%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET638^5 : 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 : n014.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 08:23:46 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET638^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:40:15 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.09/0.25 % (2672248)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (2672262)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=778752353:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.09/0.25 % (2672262)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (2672262) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2672248-2672262"...
% 0.09/0.25 % (2672259)% WARNING: option uhcvi not known.
% 0.09/0.25 % (2672262)...printing done.
% 0.09/0.25 % (2672262)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, a: $tType).
% 0.09/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_3, type, vAND: ($o > $o > $o)).
% 0.09/0.25 thf(func_def_4, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_5, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.25 thf(func_def_6, type, sK0: (a > $o)).
% 0.09/0.25 thf(func_def_7, type, sK1: (a > $o)).
% 0.09/0.25 thf(func_def_8, type, sK2: (a > $o)).
% 0.09/0.25 thf(func_def_9, type, sK3: a).
% 0.09/0.25 thf(f1,conjecture,(
% 0.09/0.25 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[X3 : a] : ((X2 @ X3) & (X0 @ X3))) = (^[X3 : a] : ($false))) & ! [X3 : a] : ((X0 @ X3) => ((X2 @ X3) | (X1 @ X3)))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)))),
% 0.09/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_120_pme)).
% 0.09/0.25 thf(f2,negated_conjecture,(
% 0.09/0.25 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[X3 : a] : ((X2 @ X3) & (X0 @ X3))) = (^[X3 : a] : ($false))) & ! [X3 : a] : ((X0 @ X3) => ((X2 @ X3) | (X1 @ X3)))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.25 thf(f3,plain,(
% 0.09/0.25 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[X3 : a] : ((X2 @ X3) & (X0 @ X3))) = (^[X4 : a] : ($false))) & ! [X5 : a] : ((X0 @ X5) => ((X2 @ X5) | (X1 @ X5)))) => ! [X6 : a] : ((X0 @ X6) => (X1 @ X6)))),
% 0.09/0.25 inference(rectify,[],[f2])).
% 0.09/0.25 thf(f4,plain,(
% 0.09/0.25 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[Y0 : a]: ((X0 @ Y0) & (X2 @ Y0))) = (^[Y0 : a]: ($false))) & ! [X5 : a] : ((((X0 @ X5)) = $true) => ((((X2 @ X5)) = $true) | (((X1 @ X5)) = $true)))) => ! [X6 : a] : ((((X0 @ X6)) = $true) => (((X1 @ X6)) = $true)))),
% 0.09/0.25 inference(fool_elimination,[],[f3])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[Y0 : a]: ((X0 @ Y0) & (X2 @ Y0))) = (^[Y0 : a]: ($false))) & ! [X3 : a] : ((((X0 @ X3)) = $true) => ((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true)))) => ! [X4 : a] : (($true = ((X0 @ X4))) => ($true = ((X1 @ X4)))))),
% 0.09/0.25 inference(rectify,[],[f4])).
% 0.09/0.25 thf(f6,plain,(
% 0.09/0.25 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X4 : a] : (($true != ((X1 @ X4))) & ($true = ((X0 @ X4)))) & (((^[Y0 : a]: ((X0 @ Y0) & (X2 @ Y0))) = (^[Y0 : a]: ($false))) & ! [X3 : a] : (((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true)) | (((X0 @ X3)) != $true))))),
% 0.09/0.25 inference(ennf_transformation,[],[f5])).
% 0.09/0.25 thf(f7,plain,(
% 0.09/0.25 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X4 : a] : (($true != ((X1 @ X4))) & ($true = ((X0 @ X4)))) & ((^[Y0 : a]: ((X0 @ Y0) & (X2 @ Y0))) = (^[Y0 : a]: ($false))) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true) | (((X0 @ X3)) != $true)))),
% 0.09/0.25 inference(flattening,[],[f6])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : ((((X1 @ X3)) != $true) & (((X0 @ X3)) = $true)) & ((^[Y0 : a]: ((X0 @ Y0) & (X2 @ Y0))) = (^[Y0 : a]: ($false))) & ! [X4 : a] : (($true = ((X2 @ X4))) | ($true = ((X1 @ X4))) | ($true != ((X0 @ X4)))))),
% 0.09/0.25 inference(rectify,[],[f7])).
% 0.09/0.25 thf(f9,plain,(
% 0.09/0.25 (($true != ((sK1 @ sK3))) & ($true = ((sK0 @ sK3)))) & ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK2 @ Y0)))) & ! [X4 : a] : (($true = ((sK2 @ X4))) | ($true = ((sK1 @ X4))) | ($true != ((sK0 @ X4))))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f8])).
% 0.09/0.25 thf(f10,plain,(
% 0.09/0.25 ( ! [X4 : a] : (($true = ((sK2 @ X4))) | ($true = ((sK1 @ X4))) | ($true != ((sK0 @ X4)))) )),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f11,plain,(
% 0.09/0.25 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK2 @ Y0))))),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f12,plain,(
% 0.09/0.25 ($true = ((sK0 @ sK3)))),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f13,plain,(
% 0.09/0.25 ($true != ((sK1 @ sK3)))),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f15,definition,(
% 0.09/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.25 thf(f16,plain,(
% 0.09/0.25 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = (((^[Y0 : a]: ((sK0 @ Y0) & (sK2 @ Y0))) @ X1)))) )),
% 0.09/0.25 inference(argument_congruence,[],[f11])).
% 0.09/0.25 thf(f17,plain,(
% 0.09/0.25 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ($false)) @ X1))) | ($false = (((^[Y0 : a]: ((sK0 @ Y0) & (sK2 @ Y0))) @ X1)))) )),
% 0.09/0.25 inference(iff_proxy_clausification,[],[f16])).
% 0.09/0.25 thf(f22,plain,(
% 0.09/0.25 ( ! [X1 : a] : (($true = $false) | ($false = (((sK0 @ X1) & (sK2 @ X1))))) )),
% 0.09/0.25 inference(beta-eta_normalization,[],[f17])).
% 0.09/0.25 thf(f23,plain,(
% 0.09/0.25 ( ! [X1 : a] : (($true = $false) | ($false = ((sK2 @ X1))) | ($false = ((sK0 @ X1)))) )),
% 0.09/0.25 inference(and_proxy_clausification,[],[f22])).
% 0.09/0.25 thf(f24,plain,(
% 0.09/0.25 ( ! [X1 : a] : (($false = ((sK2 @ X1))) | ($false = ((sK0 @ X1)))) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f23])).
% 0.09/0.25 thf(f39,plain,(
% 0.09/0.25 ( ! [X0 : a] : (($true = $false) | ($true = ((sK1 @ X0))) | ($true != ((sK0 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.09/0.25 inference(constrained_superposition,[],[f10,f24])).
% 0.09/0.25 thf(f40,plain,(
% 0.09/0.25 ( ! [X0 : a] : (($true = ((sK1 @ X0))) | ($true != ((sK0 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f39])).
% 0.09/0.25 thf(f43,plain,(
% 0.09/0.25 ( ! [X0 : a] : (($true = ((sK1 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f40,f15])).
% 0.09/0.25 thf(f47,plain,(
% 0.09/0.25 ($true != $true) | ($false = ((sK0 @ sK3)))),
% 0.09/0.25 inference(constrained_superposition,[],[f13,f43])).
% 0.09/0.25 thf(f48,plain,(
% 0.09/0.25 ($false = ((sK0 @ sK3)))),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f47])).
% 0.09/0.25 thf(f53,plain,(
% 0.09/0.25 ($true = $false)),
% 0.09/0.25 inference(constrained_superposition,[],[f12,f48])).
% 0.09/0.25 thf(f54,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f53])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (2672262)------------------------------
% 0.09/0.25 % (2672262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (2672262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (2672262)CaDiCaL version: 2.1.3
% 0.09/0.25 % (2672262)Termination reason: Refutation
% 0.09/0.25 % (2672262)Time elapsed: 0.002 s
% 0.09/0.25 % (2672262)Peak memory usage: 12 MB
% 0.09/0.25 % (2672262)Instructions burned: 3 (million)
% 0.09/0.25 % (2672248)Success in time 0.018 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------