%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU924^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:34:24 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU924^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n007.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 14:44:41 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (3458615)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (3458624)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=826081411:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (3458624)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (3458624) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3458615-3458624"...
% 0.21/0.28 % (3458624)...printing done.
% 0.21/0.28 % (3458624)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_1, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_5, type, sK1: ($i > $i)).
% 0.21/0.28 thf(func_def_7, type, sK3: ((($i > $i) > $o) > $i > $i)).
% 0.21/0.28 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.28 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ! [X0 : $i,X1 : ($i > $i)] : (! [X2 : (($i > $i) > $o)] : ((! [X4 : ($i > $i)] : ((X2 @ X4) => (X2 @ (^[X3 : $i] : (X0)))) & (X2 @ (^[X3 : $i] : (X0)))) => (X2 @ X1)) => ! [X3 : $i] : (((X1 @ X3)) = X0))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM134_pme)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~ ! [X0 : $i,X1 : ($i > $i)] : (! [X2 : (($i > $i) > $o)] : ((! [X4 : ($i > $i)] : ((X2 @ X4) => (X2 @ (^[X3 : $i] : (X0)))) & (X2 @ (^[X3 : $i] : (X0)))) => (X2 @ X1)) => ! [X3 : $i] : (((X1 @ X3)) = X0))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~ ! [X0 : $i,X1 : ($i > $i)] : (! [X2 : (($i > $i) > $o)] : ((! [X3 : ($i > $i)] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : (X0)))) & (X2 @ (^[X5 : $i] : (X0)))) => (X2 @ X1)) => ! [X6 : $i] : (((X1 @ X6)) = X0))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~ ! [X0 : $i,X1 : ($i > $i)] : (! [X2 : (($i > $i) > $o)] : ((! [X3 : ($i > $i)] : ((((X2 @ X3)) = $true) => (((X2 @ (^[Y0 : $i]: (X0)))) = $true)) & (((X2 @ (^[Y0 : $i]: (X0)))) = $true)) => (((X2 @ X1)) = $true)) => ! [X6 : $i] : (((X1 @ X6)) = X0))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~ ! [X0 : $i,X1 : ($i > $i)] : (! [X2 : (($i > $i) > $o)] : ((! [X3 : ($i > $i)] : ((((X2 @ X3)) = $true) => (((X2 @ (^[Y0 : $i]: (X0)))) = $true)) & (((X2 @ (^[Y0 : $i]: (X0)))) = $true)) => (((X2 @ X1)) = $true)) => ! [X4 : $i] : (((X1 @ X4)) = X0))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ? [X0 : $i,X1 : ($i > $i)] : (? [X4 : $i] : (((X1 @ X4)) != X0) & ! [X2 : (($i > $i) > $o)] : ((((X2 @ X1)) = $true) | (? [X3 : ($i > $i)] : ((((X2 @ (^[Y0 : $i]: (X0)))) != $true) & (((X2 @ X3)) = $true)) | (((X2 @ (^[Y0 : $i]: (X0)))) != $true))))),
% 0.21/0.28 inference(ennf_transformation,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ? [X0 : $i,X1 : ($i > $i)] : (? [X4 : $i] : (((X1 @ X4)) != X0) & ! [X2 : (($i > $i) > $o)] : ((((X2 @ X1)) = $true) | ? [X3 : ($i > $i)] : ((((X2 @ (^[Y0 : $i]: (X0)))) != $true) & (((X2 @ X3)) = $true)) | (((X2 @ (^[Y0 : $i]: (X0)))) != $true)))),
% 0.21/0.28 inference(flattening,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ? [X0 : $i,X1 : ($i > $i)] : (? [X2 : $i] : (((X1 @ X2)) != X0) & ! [X3 : (($i > $i) > $o)] : (($true = ((X3 @ X1))) | ? [X4 : ($i > $i)] : (($true != ((X3 @ (^[Y0 : $i]: (X0))))) & ($true = ((X3 @ X4)))) | ($true != ((X3 @ (^[Y0 : $i]: (X0)))))))),
% 0.21/0.28 inference(rectify,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 (sK0 != ((sK1 @ sK2))) & ! [X3 : (($i > $i) > $o)] : (($true = ((X3 @ sK1))) | (($true != ((X3 @ (^[Y0 : $i]: (sK0))))) & ($true = ((X3 @ (sK3 @ X3))))) | ($true != ((X3 @ (^[Y0 : $i]: (sK0))))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3 @ X3)],[f8])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ( ! [X3 : (($i > $i) > $o)] : (($true = ((X3 @ sK1))) | ($true != ((X3 @ (^[Y0 : $i]: (sK0))))) | ($true != ((X3 @ (^[Y0 : $i]: (sK0)))))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 (sK0 != ((sK1 @ sK2)))),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ( ! [X3 : (($i > $i) > $o)] : (($true != ((X3 @ (^[Y0 : $i]: (sK0))))) | ($true = ((X3 @ sK1)))) )),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f11])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 (sK1 = (^[Y0 : $i]: (sK0)))),
% 0.21/0.28 inference(leibniz_equality_elimination,[],[f15])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ( ! [X1 : $i] : ((((sK1 @ X1)) = (((^[Y0 : $i]: (sK0)) @ X1)))) )),
% 0.21/0.28 inference(argument_congruence,[],[f17])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 ( ! [X1 : $i] : ((sK0 = ((sK1 @ X1)))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f28])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 (sK0 != sK0)),
% 0.21/0.28 inference(constrained_superposition,[],[f12,f30])).
% 0.21/0.28 thf(f32,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f31])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (3458624)------------------------------
% 0.21/0.28 % (3458624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3458624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3458624)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3458624)Termination reason: Refutation
% 0.21/0.28 % (3458624)Time elapsed: 0.001 s
% 0.21/0.28 % (3458624)Peak memory usage: 12 MB
% 0.21/0.28 % (3458624)Instructions burned: 2 (million)
% 0.21/0.28 % (3458615)Success in time 0.031 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------