))))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.44/1.17 tff(55,plain,
% 1.44/1.17 (~((~((~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)))))))))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[54, 51, 35, 34])).
% 1.44/1.17 tff(56,plain,
% 1.44/1.17 (((~((~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) | (~((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)))))))),
% 1.44/1.17 inference(tautology,[status(thm)],[])).
% 1.44/1.17 tff(57,plain,
% 1.44/1.17 (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))))))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[56, 55])).
% 1.44/1.17 tff(58,plain,
% 1.44/1.17 (~one_to_one(A!14)),
% 1.44/1.17 inference(and_elim,[status(thm)],[28])).
% 1.44/1.17 tff(59,plain,
% 1.44/1.17 ((~(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) | (~((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))))))),
% 1.44/1.17 inference(tautology,[status(thm)],[])).
% 1.44/1.17 tff(60,plain,
% 1.44/1.17 ((~(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)))))))) | (~((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))))))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[59, 58])).
% 1.44/1.17 tff(61,plain,
% 1.44/1.17 (~((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)))))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[60, 57])).
% 1.44/1.17 tff(62,plain,
% 1.44/1.17 (((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))))) | (apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14)))),
% 1.44/1.17 inference(tautology,[status(thm)],[])).
% 1.44/1.17 tff(63,plain,
% 1.44/1.17 (apply(A!14, tptp_fun_B_2(A!14)) = apply(A!14, tptp_fun_C_1(A!14))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[62, 61])).
% 1.44/1.17 tff(64,plain,
% 1.44/1.17 (singleton(apply(A!14, tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 1.44/1.17 inference(monotonicity,[status(thm)],[63])).
% 1.44/1.17 tff(65,plain,
% 1.44/1.17 (((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))))) | in(tptp_fun_B_2(A!14), relation_dom(A!14))),
% 1.44/1.17 inference(tautology,[status(thm)],[])).
% 1.44/1.17 tff(66,plain,
% 1.44/1.17 (in(tptp_fun_B_2(A!14), relation_dom(A!14))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[65, 61])).
% 1.44/1.17 tff(67,plain,
% 1.44/1.17 (^[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))))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(68,plain,
% 1.44/1.17 (![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)))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[67])).
% 1.44/1.17 tff(69,plain,
% 1.44/1.17 (^[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)))))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(70,plain,
% 1.44/1.17 (![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)))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[69])).
% 1.44/1.17 tff(71,plain,
% 1.44/1.17 (![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))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(72,plain,
% 1.44/1.17 (^[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))))))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(73,plain,
% 1.44/1.17 (![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))))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[72])).
% 1.44/1.17 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')).
% 1.44/1.17 tff(75,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.44/1.17 tff(76,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.44/1.17 tff(77,plain,(
% 1.44/1.17 ![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~(relation(B) & function(B))) | (~in(A, relation_dom(B))))),
% 1.44/1.17 inference(skolemize,[status(sab)],[76])).
% 1.44/1.17 tff(78,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.44/1.17 tff(79,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[78, 68])).
% 1.44/1.17 tff(80,plain,
% 1.44/1.17 (((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(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)))) | (~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(81,plain,
% 1.44/1.17 (((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))) <=> ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(82,plain,
% 1.44/1.17 (((~![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)))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14))))))),
% 1.44/1.17 inference(monotonicity,[status(thm)],[81])).
% 1.44/1.17 tff(83,plain,
% 1.44/1.17 (((~![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)))) | (~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))))),
% 1.44/1.17 inference(transitivity,[status(thm)],[82, 80])).
% 1.44/1.17 tff(84,plain,
% 1.44/1.17 ((~![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)))),
% 1.44/1.17 inference(quant_inst,[status(thm)],[])).
% 1.44/1.17 tff(85,plain,
% 1.44/1.17 ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | (~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_B_2(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.44/1.17 tff(86,plain,
% 1.44/1.17 (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_B_2(A!14)))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[85, 79, 35, 34, 66])).
% 1.44/1.17 tff(87,plain,
% 1.44/1.17 (relation_image(A!14, singleton(tptp_fun_B_2(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 1.44/1.17 inference(transitivity,[status(thm)],[86, 64])).
% 1.44/1.17 tff(88,plain,
% 1.44/1.17 (((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))))) | in(tptp_fun_C_1(A!14), relation_dom(A!14))),
% 1.44/1.17 inference(tautology,[status(thm)],[])).
% 1.44/1.17 tff(89,plain,
% 1.44/1.17 (in(tptp_fun_C_1(A!14), relation_dom(A!14))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[88, 61])).
% 1.44/1.17 tff(90,plain,
% 1.44/1.17 (((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_C_1(A!14), relation_dom(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)))) | (~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(91,plain,
% 1.44/1.17 (((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))) <=> ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(92,plain,
% 1.44/1.17 (((~![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)))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 1.44/1.17 inference(monotonicity,[status(thm)],[91])).
% 1.44/1.17 tff(93,plain,
% 1.44/1.17 (((~![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)))) | (~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.17 inference(transitivity,[status(thm)],[92, 90])).
% 1.44/1.17 tff(94,plain,
% 1.44/1.17 ((~![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)))),
% 1.44/1.17 inference(quant_inst,[status(thm)],[])).
% 1.44/1.17 tff(95,plain,
% 1.44/1.17 ((~![A: $i, B: $i] : ((relation_image(B, singleton(A)) = singleton(apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(B)) | (~function(B)))) | (~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_C_1(A!14), relation_dom(A!14))) | (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.44/1.17 tff(96,plain,
% 1.44/1.17 (relation_image(A!14, singleton(tptp_fun_C_1(A!14))) = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[95, 79, 35, 34, 89])).
% 1.44/1.17 tff(97,plain,
% 1.44/1.17 (set_intersection2(relation_image(A!14, singleton(tptp_fun_C_1(A!14))), relation_image(A!14, singleton(tptp_fun_B_2(A!14)))) = set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.17 inference(monotonicity,[status(thm)],[96, 87])).
% 1.44/1.17 tff(98,plain,
% 1.44/1.17 (set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = set_intersection2(relation_image(A!14, singleton(tptp_fun_C_1(A!14))), relation_image(A!14, singleton(tptp_fun_B_2(A!14))))),
% 1.44/1.17 inference(symmetry,[status(thm)],[97])).
% 1.44/1.17 tff(99,plain,
% 1.44/1.17 (singleton(apply(A!14, tptp_fun_C_1(A!14))) = set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.17 inference(symmetry,[status(thm)],[11])).
% 1.44/1.17 tff(100,plain,
% 1.44/1.17 (singleton(apply(A!14, tptp_fun_C_1(A!14))) = relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))),
% 1.44/1.17 inference(transitivity,[status(thm)],[99, 98, 33])).
% 1.44/1.17 tff(101,plain,
% 1.44/1.17 (set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = set_intersection2(relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))), relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))))),
% 1.44/1.17 inference(monotonicity,[status(thm)],[100, 100])).
% 1.44/1.17 tff(102,plain,
% 1.44/1.17 (set_intersection2(relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))), relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))) = set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.17 inference(symmetry,[status(thm)],[101])).
% 1.44/1.17 tff(103,plain,
% 1.44/1.17 ((~![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(set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))), set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))) = set_intersection2(relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))), relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))))),
% 1.44/1.17 inference(quant_inst,[status(thm)],[])).
% 1.44/1.17 tff(104,plain,
% 1.44/1.17 (relation_image(A!14, set_intersection2(set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))), set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))) = set_intersection2(relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))), relation_image(A!14, set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[103, 30])).
% 1.44/1.17 tff(105,plain,
% 1.44/1.17 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(106,plain,
% 1.44/1.17 (![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))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[105])).
% 1.44/1.17 tff(107,plain,
% 1.44/1.17 (![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))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(108,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_xboole_0')).
% 1.44/1.17 tff(109,plain,
% 1.44/1.17 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.44/1.17 tff(110,plain,(
% 1.44/1.17 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 1.44/1.17 inference(skolemize,[status(sab)],[109])).
% 1.44/1.17 tff(111,plain,
% 1.44/1.17 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[110, 106])).
% 1.44/1.17 tff(112,plain,
% 1.44/1.17 ((~![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))),
% 1.44/1.17 inference(quant_inst,[status(thm)],[])).
% 1.44/1.17 tff(113,plain,
% 1.44/1.17 (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)),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[112, 111])).
% 1.44/1.17 tff(114,plain,
% 1.44/1.17 (((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))))) | (~(tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14)))),
% 1.44/1.17 inference(tautology,[status(thm)],[])).
% 1.44/1.17 tff(115,plain,
% 1.44/1.17 (~(tptp_fun_B_2(A!14) = tptp_fun_C_1(A!14))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[114, 61])).
% 1.44/1.17 tff(116,plain,
% 1.44/1.17 (^[A: $i, B: $i] : refl(((A = B) | disjoint(singleton(A), singleton(B))) <=> ((A = B) | disjoint(singleton(A), singleton(B))))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(117,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[116])).
% 1.44/1.17 tff(118,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(119,plain,
% 1.44/1.17 (^[A: $i, B: $i] : rewrite(((~(A = B)) => disjoint(singleton(A), singleton(B))) <=> ((A = B) | disjoint(singleton(A), singleton(B))))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(120,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((~(A = B)) => disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[119])).
% 1.44/1.17 tff(121,axiom,(![A: $i, B: $i] : ((~(A = B)) => disjoint(singleton(A), singleton(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_zfmisc_1')).
% 1.44/1.17 tff(122,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.44/1.17 tff(123,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.44/1.17 tff(124,plain,(
% 1.44/1.17 ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 1.44/1.17 inference(skolemize,[status(sab)],[123])).
% 1.44/1.17 tff(125,plain,
% 1.44/1.17 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[124, 117])).
% 1.44/1.17 tff(126,plain,
% 1.44/1.17 (((~![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))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(127,plain,
% 1.44/1.17 ((~![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))))),
% 1.44/1.17 inference(quant_inst,[status(thm)],[])).
% 1.44/1.17 tff(128,plain,
% 1.44/1.17 ((~![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)))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.44/1.17 tff(129,plain,
% 1.44/1.17 (disjoint(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[128, 125, 115])).
% 1.44/1.17 tff(130,plain,
% 1.44/1.17 ((~(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)),
% 1.44/1.17 inference(tautology,[status(thm)],[])).
% 1.44/1.17 tff(131,plain,
% 1.44/1.17 (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = empty_set),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[130, 129, 113])).
% 1.44/1.17 tff(132,plain,
% 1.44/1.17 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 1.44/1.17 inference(bind,[status(th)],[])).
% 1.44/1.17 tff(133,plain,
% 1.44/1.17 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 1.44/1.17 inference(quant_intro,[status(thm)],[132])).
% 1.44/1.17 tff(134,plain,
% 1.44/1.17 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(135,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 1.44/1.17 tff(136,plain,
% 1.44/1.17 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.44/1.17 tff(137,plain,(
% 1.44/1.17 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 1.44/1.17 inference(skolemize,[status(sab)],[136])).
% 1.44/1.17 tff(138,plain,
% 1.44/1.17 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 1.44/1.17 inference(modus_ponens,[status(thm)],[137, 133])).
% 1.44/1.17 tff(139,plain,
% 1.44/1.17 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))),
% 1.44/1.17 inference(quant_inst,[status(thm)],[])).
% 1.44/1.17 tff(140,plain,
% 1.44/1.17 (set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14))) = set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))),
% 1.44/1.17 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.44/1.17 tff(141,plain,
% 1.44/1.17 (set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))) = set_intersection2(singleton(tptp_fun_B_2(A!14)), singleton(tptp_fun_C_1(A!14)))),
% 1.44/1.17 inference(symmetry,[status(thm)],[140])).
% 1.44/1.17 tff(142,plain,
% 1.44/1.17 ((~![A: $i] : (set_intersection2(A, A) = A)) | (set_intersection2(set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))), set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))) = set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))),
% 1.44/1.17 inference(quant_inst,[status(thm)],[])).
% 1.44/1.17 tff(143,plain,
% 1.44/1.17 (set_intersection2(set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))), set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))) = set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[142, 9])).
% 1.44/1.18 tff(144,plain,
% 1.44/1.18 (set_intersection2(set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))), set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))) = empty_set),
% 1.44/1.18 inference(transitivity,[status(thm)],[143, 141, 131])).
% 1.44/1.18 tff(145,plain,
% 1.44/1.18 (relation_image(A!14, set_intersection2(set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))), set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))))) = relation_image(A!14, empty_set)),
% 1.44/1.18 inference(monotonicity,[status(thm)],[144])).
% 1.44/1.18 tff(146,plain,
% 1.44/1.18 (relation_image(A!14, empty_set) = relation_image(A!14, set_intersection2(set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14))), set_intersection2(singleton(tptp_fun_C_1(A!14)), singleton(tptp_fun_B_2(A!14)))))),
% 1.44/1.18 inference(symmetry,[status(thm)],[145])).
% 1.44/1.18 tff(147,plain,
% 1.44/1.18 (^[A: $i] : refl(((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ((~relation(A)) | (relation_image(A, empty_set) = empty_set)))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(148,plain,
% 1.44/1.18 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[147])).
% 1.44/1.18 tff(149,plain,
% 1.44/1.18 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(150,plain,
% 1.44/1.18 (^[A: $i] : rewrite((relation(A) => (relation_image(A, empty_set) = empty_set)) <=> ((~relation(A)) | (relation_image(A, empty_set) = empty_set)))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(151,plain,
% 1.44/1.18 (![A: $i] : (relation(A) => (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[150])).
% 1.44/1.18 tff(152,axiom,(![A: $i] : (relation(A) => (relation_image(A, empty_set) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t149_relat_1')).
% 1.44/1.18 tff(153,plain,
% 1.44/1.18 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.44/1.18 tff(154,plain,
% 1.44/1.18 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[153, 149])).
% 1.44/1.18 tff(155,plain,(
% 1.44/1.18 ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 1.44/1.18 inference(skolemize,[status(sab)],[154])).
% 1.44/1.18 tff(156,plain,
% 1.44/1.18 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[155, 148])).
% 1.44/1.18 tff(157,plain,
% 1.44/1.18 (((~![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))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(158,plain,
% 1.44/1.18 ((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | ((~relation(A!14)) | (relation_image(A!14, empty_set) = empty_set))),
% 1.44/1.18 inference(quant_inst,[status(thm)],[])).
% 1.44/1.18 tff(159,plain,
% 1.44/1.18 ((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | (~relation(A!14)) | (relation_image(A!14, empty_set) = empty_set)),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.44/1.18 tff(160,plain,
% 1.44/1.18 (relation_image(A!14, empty_set) = empty_set),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[159, 35, 156])).
% 1.44/1.18 tff(161,plain,
% 1.44/1.18 (empty_set = relation_image(A!14, empty_set)),
% 1.44/1.18 inference(symmetry,[status(thm)],[160])).
% 1.44/1.18 tff(162,plain,
% 1.44/1.18 (empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14)))),
% 1.44/1.18 inference(transitivity,[status(thm)],[161, 146, 104, 102, 11])).
% 1.44/1.18 tff(163,plain,
% 1.44/1.18 ((singleton(apply(A!14, tptp_fun_C_1(A!14))) = empty_set) <=> (empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.18 inference(commutativity,[status(thm)],[])).
% 1.44/1.18 tff(164,plain,
% 1.44/1.18 ((set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set) <=> (singleton(apply(A!14, tptp_fun_C_1(A!14))) = empty_set)),
% 1.44/1.18 inference(monotonicity,[status(thm)],[11])).
% 1.44/1.18 tff(165,plain,
% 1.44/1.18 ((set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set) <=> (empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.18 inference(transitivity,[status(thm)],[164, 163])).
% 1.44/1.18 tff(166,plain,
% 1.44/1.18 ((~(set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set)) <=> (~(empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.18 inference(monotonicity,[status(thm)],[165])).
% 1.44/1.18 tff(167,plain,
% 1.44/1.18 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> (set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set))),
% 1.44/1.18 inference(quant_inst,[status(thm)],[])).
% 1.44/1.18 tff(168,plain,
% 1.44/1.18 (disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> (set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set)),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[167, 111])).
% 1.44/1.18 tff(169,plain,
% 1.44/1.18 (^[A: $i] : refl((~empty(singleton(A))) <=> (~empty(singleton(A))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(170,plain,
% 1.44/1.18 (![A: $i] : (~empty(singleton(A))) <=> ![A: $i] : (~empty(singleton(A)))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[169])).
% 1.44/1.18 tff(171,plain,
% 1.44/1.18 (![A: $i] : (~empty(singleton(A))) <=> ![A: $i] : (~empty(singleton(A)))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(172,axiom,(![A: $i] : (~empty(singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_subset_1')).
% 1.44/1.18 tff(173,plain,
% 1.44/1.18 (![A: $i] : (~empty(singleton(A)))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.44/1.18 tff(174,plain,(
% 1.44/1.18 ![A: $i] : (~empty(singleton(A)))),
% 1.44/1.18 inference(skolemize,[status(sab)],[173])).
% 1.44/1.18 tff(175,plain,
% 1.44/1.18 (![A: $i] : (~empty(singleton(A)))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[174, 170])).
% 1.44/1.18 tff(176,plain,
% 1.44/1.18 ((~![A: $i] : (~empty(singleton(A)))) | (~empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.18 inference(quant_inst,[status(thm)],[])).
% 1.44/1.18 tff(177,plain,
% 1.44/1.18 (~empty(singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[176, 175])).
% 1.44/1.18 tff(178,plain,
% 1.44/1.18 (^[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))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(179,plain,
% 1.44/1.18 (![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)))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[178])).
% 1.44/1.18 tff(180,plain,
% 1.44/1.18 (^[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)))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(181,plain,
% 1.44/1.18 (![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)))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[180])).
% 1.44/1.18 tff(182,plain,
% 1.44/1.18 (![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)))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(183,plain,
% 1.44/1.18 (^[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))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(184,plain,
% 1.44/1.18 (![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)))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[183])).
% 1.44/1.18 tff(185,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')).
% 1.44/1.18 tff(186,plain,
% 1.44/1.18 (![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.44/1.18 tff(187,plain,
% 1.44/1.18 (![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[186, 182])).
% 1.44/1.18 tff(188,plain,(
% 1.44/1.18 ![A: $i, B: $i] : ((~((~empty(A)) & (~empty(B)))) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 1.44/1.18 inference(skolemize,[status(sab)],[187])).
% 1.44/1.18 tff(189,plain,
% 1.44/1.18 (![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[188, 181])).
% 1.44/1.18 tff(190,plain,
% 1.44/1.18 (![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[189, 179])).
% 1.44/1.18 tff(191,plain,
% 1.44/1.18 (((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))) <=> ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(192,plain,
% 1.44/1.18 ((empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))) <=> (empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(193,plain,
% 1.44/1.18 (((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))) <=> ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))))),
% 1.44/1.18 inference(monotonicity,[status(thm)],[192])).
% 1.44/1.18 tff(194,plain,
% 1.44/1.18 (((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))) <=> ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 1.44/1.18 inference(transitivity,[status(thm)],[193, 191])).
% 1.44/1.18 tff(195,plain,
% 1.44/1.18 ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | (empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 1.44/1.18 inference(quant_inst,[status(thm)],[])).
% 1.44/1.18 tff(196,plain,
% 1.44/1.18 ((~![A: $i, B: $i] : (empty(B) | empty(A) | (disjoint_nonempty(A, B) <=> disjoint(A, B)))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.44/1.18 tff(197,plain,
% 1.44/1.18 (disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[196, 190, 177])).
% 1.44/1.18 tff(198,plain,
% 1.44/1.18 (((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14))) | one_to_one(A!14)),
% 1.44/1.18 inference(tautology,[status(thm)],[])).
% 1.44/1.18 tff(199,plain,
% 1.44/1.18 ((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[198, 58])).
% 1.44/1.18 tff(200,plain,
% 1.44/1.18 (^[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))))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(201,plain,
% 1.44/1.18 (![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)))))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[200])).
% 1.44/1.18 tff(202,plain,
% 1.44/1.18 (^[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)))))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(203,plain,
% 1.44/1.18 (![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)))))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[202])).
% 1.44/1.18 tff(204,plain,
% 1.44/1.18 (![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)))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(205,plain,
% 1.44/1.18 (^[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)))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(206,plain,
% 1.44/1.18 (![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)))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[205])).
% 1.44/1.18 tff(207,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')).
% 1.44/1.18 tff(208,plain,
% 1.44/1.18 (![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.44/1.18 tff(209,plain,
% 1.44/1.18 (![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.44/1.18 tff(210,plain,(
% 1.44/1.18 ![A: $i] : ((~(relation(A) & empty(A) & function(A))) | (relation(A) & function(A) & one_to_one(A)))),
% 1.44/1.18 inference(skolemize,[status(sab)],[209])).
% 1.44/1.18 tff(211,plain,
% 1.44/1.18 (![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.44/1.18 tff(212,plain,
% 1.44/1.18 (![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[211, 201])).
% 1.44/1.18 tff(213,plain,
% 1.44/1.18 (((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | ((~relation(A!14)) | (~function(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14)))))) <=> ((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | (~relation(A!14)) | (~function(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14)))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(214,plain,
% 1.44/1.18 (((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14))))) <=> ((~relation(A!14)) | (~function(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14)))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(215,plain,
% 1.44/1.18 ((~((~relation(A!14)) | (~one_to_one(A!14)) | (~function(A!14)))) <=> (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(216,plain,
% 1.44/1.18 (((~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)) | (~relation(A!14)) | (~function(A!14)))))),
% 1.44/1.18 inference(monotonicity,[status(thm)],[215])).
% 1.44/1.18 tff(217,plain,
% 1.44/1.18 (((~empty(A!14)) | (~relation(A!14)) | (~function(A!14)) | (~((~relation(A!14)) | (~one_to_one(A!14)) | (~function(A!14))))) <=> ((~relation(A!14)) | (~function(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14)))))),
% 1.44/1.18 inference(transitivity,[status(thm)],[216, 214])).
% 1.44/1.18 tff(218,plain,
% 1.44/1.18 (((~![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)))))) | ((~relation(A!14)) | (~function(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14))))))),
% 1.44/1.18 inference(monotonicity,[status(thm)],[217])).
% 1.44/1.18 tff(219,plain,
% 1.44/1.18 (((~![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)))))) | (~relation(A!14)) | (~function(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14)))))),
% 1.44/1.18 inference(transitivity,[status(thm)],[218, 213])).
% 1.44/1.18 tff(220,plain,
% 1.44/1.18 ((~![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)))))),
% 1.44/1.18 inference(quant_inst,[status(thm)],[])).
% 1.44/1.18 tff(221,plain,
% 1.44/1.18 ((~![A: $i] : ((~empty(A)) | (~relation(A)) | (~function(A)) | (~((~relation(A)) | (~one_to_one(A)) | (~function(A)))))) | (~relation(A!14)) | (~function(A!14)) | (~empty(A!14)) | (~((~one_to_one(A!14)) | (~relation(A!14)) | (~function(A!14))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.44/1.18 tff(222,plain,
% 1.44/1.18 (~empty(A!14)),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[221, 212, 35, 34, 199])).
% 1.44/1.18 tff(223,plain,
% 1.44/1.18 (^[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)))))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(224,plain,
% 1.44/1.18 (![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))))))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[223])).
% 1.44/1.18 tff(225,plain,
% 1.44/1.18 (^[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)))))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(226,plain,
% 1.44/1.18 (![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))))))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[225])).
% 1.44/1.18 tff(227,plain,
% 1.44/1.18 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> ![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(228,plain,
% 1.44/1.18 (^[A: $i] : rewrite(((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(229,plain,
% 1.44/1.18 (![A: $i] : ((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> ![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[228])).
% 1.44/1.18 tff(230,axiom,(![A: $i] : ((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_subset_1')).
% 1.44/1.18 tff(231,plain,
% 1.44/1.18 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.44/1.18 tff(232,plain,
% 1.44/1.18 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[231, 227])).
% 1.44/1.18 tff(233,plain,(
% 1.44/1.18 ![A: $i] : (empty(A) | (element(tptp_fun_B_6(A), powerset(A)) & (~empty(tptp_fun_B_6(A)))))),
% 1.44/1.18 inference(skolemize,[status(sab)],[232])).
% 1.44/1.18 tff(234,plain,
% 1.44/1.18 (![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[233, 226])).
% 1.44/1.18 tff(235,plain,
% 1.44/1.18 (![A: $i] : (empty(A) | (~(empty(tptp_fun_B_6(A)) | (~element(tptp_fun_B_6(A), powerset(A))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[234, 224])).
% 1.44/1.18 tff(236,plain,
% 1.44/1.18 (((~![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))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(237,plain,
% 1.44/1.18 ((~![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))))))),
% 1.44/1.18 inference(quant_inst,[status(thm)],[])).
% 1.44/1.18 tff(238,plain,
% 1.44/1.18 ((~![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)))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[237, 236])).
% 1.44/1.18 tff(239,plain,
% 1.44/1.18 (~(empty(tptp_fun_B_6(A!14)) | (~element(tptp_fun_B_6(A!14), powerset(A!14))))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[238, 235, 222])).
% 1.44/1.18 tff(240,plain,
% 1.44/1.18 ((empty(tptp_fun_B_6(A!14)) | (~element(tptp_fun_B_6(A!14), powerset(A!14)))) | (~empty(tptp_fun_B_6(A!14)))),
% 1.44/1.18 inference(tautology,[status(thm)],[])).
% 1.44/1.18 tff(241,plain,
% 1.44/1.18 (~empty(tptp_fun_B_6(A!14))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[240, 239])).
% 1.44/1.18 tff(242,plain,
% 1.44/1.18 (((~![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)))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(243,plain,
% 1.44/1.18 ((~![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)))))))),
% 1.44/1.18 inference(quant_inst,[status(thm)],[])).
% 1.44/1.18 tff(244,plain,
% 1.44/1.18 ((~![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))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.44/1.18 tff(245,plain,
% 1.44/1.18 (~(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)))))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[244, 235, 241])).
% 1.44/1.18 tff(246,plain,
% 1.44/1.18 ((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))))),
% 1.44/1.18 inference(tautology,[status(thm)],[])).
% 1.44/1.18 tff(247,plain,
% 1.44/1.18 (~empty(tptp_fun_B_6(tptp_fun_B_6(A!14)))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[246, 245])).
% 1.44/1.18 tff(248,plain,
% 1.44/1.18 (^[A: $i, B: $i] : refl((empty(B) | (~disjoint_nonempty(A, A)) | empty(A)) <=> (empty(B) | (~disjoint_nonempty(A, A)) | empty(A)))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(249,plain,
% 1.44/1.18 (![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A)) <=> ![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[248])).
% 1.44/1.18 tff(250,plain,
% 1.44/1.18 (^[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))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(251,plain,
% 1.44/1.18 (![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B))))) <=> ![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[250])).
% 1.44/1.18 tff(252,plain,
% 1.44/1.18 (![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B))))) <=> ![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(253,plain,
% 1.44/1.18 (^[A: $i, B: $i] : rewrite((((~empty(A)) & (~empty(B))) => (~disjoint_nonempty(A, A))) <=> ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B))))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(254,plain,
% 1.44/1.18 (![A: $i, B: $i] : (((~empty(A)) & (~empty(B))) => (~disjoint_nonempty(A, A))) <=> ![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[253])).
% 1.44/1.18 tff(255,axiom,(![A: $i, B: $i] : (((~empty(A)) & (~empty(B))) => (~disjoint_nonempty(A, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','irreflexivity_r1_subset_1')).
% 1.44/1.18 tff(256,plain,
% 1.44/1.18 (![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.44/1.18 tff(257,plain,
% 1.44/1.18 (![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[256, 252])).
% 1.44/1.18 tff(258,plain,(
% 1.44/1.18 ![A: $i, B: $i] : ((~disjoint_nonempty(A, A)) | (~((~empty(A)) & (~empty(B)))))),
% 1.44/1.18 inference(skolemize,[status(sab)],[257])).
% 1.44/1.18 tff(259,plain,
% 1.44/1.18 (![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[258, 251])).
% 1.44/1.18 tff(260,plain,
% 1.44/1.18 (![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[259, 249])).
% 1.44/1.18 tff(261,plain,
% 1.44/1.18 (((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | (empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))) <=> ((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(262,plain,
% 1.44/1.18 ((empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14))))) <=> (empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(263,plain,
% 1.44/1.18 (((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | (empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))))) <=> ((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | (empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))))),
% 1.44/1.18 inference(monotonicity,[status(thm)],[262])).
% 1.44/1.18 tff(264,plain,
% 1.44/1.18 (((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | (empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))))) <=> ((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))))),
% 1.44/1.18 inference(transitivity,[status(thm)],[263, 261])).
% 1.44/1.18 tff(265,plain,
% 1.44/1.18 ((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | (empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.18 inference(quant_inst,[status(thm)],[])).
% 1.44/1.18 tff(266,plain,
% 1.44/1.18 ((~![A: $i, B: $i] : (empty(B) | (~disjoint_nonempty(A, A)) | empty(A))) | empty(tptp_fun_B_6(tptp_fun_B_6(A!14))) | empty(singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[265, 264])).
% 1.44/1.18 tff(267,plain,
% 1.44/1.18 (~disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[266, 260, 247, 177])).
% 1.44/1.18 tff(268,plain,
% 1.44/1.18 ((~(disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))) | disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.18 inference(tautology,[status(thm)],[])).
% 1.44/1.18 tff(269,plain,
% 1.44/1.18 ((~(disjoint_nonempty(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))) | (~disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[268, 267])).
% 1.44/1.18 tff(270,plain,
% 1.44/1.18 (~disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[269, 197])).
% 1.44/1.18 tff(271,plain,
% 1.44/1.18 ((~(disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> (set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set))) | disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) | (~(set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set))),
% 1.44/1.19 inference(tautology,[status(thm)],[])).
% 1.44/1.19 tff(272,plain,
% 1.44/1.19 ((~(disjoint(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) <=> (set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set))) | (~(set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set))),
% 1.44/1.19 inference(unit_resolution,[status(thm)],[271, 270])).
% 1.44/1.19 tff(273,plain,
% 1.44/1.19 (~(set_intersection2(singleton(apply(A!14, tptp_fun_C_1(A!14))), singleton(apply(A!14, tptp_fun_C_1(A!14)))) = empty_set)),
% 1.44/1.19 inference(unit_resolution,[status(thm)],[272, 168])).
% 1.44/1.19 tff(274,plain,
% 1.44/1.19 (~(empty_set = singleton(apply(A!14, tptp_fun_C_1(A!14))))),
% 1.44/1.19 inference(modus_ponens,[status(thm)],[273, 166])).
% 1.44/1.19 tff(275,plain,
% 1.44/1.19 ($false),
% 1.44/1.19 inference(unit_resolution,[status(thm)],[274, 162])).
% 1.44/1.19 % SZS output end Proof
%------------------------------------------------------------------------------