%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU894^5 : 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 : n004.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 08:34:21 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU894^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n004.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 14:44:22 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.10/0.26 % (1384823)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (1384832)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2123933479:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.26 % (1384832)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (1384832) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1384823-1384832"...
% 0.10/0.26 % (1384832)...printing done.
% 0.10/0.26 % (1384832)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% 0.10/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.26 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.10/0.26 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.10/0.26 thf(func_def_5, type, sK0: ($i > $i)).
% 0.10/0.26 thf(func_def_6, type, sK1: (($i > $i) > $i)).
% 0.10/0.26 thf(func_def_7, type, sK2: ((($i > $i) > $o) > $i > $i)).
% 0.10/0.26 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.10/0.26 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.10/0.26 thf(f1,conjecture,(
% 0.10/0.26 ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((? [X5 : $i] : (! [X6 : $i] : ((((X1 @ X6)) = X6) => (X5 = X6)) & (((X1 @ X5)) = X5)) & ! [X2 : (($i > $i) > $o)] : ((! [X3 : ($i > $i)] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : ((X0 @ (X3 @ X4)))))) & (X2 @ X0)) => (X2 @ X1))) => ? [X6 : $i] : (((X0 @ X6)) = X6))),
% 0.10/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM15_0_pme)).
% 0.10/0.26 thf(f2,negated_conjecture,(
% 0.10/0.26 ~ ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((? [X5 : $i] : (! [X6 : $i] : ((((X1 @ X6)) = X6) => (X5 = X6)) & (((X1 @ X5)) = X5)) & ! [X2 : (($i > $i) > $o)] : ((! [X3 : ($i > $i)] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : ((X0 @ (X3 @ X4)))))) & (X2 @ X0)) => (X2 @ X1))) => ? [X6 : $i] : (((X0 @ X6)) = X6))),
% 0.10/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.10/0.26 thf(f3,plain,(
% 0.10/0.26 ~ ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((? [X2 : $i] : (! [X3 : $i] : ((((X1 @ X3)) = X3) => (X2 = X3)) & (((X1 @ X2)) = X2)) & ! [X4 : (($i > $i) > $o)] : ((! [X5 : ($i > $i)] : ((X4 @ X5) => (X4 @ (^[X6 : $i] : ((X0 @ (X5 @ X6)))))) & (X4 @ X0)) => (X4 @ X1))) => ? [X7 : $i] : (((X0 @ X7)) = X7))),
% 0.10/0.26 inference(rectify,[],[f2])).
% 0.10/0.26 thf(f4,plain,(
% 0.10/0.26 ~ ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((? [X2 : $i] : (! [X3 : $i] : ((((X1 @ X3)) = X3) => (X2 = X3)) & (((X1 @ X2)) = X2)) & ! [X4 : (($i > $i) > $o)] : ((! [X5 : ($i > $i)] : ((((X4 @ X5)) = $true) => ($true = ((X4 @ (^[Y0 : $i]: (X0 @ (X5 @ Y0))))))) & (((X4 @ X0)) = $true)) => (((X4 @ X1)) = $true))) => ? [X7 : $i] : (((X0 @ X7)) = X7))),
% 0.10/0.26 inference(fool_elimination,[],[f3])).
% 0.10/0.26 thf(f5,plain,(
% 0.10/0.26 ~ ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((? [X2 : $i] : (! [X3 : $i] : ((((X1 @ X3)) = X3) => (X2 = X3)) & (((X1 @ X2)) = X2)) & ! [X4 : (($i > $i) > $o)] : ((! [X5 : ($i > $i)] : ((((X4 @ X5)) = $true) => ($true = ((X4 @ (^[Y0 : $i]: (X0 @ (X5 @ Y0))))))) & (((X4 @ X0)) = $true)) => (((X4 @ X1)) = $true))) => ? [X6 : $i] : (((X0 @ X6)) = X6))),
% 0.10/0.26 inference(rectify,[],[f4])).
% 0.10/0.26 thf(f6,plain,(
% 0.10/0.26 ? [X0 : ($i > $i)] : ! [X1 : ($i > $i)] : (! [X6 : $i] : (((X0 @ X6)) != X6) & (? [X2 : $i] : (! [X3 : $i] : ((X2 = X3) | (((X1 @ X3)) != X3)) & (((X1 @ X2)) = X2)) & ! [X4 : (($i > $i) > $o)] : ((((X4 @ X1)) = $true) | (? [X5 : ($i > $i)] : (($true != ((X4 @ (^[Y0 : $i]: (X0 @ (X5 @ Y0)))))) & (((X4 @ X5)) = $true)) | (((X4 @ X0)) != $true)))))),
% 0.10/0.26 inference(ennf_transformation,[],[f5])).
% 0.10/0.26 thf(f7,plain,(
% 0.10/0.26 ? [X0 : ($i > $i)] : ! [X1 : ($i > $i)] : (! [X6 : $i] : (((X0 @ X6)) != X6) & ? [X2 : $i] : (! [X3 : $i] : ((X2 = X3) | (((X1 @ X3)) != X3)) & (((X1 @ X2)) = X2)) & ! [X4 : (($i > $i) > $o)] : ((((X4 @ X1)) = $true) | ? [X5 : ($i > $i)] : (($true != ((X4 @ (^[Y0 : $i]: (X0 @ (X5 @ Y0)))))) & (((X4 @ X5)) = $true)) | (((X4 @ X0)) != $true)))),
% 0.10/0.26 inference(flattening,[],[f6])).
% 0.10/0.26 thf(f8,plain,(
% 0.10/0.26 ? [X0 : ($i > $i)] : ! [X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) != X2) & ? [X3 : $i] : (! [X4 : $i] : ((X3 = X4) | (((X1 @ X4)) != X4)) & (((X1 @ X3)) = X3)) & ! [X5 : (($i > $i) > $o)] : (($true = ((X5 @ X1))) | ? [X6 : ($i > $i)] : (($true != ((X5 @ (^[Y0 : $i]: (X0 @ (X6 @ Y0)))))) & ($true = ((X5 @ X6)))) | ($true != ((X5 @ X0)))))),
% 0.10/0.26 inference(rectify,[],[f7])).
% 0.10/0.26 thf(f9,plain,(
% 0.10/0.26 ! [X1 : ($i > $i)] : (! [X2 : $i] : (((sK0 @ X2)) != X2) & (! [X4 : $i] : ((((sK1 @ X1)) = X4) | (((X1 @ X4)) != X4)) & (((sK1 @ X1)) = ((X1 @ (sK1 @ X1))))) & ! [X5 : (($i > $i) > $o)] : (($true = ((X5 @ X1))) | (($true != ((X5 @ (^[Y0 : $i]: (sK0 @ (sK2 @ X5 @ Y0)))))) & ($true = ((X5 @ (sK2 @ X5))))) | ($true != ((X5 @ sK0)))))),
% 0.10/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X6,sK2 @ X5),skolemize(X6,sK2 @ X5)],[f8])).
% 0.10/0.26 thf(f12,plain,(
% 0.10/0.26 ( ! [X1 : ($i > $i)] : ((((sK1 @ X1)) = ((X1 @ (sK1 @ X1))))) )),
% 0.10/0.26 inference(cnf_transformation,[],[f9])).
% 0.10/0.26 thf(f13,plain,(
% 0.10/0.26 ( ! [X1 : ($i > $i),X4 : $i] : ((((sK1 @ X1)) = X4) | (((X1 @ X4)) != X4)) )),
% 0.10/0.26 inference(cnf_transformation,[],[f9])).
% 0.10/0.26 thf(f14,plain,(
% 0.10/0.26 ( ! [X2 : $i] : ((((sK0 @ X2)) != X2)) )),
% 0.10/0.26 inference(cnf_transformation,[],[f9])).
% 0.10/0.26 thf(f20,plain,(
% 0.10/0.26 ( ! [X0 : $i] : ((((sK1 @ (^[Y0 : $i]: (Y0)))) = X0) | ((((^[Y0 : $i]: (Y0)) @ X0)) != X0)) )),
% 0.10/0.26 inference(constrained_superposition,[],[f12,f13])).
% 0.10/0.26 thf(f25,plain,(
% 0.10/0.26 ( ! [X0 : $i] : ((((sK1 @ (^[Y0 : $i]: (Y0)))) = X0) | (X0 != X0)) )),
% 0.10/0.26 inference(beta-eta_normalization,[],[f20])).
% 0.10/0.26 thf(f26,plain,(
% 0.10/0.26 ( ! [X0 : $i] : ((((sK1 @ (^[Y0 : $i]: (Y0)))) = X0)) )),
% 0.10/0.26 inference(trivial_inequality_removal,[],[f25])).
% 0.10/0.26 thf(f36,plain,(
% 0.10/0.26 ( ! [X0 : $i] : ((((sK1 @ (^[Y0 : $i]: (Y0)))) != X0)) )),
% 0.10/0.26 inference(constrained_superposition,[],[f14,f26])).
% 0.10/0.26 thf(f46,plain,(
% 0.10/0.26 $false),
% 0.10/0.26 inference(forward_subsumption_resolution,[],[f36,f26])).
% 0.10/0.26 % SZS output end Proof for theBenchmark
% 0.10/0.26 % (1384832)------------------------------
% 0.10/0.26 % (1384832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (1384832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (1384832)CaDiCaL version: 2.1.3
% 0.10/0.26 % (1384832)Termination reason: Refutation
% 0.10/0.26 % (1384832)Time elapsed: 0.003 s
% 0.10/0.26 % (1384832)Peak memory usage: 12 MB
% 0.10/0.26 % (1384832)Instructions burned: 4 (million)
% 0.10/0.26 % (1384823)Success in time 0.033 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------