%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU525^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 08:32:18 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU525^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n006.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:47:54 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.25 % (743775)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (743787)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3576312105:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.25 % (743787) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-743775-743787"...
% 0.10/0.25 % (743787)...printing done.
% 0.10/0.25 % (743783)% WARNING: option uhcvi not known.
% 0.10/0.25 % (743787)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% 0.10/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.25 thf(func_def_0, type, exu: (($i > $o) > $o)).
% 0.10/0.25 thf(func_def_2, type, exuE1: $o).
% 0.10/0.25 thf(func_def_3, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.10/0.25 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.10/0.25 thf(func_def_5, type, db1: !>[X0: $tType]:(X0)).
% 0.10/0.25 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.10/0.25 thf(func_def_7, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.10/0.25 thf(func_def_8, type, vIMP: ($o > $o > $o)).
% 0.10/0.25 thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
% 0.10/0.25 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.10/0.25 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.10/0.25 thf(func_def_14, type, sK0: ($i > $o)).
% 0.10/0.25 thf(func_def_15, type, sK1: ($i > $i)).
% 0.10/0.25 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.10/0.25 thf(func_def_18, type, sK3: (($i > $o) > $i)).
% 0.10/0.25 thf(func_def_19, type, sK4: (($i > $o) > $i > $i)).
% 0.10/0.25 thf(f1,axiom,(
% 0.10/0.25 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.10/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu)).
% 0.10/0.25 thf(f3,conjecture,(
% 0.10/0.25 exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X2 = X1)))),
% 0.10/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2)).
% 0.10/0.25 thf(f4,negated_conjecture,(
% 0.10/0.25 ~(exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X2 = X1))))),
% 0.10/0.25 inference(negated_conjecture,[status(cth)],[f3])).
% 0.10/0.25 thf(f5,plain,(
% 0.10/0.25 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.10/0.25 inference(rectify,[],[f1])).
% 0.10/0.25 thf(f6,plain,(
% 0.10/0.25 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.10/0.25 inference(fool_elimination,[],[f5])).
% 0.10/0.25 thf(f9,plain,(
% 0.10/0.25 ~(exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : ! [X3 : $i] : ((X0 @ X3) <=> (X2 = X3))))),
% 0.10/0.25 inference(rectify,[],[f4])).
% 0.10/0.25 thf(f10,plain,(
% 0.10/0.25 ~((exuE1 = $true) => ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X2 : $i] : ! [X3 : $i] : ((((X0 @ X3)) = $true) <=> (X2 = X3))))),
% 0.10/0.25 inference(fool_elimination,[],[f9])).
% 0.10/0.25 thf(f11,plain,(
% 0.10/0.25 ~((exuE1 = $true) => ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X1 : $i] : ! [X2 : $i] : ((((X0 @ X2)) = $true) <=> (X1 = X2))))),
% 0.10/0.25 inference(rectify,[],[f10])).
% 0.10/0.25 thf(f12,plain,(
% 0.10/0.25 ? [X0 : ($i > $o)] : (! [X1 : $i] : ? [X2 : $i] : ((((X0 @ X2)) = $true) <~> (X1 = X2)) & ($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0)))))) & (exuE1 = $true)),
% 0.10/0.25 inference(ennf_transformation,[],[f11])).
% 0.10/0.25 thf(f13,plain,(
% 0.10/0.25 ? [X0 : ($i > $o)] : (! [X1 : $i] : ? [X2 : $i] : (((X1 != X2) | (((X0 @ X2)) != $true)) & ((X1 = X2) | (((X0 @ X2)) = $true))) & ($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0)))))) & (exuE1 = $true)),
% 0.10/0.25 inference(nnf_transformation,[],[f12])).
% 0.10/0.25 thf(f14,plain,(
% 0.10/0.25 (! [X1 : $i] : (((((sK1 @ X1)) != X1) | ($true != ((sK0 @ (sK1 @ X1))))) & ((((sK1 @ X1)) = X1) | ($true = ((sK0 @ (sK1 @ X1)))))) & ($true = ((exu @ (^[Y0 : $i]: (sK0 @ Y0)))))) & (exuE1 = $true)),
% 0.10/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X2,sK1 @ X1)],[f13])).
% 0.10/0.25 thf(f15,plain,(
% 0.10/0.25 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.10/0.25 inference(cnf_transformation,[],[f6])).
% 0.10/0.25 thf(f18,plain,(
% 0.10/0.25 ($true = ((exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.10/0.25 inference(cnf_transformation,[],[f14])).
% 0.10/0.25 thf(f19,plain,(
% 0.10/0.25 ( ! [X1 : $i] : (($true = ((sK0 @ (sK1 @ X1)))) | (((sK1 @ X1)) = X1)) )),
% 0.10/0.25 inference(cnf_transformation,[],[f14])).
% 0.10/0.25 thf(f20,plain,(
% 0.10/0.25 ( ! [X1 : $i] : (($true != ((sK0 @ (sK1 @ X1)))) | (((sK1 @ X1)) != X1)) )),
% 0.10/0.25 inference(cnf_transformation,[],[f14])).
% 0.10/0.25 thf(f24,plain,(
% 0.10/0.25 ($true = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.10/0.25 inference(definition_unfolding,[],[f18,f15])).
% 0.10/0.25 thf(f25,plain,(
% 0.10/0.25 ($true = ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))))))),
% 0.10/0.25 inference(beta-eta_normalization,[],[f24])).
% 0.10/0.25 thf(f26,plain,(
% 0.10/0.25 ($true = (((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ sK2)))),
% 0.10/0.25 inference(sigma_proxy_clausification,[],[f25])).
% 0.10/0.25 thf(f27,plain,(
% 0.10/0.25 ($true = (((sK0 @ sK2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0)))))))),
% 0.10/0.25 inference(beta-eta_normalization,[],[f26])).
% 0.10/0.25 thf(f28,plain,(
% 0.10/0.25 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0))))))),
% 0.10/0.25 inference(and_proxy_clausification,[],[f27])).
% 0.10/0.25 thf(f29,plain,(
% 0.10/0.25 ($true = ((sK0 @ sK2)))),
% 0.10/0.25 inference(and_proxy_clausification,[],[f27])).
% 0.10/0.25 thf(f30,plain,(
% 0.10/0.25 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0))) @ X1)))) )),
% 0.10/0.25 inference(pi_proxy_clausification,[],[f28])).
% 0.10/0.25 thf(f31,plain,(
% 0.10/0.25 ( ! [X1 : $i] : (($true = (((sK0 @ X1) => (sK2 = X1))))) )),
% 0.10/0.25 inference(beta-eta_normalization,[],[f30])).
% 0.10/0.25 thf(f32,plain,(
% 0.10/0.25 ( ! [X1 : $i] : (($false = ((sK0 @ X1))) | ($true = ((sK2 = X1)))) )),
% 0.10/0.25 inference(imp_proxy_clausification,[],[f31])).
% 0.10/0.25 thf(f33,plain,(
% 0.10/0.25 ( ! [X1 : $i] : (($false = ((sK0 @ X1))) | (sK2 = X1)) )),
% 0.10/0.25 inference(equality_proxy_clausification,[],[f32])).
% 0.10/0.25 thf(f59,plain,(
% 0.10/0.25 ( ! [X0 : $i] : (($true = $false) | (((sK1 @ X0)) = X0) | (sK2 = ((sK1 @ X0)))) )),
% 0.10/0.25 inference(constrained_superposition,[],[f19,f33])).
% 0.10/0.25 thf(f61,plain,(
% 0.10/0.25 ( ! [X0 : $i] : ((((sK1 @ X0)) = X0) | (sK2 = ((sK1 @ X0)))) )),
% 0.10/0.25 inference(trivial_inequality_removal,[],[f59])).
% 0.10/0.25 thf(f72,plain,(
% 0.10/0.25 ( ! [X0 : $i] : ((sK2 != X0) | (sK2 = ((sK1 @ X0)))) )),
% 0.10/0.25 inference(equality_factoring,[],[f61])).
% 0.10/0.25 thf(f77,plain,(
% 0.10/0.25 (sK2 = ((sK1 @ sK2)))),
% 0.10/0.25 inference(equality_resolution,[],[f72])).
% 0.10/0.25 thf(f91,plain,(
% 0.10/0.25 ($true != ((sK0 @ sK2))) | (sK2 != sK2)),
% 0.10/0.25 inference(constrained_superposition,[],[f20,f77])).
% 0.10/0.25 thf(f92,plain,(
% 0.10/0.25 ($true != ((sK0 @ sK2)))),
% 0.10/0.25 inference(trivial_inequality_removal,[],[f91])).
% 0.10/0.25 thf(f93,plain,(
% 0.10/0.25 $false),
% 0.10/0.25 inference(forward_subsumption_resolution,[],[f92,f29])).
% 0.10/0.25 % SZS output end Proof for theBenchmark
% 0.10/0.25 % (743787)------------------------------
% 0.10/0.25 % (743787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (743787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (743787)CaDiCaL version: 2.1.3
% 0.10/0.25 % (743787)Termination reason: Refutation
% 0.10/0.25 % (743787)Time elapsed: 0.002 s
% 0.10/0.25 % (743787)Peak memory usage: 12 MB
% 0.10/0.25 % (743787)Instructions burned: 6 (million)
% 0.10/0.25 % (743775)Success in time 0.036 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------