TSTP Solution File: SEU284+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 07:28:41 EDT 2022
% Result : Theorem 0.15s 0.42s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n026.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 11:46:24 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.30 Usage: tptp [options] [-file:]file
% 0.10/0.30 -h, -? prints this message.
% 0.10/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.30 -m, -model generate model.
% 0.10/0.30 -p, -proof generate proof.
% 0.10/0.30 -c, -core generate unsat core of named formulas.
% 0.10/0.30 -st, -statistics display statistics.
% 0.10/0.30 -t:timeout set timeout (in second).
% 0.10/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.30 -<param>:<value> configuration parameter and value.
% 0.10/0.30 -o:<output-file> file to place output in.
% 0.15/0.42 % SZS status Theorem
% 0.15/0.42 % SZS output start Proof
% 0.15/0.42 tff(tptp_fun_D_3_type, type, (
% 0.15/0.42 tptp_fun_D_3: $i > $i)).
% 0.15/0.42 tff(tptp_fun_A_0_type, type, (
% 0.15/0.42 tptp_fun_A_0: $i)).
% 0.15/0.42 tff(tptp_fun_C_4_type, type, (
% 0.15/0.42 tptp_fun_C_4: $i > $i)).
% 0.15/0.42 tff(singleton_type, type, (
% 0.15/0.42 singleton: $i > $i)).
% 0.15/0.42 tff(tptp_fun_B_5_type, type, (
% 0.15/0.42 tptp_fun_B_5: $i > $i)).
% 0.15/0.42 tff(in_type, type, (
% 0.15/0.42 in: ( $i * $i ) > $o)).
% 0.15/0.42 tff(tptp_fun_B_6_type, type, (
% 0.15/0.42 tptp_fun_B_6: $i > $i)).
% 0.15/0.42 tff(relation_dom_type, type, (
% 0.15/0.42 relation_dom: $i > $i)).
% 0.15/0.42 tff(tptp_fun_B_7_type, type, (
% 0.15/0.42 tptp_fun_B_7: $i > $i)).
% 0.15/0.42 tff(apply_type, type, (
% 0.15/0.42 apply: ( $i * $i ) > $i)).
% 0.15/0.42 tff(function_type, type, (
% 0.15/0.42 function: $i > $o)).
% 0.15/0.42 tff(relation_type, type, (
% 0.15/0.42 relation: $i > $o)).
% 0.15/0.42 tff(tptp_fun_C_1_type, type, (
% 0.15/0.42 tptp_fun_C_1: $i > $i)).
% 0.15/0.42 tff(1,plain,
% 0.15/0.42 (((~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))) | $false) <=> (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0)))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(2,plain,
% 0.15/0.42 ((~$true) <=> $false),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(3,plain,
% 0.15/0.42 ((singleton(tptp_fun_B_6(A!0)) = singleton(tptp_fun_B_6(A!0))) <=> $true),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(4,plain,
% 0.15/0.42 ((~(singleton(tptp_fun_B_6(A!0)) = singleton(tptp_fun_B_6(A!0)))) <=> (~$true)),
% 0.15/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.15/0.42 tff(5,plain,
% 0.15/0.42 ((~(singleton(tptp_fun_B_6(A!0)) = singleton(tptp_fun_B_6(A!0)))) <=> $false),
% 0.15/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.15/0.42 tff(6,plain,
% 0.15/0.42 (((~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))) | (~(singleton(tptp_fun_B_6(A!0)) = singleton(tptp_fun_B_6(A!0))))) <=> ((~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))) | $false)),
% 0.15/0.42 inference(monotonicity,[status(thm)],[5])).
% 0.15/0.42 tff(7,plain,
% 0.15/0.42 (((~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))) | (~(singleton(tptp_fun_B_6(A!0)) = singleton(tptp_fun_B_6(A!0))))) <=> (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0)))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[6, 1])).
% 0.15/0.42 tff(8,plain,
% 0.15/0.42 ((~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))) | (~(singleton(tptp_fun_B_6(A!0)) = singleton(tptp_fun_B_6(A!0))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(9,plain,
% 0.15/0.42 (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.15/0.42 tff(10,plain,
% 0.15/0.42 (((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0)))))) | ![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(11,plain,
% 0.15/0.42 ((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0)))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.15/0.42 tff(12,assumption,(~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)))), introduced(assumption)).
% 0.15/0.42 tff(13,plain,
% 0.15/0.42 (((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0))) | (relation_dom(tptp_fun_B_7(A!0)) = A!0)),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(14,plain,
% 0.15/0.42 (relation_dom(tptp_fun_B_7(A!0)) = A!0),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.15/0.42 tff(15,plain,
% 0.15/0.42 (((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0))) | function(tptp_fun_B_7(A!0))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(16,plain,
% 0.15/0.42 (function(tptp_fun_B_7(A!0))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.15/0.42 tff(17,plain,
% 0.15/0.42 (((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0))) | relation(tptp_fun_B_7(A!0))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(18,plain,
% 0.15/0.42 (relation(tptp_fun_B_7(A!0))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[17, 12])).
% 0.15/0.42 tff(19,plain,
% 0.15/0.42 (^[B: $i] : refl(((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B)))))) <=> ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B)))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(20,plain,
% 0.15/0.42 (![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B)))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.15/0.42 tff(21,plain,
% 0.15/0.42 ((~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))) <=> (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(22,plain,
% 0.15/0.42 ((~![A: $i] : ?[B: $i] : (((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C))))) <=> (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(23,axiom,(~![A: $i] : ?[B: $i] : (((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s3_funct_1__e16_22__wellord2')).
% 0.15/0.42 tff(24,plain,
% 0.15/0.42 (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.15/0.42 tff(25,plain,
% 0.15/0.42 (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.15/0.42 tff(26,plain,
% 0.15/0.42 (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.15/0.42 tff(27,plain,
% 0.15/0.42 (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.15/0.42 tff(28,plain,
% 0.15/0.42 (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.15/0.42 tff(29,plain,
% 0.15/0.42 (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.15/0.42 tff(30,plain,
% 0.15/0.42 (~![A: $i] : ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.15/0.42 tff(31,plain,(
% 0.15/0.42 $oeq((~?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A!0) & ![C: $i] : ((~in(C, A!0)) | (apply(B, C) = singleton(C))))), ![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B)))))))),
% 0.15/0.42 inference(transitivity,[status(sab)],[30])).
% 0.15/0.42 tff(32,plain,
% 0.15/0.42 (![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[31, 20])).
% 0.15/0.42 tff(33,plain,
% 0.15/0.42 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B))))))) | ((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)) | (~((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0)))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B))))))) | (~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)) | (~((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0)))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(34,plain,
% 0.15/0.42 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B))))))) | ((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)) | (~((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0)))))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(35,plain,
% 0.15/0.42 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B) = A!0)) | (~((~in(tptp_fun_C_1(B), A!0)) | (apply(B, tptp_fun_C_1(B)) = singleton(tptp_fun_C_1(B))))))) | (~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)) | (~((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.15/0.42 tff(36,plain,
% 0.15/0.42 (~((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0)))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[35, 32, 18, 16, 14])).
% 0.15/0.42 tff(37,plain,
% 0.15/0.42 (((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0))))) | (~(apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0)))))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(38,plain,
% 0.15/0.42 (~(apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.15/0.42 tff(39,plain,
% 0.15/0.42 (((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0))))) | in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(40,plain,
% 0.15/0.42 (in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.15/0.42 tff(41,plain,
% 0.15/0.42 (((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0))) | ![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(42,plain,
% 0.15/0.42 (![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[41, 12])).
% 0.15/0.42 tff(43,plain,
% 0.15/0.42 (((~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | ((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0)))))) <=> ((~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0)))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(44,plain,
% 0.15/0.42 ((~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | ((~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0)))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(45,plain,
% 0.15/0.42 ((~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~in(tptp_fun_C_1(tptp_fun_B_7(A!0)), A!0)) | (apply(tptp_fun_B_7(A!0), tptp_fun_C_1(tptp_fun_B_7(A!0))) = singleton(tptp_fun_C_1(tptp_fun_B_7(A!0))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.15/0.42 tff(46,plain,
% 0.15/0.42 ($false),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[45, 42, 40, 38])).
% 0.15/0.42 tff(47,plain,((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.42 tff(48,plain,
% 0.15/0.42 (^[A: $i] : rewrite(((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))))) <=> ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(49,plain,
% 0.15/0.42 (![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))))) <=> ![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.15/0.42 tff(50,plain,
% 0.15/0.42 (^[A: $i] : rewrite(((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))) <=> ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(51,plain,
% 0.15/0.42 (![A: $i] : ((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))) <=> ![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.15/0.42 tff(52,plain,
% 0.15/0.42 (^[A: $i] : trans(monotonicity(monotonicity(rewrite((in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))) <=> (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))), (((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))) <=> ((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))))), rewrite((relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))) <=> (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))), ((((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))) <=> (((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))))), rewrite((((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))) <=> ((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))), ((((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))) <=> ((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(53,plain,
% 0.15/0.42 (![A: $i] : (((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C))))) <=> ![A: $i] : ((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[52])).
% 0.15/0.43 tff(54,plain,
% 0.15/0.43 (![A: $i] : ((~(![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B))))))) | ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))) <=> ![A: $i] : ((~(![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B))))))) | ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(55,plain,
% 0.15/0.43 (^[A: $i] : trans(monotonicity(rewrite((![B: $i, C: $i, D: $i] : (((in(B, A) & (C = singleton(B))) & (D = singleton(B))) => (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B)))))) <=> (![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B))))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((relation(B) & function(B)) & (relation_dom(B) = A)) <=> (relation(B) & function(B) & (relation_dom(B) = A))), quant_intro(proof_bind(^[C: $i] : rewrite((in(C, A) => (apply(B, C) = singleton(C))) <=> ((~in(C, A)) | (apply(B, C) = singleton(C))))), (![C: $i] : (in(C, A) => (apply(B, C) = singleton(C))) <=> ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))), ((((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C)))) <=> ((relation(B) & function(B) & (relation_dom(B) = A)) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))), rewrite(((relation(B) & function(B) & (relation_dom(B) = A)) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))) <=> (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))), ((((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C)))) <=> (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))))), (?[B: $i] : (((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C)))) <=> ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))), (((![B: $i, C: $i, D: $i] : (((in(B, A) & (C = singleton(B))) & (D = singleton(B))) => (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B)))))) => ?[B: $i] : (((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C))))) <=> ((![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B)))))) => ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))))), rewrite(((![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B)))))) => ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C))))) <=> ((~(![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B))))))) | ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))), (((![B: $i, C: $i, D: $i] : (((in(B, A) & (C = singleton(B))) & (D = singleton(B))) => (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B)))))) => ?[B: $i] : (((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C))))) <=> ((~(![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B))))))) | ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(56,plain,
% 0.15/0.43 (![A: $i] : ((![B: $i, C: $i, D: $i] : (((in(B, A) & (C = singleton(B))) & (D = singleton(B))) => (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B)))))) => ?[B: $i] : (((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C))))) <=> ![A: $i] : ((~(![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B))))))) | ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.15/0.43 tff(57,axiom,(![A: $i] : ((![B: $i, C: $i, D: $i] : (((in(B, A) & (C = singleton(B))) & (D = singleton(B))) => (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B)))))) => ?[B: $i] : (((relation(B) & function(B)) & (relation_dom(B) = A)) & ![C: $i] : (in(C, A) => (apply(B, C) = singleton(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s2_funct_1__e16_22__wellord2__1')).
% 0.15/0.43 tff(58,plain,
% 0.15/0.43 (![A: $i] : ((~(![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B))))))) | ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.15/0.43 tff(59,plain,
% 0.15/0.43 (![A: $i] : ((~(![B: $i, C: $i, D: $i] : ((~(in(B, A) & (C = singleton(B)) & (D = singleton(B)))) | (C = D)) & ![B: $i] : (~(in(B, A) & ![C: $i] : (~(C = singleton(B))))))) | ?[B: $i] : (relation(B) & function(B) & (relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = singleton(C)))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.15/0.43 tff(60,plain,(
% 0.15/0.43 ![A: $i] : (((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A)))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))),
% 0.15/0.43 inference(skolemize,[status(sab)],[59])).
% 0.15/0.43 tff(61,plain,
% 0.15/0.43 (![A: $i] : ((~((~(in(tptp_fun_B_5(A), A) & (tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A))) & (tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A))))) | (tptp_fun_C_4(A) = tptp_fun_D_3(A)))) | (in(tptp_fun_B_6(A), A) & ![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))) | (relation(tptp_fun_B_7(A)) & function(tptp_fun_B_7(A)) & (relation_dom(tptp_fun_B_7(A)) = A) & ![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.15/0.43 tff(62,plain,
% 0.15/0.43 (![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.15/0.43 tff(63,plain,
% 0.15/0.43 (![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[62, 49])).
% 0.15/0.43 tff(64,plain,
% 0.15/0.43 (((~![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))) | ((~((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)))))) <=> ((~![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))) | (~((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(65,plain,
% 0.15/0.43 (((~((tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)) | (~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C))))))) <=> ((~((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(66,plain,
% 0.15/0.43 (((~![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))) | ((~((tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)) | (~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))))))) <=> ((~![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))) | ((~((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0))))))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[65])).
% 0.15/0.43 tff(67,plain,
% 0.15/0.43 (((~![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))) | ((~((tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)) | (~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))))))) <=> ((~![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))) | (~((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)))))),
% 0.15/0.43 inference(transitivity,[status(thm)],[66, 64])).
% 0.15/0.43 tff(68,plain,
% 0.15/0.43 ((~![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))) | ((~((tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)) | (~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0)) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(69,plain,
% 0.15/0.44 ((~![A: $i] : ((~((tptp_fun_C_4(A) = tptp_fun_D_3(A)) | (~in(tptp_fun_B_5(A), A)) | (~(tptp_fun_C_4(A) = singleton(tptp_fun_B_5(A)))) | (~(tptp_fun_D_3(A) = singleton(tptp_fun_B_5(A)))))) | (~((~in(tptp_fun_B_6(A), A)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A))))))) | (~((~relation(tptp_fun_B_7(A))) | (~function(tptp_fun_B_7(A))) | (~(relation_dom(tptp_fun_B_7(A)) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(tptp_fun_B_7(A), C) = singleton(C)))))))) | (~((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.15/0.44 tff(70,plain,
% 0.15/0.44 ((~((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))) | (~((~in(tptp_fun_B_6(A!0), A!0)) | (~![C: $i] : (~(C = singleton(tptp_fun_B_6(A!0))))))) | (~((~relation(tptp_fun_B_7(A!0))) | (~function(tptp_fun_B_7(A!0))) | (~![C: $i] : ((~in(C, A!0)) | (apply(tptp_fun_B_7(A!0), C) = singleton(C)))) | (~(relation_dom(tptp_fun_B_7(A!0)) = A!0))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[69, 63])).
% 0.15/0.44 tff(71,plain,
% 0.15/0.44 (~((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[70, 47, 11])).
% 0.15/0.44 tff(72,plain,
% 0.15/0.44 (((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0))) | (tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(73,plain,
% 0.15/0.44 (tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.15/0.44 tff(74,plain,
% 0.15/0.44 ((tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)) <=> (tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))),
% 0.15/0.44 inference(monotonicity,[status(thm)],[73])).
% 0.15/0.44 tff(75,plain,
% 0.15/0.44 ((tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0))) <=> (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0))),
% 0.15/0.44 inference(symmetry,[status(thm)],[74])).
% 0.15/0.44 tff(76,plain,
% 0.15/0.44 (((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0))) | (tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(77,plain,
% 0.15/0.44 (tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[76, 71])).
% 0.15/0.44 tff(78,plain,
% 0.15/0.44 (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.15/0.44 tff(79,plain,
% 0.15/0.44 (((~in(tptp_fun_B_5(A!0), A!0)) | (~(tptp_fun_C_4(A!0) = singleton(tptp_fun_B_5(A!0)))) | (~(tptp_fun_D_3(A!0) = singleton(tptp_fun_B_5(A!0)))) | (tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0))) | (~(tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(80,plain,
% 0.15/0.44 (~(tptp_fun_C_4(A!0) = tptp_fun_D_3(A!0))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[79, 71])).
% 0.15/0.44 tff(81,plain,
% 0.15/0.44 ($false),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[80, 78])).
% 0.15/0.44 % SZS output end Proof
%------------------------------------------------------------------------------