%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO356^5 : 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 : n001.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 08:49:46 AM UTC 2026
% Result : Theorem 0.27s 0.37s
% Output : Refutation 0.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO356^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.26 % Computer : n001.cluster.edu
% 0.13/0.26 % Model : x86_64 x86_64
% 0.13/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.26 % Memory : 8046.5625MB
% 0.13/0.26 % OS : Linux 6.8.0-71-generic
% 0.13/0.26 % CPULimit : 300
% 0.13/0.26 % WCLimit : 300
% 0.13/0.26 % DateTime : Tue Sep 29 16:54:21 UTC 2026
% 0.13/0.27 % CPUTime :
% 0.13/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.27/0.32 Running first-order model finding
% 0.27/0.32 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
% 0.27/0.37 % (1498226)Will run a generic schedule for satisfiability detection.
% 0.27/0.37 % (1498237)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1152765460:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.27/0.37 % (1498237) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1498226-1498237"...
% 0.27/0.37 % (1498237)...printing done.
% 0.27/0.37 % (1498237)Refutation found. Thanks to Tanya!
% 0.27/0.37 % SZS status Theorem for theBenchmark
% 0.27/0.37 % SZS output start Proof for theBenchmark
% 0.27/0.37 thf(type_def_5, type, a: $tType).
% 0.27/0.37 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.27/0.37 thf(func_def_0, type, v: a).
% 0.27/0.37 thf(func_def_1, type, u: a).
% 0.27/0.37 thf(func_def_5, type, sK0: (a > $o)).
% 0.27/0.37 thf(func_def_6, type, sK1: ((a > a > $o) > a)).
% 0.27/0.37 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.27/0.37 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.27/0.37 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.27/0.37 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.27/0.37 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.27/0.37 thf(f1,conjecture,(
% 0.27/0.37 ! [X0 : (a > a > $o)] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : (a > $o)] : ((X2 @ u) => (X2 @ v))),
% 0.27/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE1LEIBEQ2_pme)).
% 0.27/0.37 thf(f2,negated_conjecture,(
% 0.27/0.37 ~(! [X0 : (a > a > $o)] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : (a > $o)] : ((X2 @ u) => (X2 @ v)))),
% 0.27/0.37 inference(negated_conjecture,[status(cth)],[f1])).
% 0.27/0.37 thf(f3,plain,(
% 0.27/0.37 ~(! [X0 : (a > a > $o)] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : (a > $o)] : ((X2 @ u) => (X2 @ v)))),
% 0.27/0.37 inference(rectify,[],[f2])).
% 0.27/0.37 thf(f4,plain,(
% 0.27/0.37 ~(! [X0 : (a > a > $o)] : (! [X1 : a] : (((X0 @ X1 @ X1)) = $true) => (((X0 @ u @ v)) = $true)) => ! [X2 : (a > $o)] : ((((X2 @ u)) = $true) => (((X2 @ v)) = $true)))),
% 0.27/0.37 inference(fool_elimination,[],[f3])).
% 0.27/0.37 thf(f5,plain,(
% 0.27/0.37 ? [X2 : (a > $o)] : ((((X2 @ v)) != $true) & (((X2 @ u)) = $true)) & ! [X0 : (a > a > $o)] : ((((X0 @ u @ v)) = $true) | ? [X1 : a] : (((X0 @ X1 @ X1)) != $true))),
% 0.27/0.37 inference(ennf_transformation,[],[f4])).
% 0.27/0.37 thf(f6,plain,(
% 0.27/0.37 ? [X0 : (a > $o)] : (($true != ((X0 @ v))) & ($true = ((X0 @ u)))) & ! [X1 : (a > a > $o)] : (($true = ((X1 @ u @ v))) | ? [X2 : a] : ($true != ((X1 @ X2 @ X2))))),
% 0.27/0.37 inference(rectify,[],[f5])).
% 0.27/0.37 thf(f7,plain,(
% 0.27/0.37 (($true != ((sK0 @ v))) & ($true = ((sK0 @ u)))) & ! [X1 : (a > a > $o)] : (($true = ((X1 @ u @ v))) | ($true != ((X1 @ (sK1 @ X1) @ (sK1 @ X1)))))),
% 0.27/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X2,sK1 @ X1)],[f6])).
% 0.27/0.37 thf(f8,plain,(
% 0.27/0.37 ( ! [X1 : (a > a > $o)] : (($true != ((X1 @ (sK1 @ X1) @ (sK1 @ X1)))) | ($true = ((X1 @ u @ v)))) )),
% 0.27/0.37 inference(cnf_transformation,[],[f7])).
% 0.27/0.37 thf(f9,plain,(
% 0.27/0.37 ($true = ((sK0 @ u)))),
% 0.27/0.37 inference(cnf_transformation,[],[f7])).
% 0.27/0.37 thf(f10,plain,(
% 0.27/0.37 ($true != ((sK0 @ v)))),
% 0.27/0.37 inference(cnf_transformation,[],[f7])).
% 0.27/0.37 thf(f13,plain,(
% 0.27/0.37 ($true != (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ u @ v)))),
% 0.27/0.37 inference(primitive_instantiation,[],[f8])).
% 0.27/0.37 thf(f33,plain,(
% 0.27/0.37 ($true != (((sK1 @ =) = (sK1 @ =)))) | ($true = ((u = v)))),
% 0.27/0.37 inference(beta-eta_normalization,[],[f13])).
% 0.27/0.37 thf(f34,plain,(
% 0.27/0.37 (((sK1 @ =)) != ((sK1 @ =))) | ($true = ((u = v)))),
% 0.27/0.37 inference(equality_proxy_clausification,[],[f33])).
% 0.27/0.37 thf(f35,plain,(
% 0.27/0.37 (((sK1 @ =)) != ((sK1 @ =))) | (u = v)),
% 0.27/0.37 inference(equality_proxy_clausification,[],[f34])).
% 0.27/0.37 thf(f36,plain,(
% 0.27/0.37 (u = v)),
% 0.27/0.37 inference(trivial_inequality_removal,[],[f35])).
% 0.27/0.37 thf(f37,plain,(
% 0.27/0.37 ($true = ((sK0 @ v)))),
% 0.27/0.37 inference(constrained_superposition,[],[f9,f36])).
% 0.27/0.37 thf(f38,plain,(
% 0.27/0.37 ($true != $true)),
% 0.27/0.37 inference(constrained_superposition,[],[f10,f37])).
% 0.27/0.37 thf(f42,plain,(
% 0.27/0.37 $false),
% 0.27/0.37 inference(trivial_inequality_removal,[],[f38])).
% 0.27/0.37 % SZS output end Proof for theBenchmark
% 0.27/0.37 % (1498237)------------------------------
% 0.27/0.37 % (1498237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.37 % (1498237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.37 % (1498237)CaDiCaL version: 2.1.3
% 0.27/0.37 % (1498237)Termination reason: Refutation
% 0.27/0.37 % (1498237)Time elapsed: 0.003 s
% 0.27/0.37 % (1498237)Peak memory usage: 12 MB
% 0.27/0.37 % (1498237)Instructions burned: 3 (million)
% 0.27/0.37 % (1498226)Success in time 0.04 s
% 0.27/0.37 % Vampire exiting
%------------------------------------------------------------------------------