%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV487^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:38:43 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV487^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n007.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 15:50:56 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.29 % (3537569)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3537584)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4145005667:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (3537584) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3537569-3537584"...
% 0.22/0.29 % (3537584)...printing done.
% 0.22/0.29 % (3537584)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(type_def_6, type, sK2: $tType).
% 0.22/0.29 thf(func_def_0, type, 'const/sets/pairwise': !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.29 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.29 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.22/0.29 thf(func_def_6, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.22/0.29 thf(func_def_7, type, sK1: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.22/0.29 thf(func_def_8, type, sK3: (sK2 > sK2 > $o)).
% 0.22/0.29 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.22/0.29 thf(f1,axiom,(
% 0.22/0.29 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_')).
% 0.22/0.29 thf(f2,axiom,(
% 0.22/0.29 ! [X0 : $tType,X2 : (X0 > X0 > $o),X1 : (X0 > $o)] : ((('const/sets/pairwise' @ X0 @ X2 @ X1)) = ! [X3 : X0,X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) & ('const/sets/IN' @ X0 @ X3 @ X1) & (X3 != X4)) => (X2 @ X3 @ X4)))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/pairwise_')).
% 0.22/0.29 thf(f3,conjecture,(
% 0.22/0.29 ! [X0 : $tType,X1 : (X0 > X0 > $o)] : ((('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/PAIRWISE_EMPTY_')).
% 0.22/0.29 thf(f4,negated_conjecture,(
% 0.22/0.29 ~ ! [X0 : $tType,X1 : (X0 > X0 > $o)] : ((('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.29 thf(f5,plain,(
% 0.22/0.29 ! [X0 : $tType,X1 : (X0 > X0 > $o),X2 : (X0 > $o)] : ((('const/sets/pairwise' @ X0 @ X1 @ X2)) = ! [X3 : X0,X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X2) & ('const/sets/IN' @ X0 @ X3 @ X2) & (X3 != X4)) => (X1 @ X3 @ X4)))),
% 0.22/0.29 inference(rectify,[],[f2])).
% 0.22/0.29 thf(f6,plain,(
% 0.22/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > X0 > $o)] : (($true = (('const/sets/pairwise' @ X0 @ X1 @ X2))) <=> ! [X4 : X0,X3 : X0] : ((((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) & ((('const/sets/IN' @ X0 @ X4 @ X2)) = $true) & (X3 != X4)) => ($true = ((X1 @ X3 @ X4)))))),
% 0.22/0.29 inference(fool_elimination,[],[f5])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 ~ ! [X0 : $tType,X1 : (X0 > X0 > $o)] : (((('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true) <=> $true)),
% 0.22/0.29 inference(fool_elimination,[],[f4])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.22/0.29 inference(rectify,[],[f1])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 ! [X0 : $tType,X1 : X0] : ~ ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)),
% 0.22/0.29 inference(fool_elimination,[],[f8])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 ~ ! [X0 : $tType,X1 : (X0 > X0 > $o)] : ((('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)),
% 0.22/0.29 inference(true_and_false_elimination,[],[f7])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)),
% 0.22/0.29 inference(flattening,[],[f9])).
% 0.22/0.29 thf(f12,plain,(
% 0.22/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > X0 > $o)] : (($true = (('const/sets/pairwise' @ X0 @ X1 @ X2))) <=> ! [X4 : X0,X3 : X0] : (($true = ((X1 @ X3 @ X4))) | (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X2)) != $true) | (X3 = X4))))),
% 0.22/0.29 inference(ennf_transformation,[],[f6])).
% 0.22/0.29 thf(f13,plain,(
% 0.22/0.29 ! [X0 : $tType,X1 : (X0 > X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0,X4 : X0] : ((X3 = X4) | ($true = ((X1 @ X3 @ X4))) | ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X2)) != $true)) <=> ($true = (('const/sets/pairwise' @ X0 @ X1 @ X2))))),
% 0.22/0.29 inference(flattening,[],[f12])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 ? [X0 : $tType,X1 : (X0 > X0 > $o)] : ((('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)),
% 0.22/0.29 inference(ennf_transformation,[],[f10])).
% 0.22/0.29 thf(f15,plain,(
% 0.22/0.29 ! [X0 : $tType,X1 : (X0 > X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0,X4 : X0] : ((X3 = X4) | ($true = ((X1 @ X3 @ X4))) | ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X2)) != $true)) | ($true != (('const/sets/pairwise' @ X0 @ X1 @ X2)))) & (($true = (('const/sets/pairwise' @ X0 @ X1 @ X2))) | ? [X3 : X0,X4 : X0] : ((X3 != X4) & ($true != ((X1 @ X3 @ X4))) & ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) & ((('const/sets/IN' @ X0 @ X4 @ X2)) = $true))))),
% 0.22/0.29 inference(nnf_transformation,[],[f13])).
% 0.22/0.29 thf(f16,plain,(
% 0.22/0.29 ! [X0 : $tType,X1 : (X0 > X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0,X4 : X0] : ((X3 = X4) | ($true = ((X1 @ X3 @ X4))) | ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X2)) != $true)) | ($true != (('const/sets/pairwise' @ X0 @ X1 @ X2)))) & (($true = (('const/sets/pairwise' @ X0 @ X1 @ X2))) | ? [X5 : X0,X6 : X0] : ((X5 != X6) & ($true != ((X1 @ X5 @ X6))) & ((('const/sets/IN' @ X0 @ X5 @ X2)) = $true) & ($true = (('const/sets/IN' @ X0 @ X6 @ X2))))))),
% 0.22/0.29 inference(rectify,[],[f15])).
% 0.22/0.29 thf(f17,plain,(
% 0.22/0.29 ! [X0 : $tType,X1 : (X0 > X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0,X4 : X0] : ((X3 = X4) | ($true = ((X1 @ X3 @ X4))) | ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X2)) != $true)) | ($true != (('const/sets/pairwise' @ X0 @ X1 @ X2)))) & (($true = (('const/sets/pairwise' @ X0 @ X1 @ X2))) | ((((sK1 @ X0 @ X2 @ X1)) != ((sK0 @ X0 @ X2 @ X1))) & ($true != ((X1 @ (sK0 @ X0 @ X2 @ X1) @ (sK1 @ X0 @ X2 @ X1)))) & ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2))) & ($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X2 @ X1) @ X2))))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X6,sK1 @ X0 @ X2 @ X1),skolemize(X6,sK1 @ X0 @ X2 @ X1)],[f16])).
% 0.22/0.29 thf(f18,plain,(
% 0.22/0.29 ($true != (('const/sets/pairwise' @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK2)))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f14])).
% 0.22/0.29 thf(f19,plain,(
% 0.22/0.29 ( ! [X0 : $tType,X1 : X0] : (((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f11])).
% 0.22/0.29 thf(f20,plain,(
% 0.22/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X2 @ X1) @ X2))) | ($true = (('const/sets/pairwise' @ X0 @ X1 @ X2)))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f17])).
% 0.22/0.29 thf(f25,plain,(
% 0.22/0.29 ($true != (('const/sets/pairwise' @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK2)))),
% 0.22/0.29 inference(cnf_transformation,[],[f18])).
% 0.22/0.29 thf(f27,plain,(
% 0.22/0.29 ( ! [X0 : $tType,X1 : (X0 > X0 > $o)] : (($true != $true) | ((('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)) )),
% 0.22/0.29 inference(superposition,[],[f19,f20])).
% 0.22/0.29 thf(f28,plain,(
% 0.22/0.29 ( ! [X0 : $tType,X1 : (X0 > X0 > $o)] : (((('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f27])).
% 0.22/0.29 thf(f29,plain,(
% 0.22/0.29 ($true != $true)),
% 0.22/0.29 inference(superposition,[],[f25,f28])).
% 0.22/0.29 thf(f30,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f29])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (3537584)------------------------------
% 0.22/0.29 % (3537584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3537584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3537584)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3537584)Termination reason: Refutation
% 0.22/0.29 % (3537584)Time elapsed: 0.002 s
% 0.22/0.29 % (3537584)Peak memory usage: 12 MB
% 0.22/0.29 % (3537584)Instructions burned: 3 (million)
% 0.22/0.29 % (3537569)Success in time 0.025 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------