%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO241^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:49:35 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO241^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:43:38 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.09/0.28 % (1527415)Will run a generic schedule for satisfiability detection.
% 0.09/0.28 % (1527423)dis+10_1_sil=32000:sp=arity:random_seed=3294043290:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.28 % (1527421)% WARNING: option uhcvi not known.
% 0.09/0.28 % (1527423) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1527415-1527423"...
% 0.09/0.28 % (1527423)...printing done.
% 0.09/0.28 % (1527423)Refutation found. Thanks to Tanya!
% 0.09/0.28 % SZS status Theorem for theBenchmark
% 0.09/0.28 % SZS output start Proof for theBenchmark
% 0.09/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.28 thf(func_def_3, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.28 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.09/0.28 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.09/0.28 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.28 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.28 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.28 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.28 thf(func_def_10, type, sK0: (($i > $o) > $i)).
% 0.09/0.28 thf(func_def_11, type, sK1: ($i > $o)).
% 0.09/0.28 thf(func_def_12, type, sK2: ($i > $i > $o)).
% 0.09/0.28 thf(func_def_13, type, sK3: ($i > $o)).
% 0.09/0.28 thf(func_def_15, type, sK5: ($i > $o)).
% 0.09/0.28 thf(f1,conjecture,(
% 0.09/0.28 ! [X0 : (($i > $o) > $i)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)) => ~ ? [X3 : ($i > $o)] : ((((X0 @ (^[X4 : $i] : (? [X5 : ($i > $o)] : ((X4 = ((X0 @ X5))) & ~(X5 @ (X0 @ X5))))))) = ((X0 @ X3))) & ~(X3 @ (X0 @ X3))))),
% 0.09/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM143_EXPAND)).
% 0.09/0.28 thf(f2,negated_conjecture,(
% 0.09/0.28 ~ ! [X0 : (($i > $o) > $i)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)) => ~ ? [X3 : ($i > $o)] : ((((X0 @ (^[X4 : $i] : (? [X5 : ($i > $o)] : ((X4 = ((X0 @ X5))) & ~(X5 @ (X0 @ X5))))))) = ((X0 @ X3))) & ~(X3 @ (X0 @ X3))))),
% 0.09/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.28 thf(f3,plain,(
% 0.09/0.28 ~ ! [X0 : (($i > $o) > $i)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)) => ~ ? [X3 : ($i > $o)] : ((((X0 @ (^[X4 : $i] : (? [X5 : ($i > $o)] : ((X4 = ((X0 @ X5))) & ~(X5 @ (X0 @ X5))))))) = ((X0 @ X3))) & ~(X3 @ (X0 @ X3))))),
% 0.09/0.28 inference(rectify,[],[f2])).
% 0.09/0.28 thf(f4,plain,(
% 0.09/0.28 ~ ! [X0 : (($i > $o) > $i)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)) => ~ ? [X3 : ($i > $o)] : ((((X0 @ X3)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))))) & ~ (((X3 @ (X0 @ X3))) = $true)))),
% 0.09/0.28 inference(fool_elimination,[],[f3])).
% 0.09/0.28 thf(f5,plain,(
% 0.09/0.28 ~ ! [X0 : (($i > $o) > $i)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)) => ~ ? [X3 : ($i > $o)] : ((((X0 @ X3)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))))) & (((X3 @ (X0 @ X3))) != $true)))),
% 0.09/0.28 inference(flattening,[],[f4])).
% 0.09/0.28 thf(f6,plain,(
% 0.09/0.28 ? [X0 : (($i > $o) > $i)] : (? [X3 : ($i > $o)] : ((((X0 @ X3)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))))) & (((X3 @ (X0 @ X3))) != $true)) & ! [X1 : ($i > $o),X2 : ($i > $o)] : ((X1 = X2) | (((X0 @ X1)) != ((X0 @ X2)))))),
% 0.09/0.28 inference(ennf_transformation,[],[f5])).
% 0.09/0.28 thf(f7,plain,(
% 0.09/0.28 ? [X0 : (($i > $o) > $i)] : (? [X1 : ($i > $o)] : ((((X0 @ X1)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))))) & ($true != ((X1 @ (X0 @ X1))))) & ! [X2 : ($i > $o),X3 : ($i > $o)] : ((X2 = X3) | (((X0 @ X2)) != ((X0 @ X3)))))),
% 0.09/0.28 inference(rectify,[],[f6])).
% 0.09/0.28 thf(f8,plain,(
% 0.09/0.28 ((((sK0 @ sK1)) = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))))) & ($true != ((sK1 @ (sK0 @ sK1))))) & ! [X2 : ($i > $o),X3 : ($i > $o)] : ((X2 = X3) | (((sK0 @ X2)) != ((sK0 @ X3))))),
% 0.09/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7])).
% 0.09/0.28 thf(f9,plain,(
% 0.09/0.28 ( ! [X2 : ($i > $o),X3 : ($i > $o)] : ((((sK0 @ X2)) != ((sK0 @ X3))) | (X2 = X3)) )),
% 0.09/0.28 inference(cnf_transformation,[],[f8])).
% 0.09/0.28 thf(f10,plain,(
% 0.09/0.28 ($true != ((sK1 @ (sK0 @ sK1))))),
% 0.09/0.28 inference(cnf_transformation,[],[f8])).
% 0.09/0.28 thf(f11,plain,(
% 0.09/0.28 (((sK0 @ sK1)) = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))))),
% 0.09/0.28 inference(cnf_transformation,[],[f8])).
% 0.09/0.28 thf(f13,definition,(
% 0.09/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.28 thf(f17,plain,(
% 0.09/0.28 ($true != $true) | (((sK1 @ (sK0 @ sK1))) = $false)),
% 0.09/0.28 inference(constrained_superposition,[],[f10,f13])).
% 0.09/0.28 thf(f19,plain,(
% 0.09/0.28 (((sK1 @ (sK0 @ sK1))) = $false)),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f17])).
% 0.09/0.28 thf(f27,plain,(
% 0.09/0.28 ( ! [X0 : ($i > $o)] : ((((sK0 @ sK1)) != ((sK0 @ X0))) | ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) = X0)) )),
% 0.09/0.28 inference(constrained_superposition,[],[f9,f11])).
% 0.09/0.28 thf(f29,plain,(
% 0.09/0.28 (sK1 = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))),
% 0.09/0.28 inference(equality_resolution,[],[f27])).
% 0.09/0.28 thf(f30,plain,(
% 0.09/0.28 ( ! [X1 : $i] : ((((sK1 @ X1)) = (((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) @ X1)))) )),
% 0.09/0.28 inference(argument_congruence,[],[f29])).
% 0.09/0.28 thf(f31,plain,(
% 0.09/0.28 ( ! [X1 : $i] : (($true = ((sK1 @ X1))) | ($false = (((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) @ X1)))) )),
% 0.09/0.28 inference(iff_proxy_clausification,[],[f30])).
% 0.09/0.28 thf(f40,plain,(
% 0.09/0.28 ( ! [X1 : $i] : (($true = ((sK1 @ X1))) | ($false = ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = X1))))))) )),
% 0.09/0.28 inference(beta-eta_normalization,[],[f31])).
% 0.09/0.28 thf(f41,plain,(
% 0.09/0.28 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((sK1 @ X1))) | ($false = (((^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = X1))) @ X2)))) )),
% 0.09/0.28 inference(pi_proxy_clausification,[],[f40])).
% 0.09/0.28 thf(f42,plain,(
% 0.09/0.28 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((sK1 @ X1))) | ($false = (((~ (X2 @ (sK0 @ X2))) & ((sK0 @ X2) = X1))))) )),
% 0.09/0.28 inference(beta-eta_normalization,[],[f41])).
% 0.09/0.28 thf(f43,plain,(
% 0.09/0.28 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((sK1 @ X1))) | ($false = (((sK0 @ X2) = X1))) | ($false = ((~ (X2 @ (sK0 @ X2)))))) )),
% 0.09/0.28 inference(and_proxy_clausification,[],[f42])).
% 0.09/0.28 thf(f44,plain,(
% 0.09/0.28 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((sK1 @ X1))) | (((sK0 @ X2)) != X1) | ($false = ((~ (X2 @ (sK0 @ X2)))))) )),
% 0.09/0.28 inference(equality_proxy_clausification,[],[f43])).
% 0.09/0.28 thf(f45,plain,(
% 0.09/0.28 ( ! [X2 : ($i > $o),X1 : $i] : ((((sK0 @ X2)) != X1) | ($true = ((sK1 @ X1))) | ($true = ((X2 @ (sK0 @ X2))))) )),
% 0.09/0.28 inference(not_proxy_clausification,[],[f44])).
% 0.09/0.28 thf(f47,plain,(
% 0.09/0.28 ( ! [X0 : ($i > $o)] : (($true = ((sK1 @ (sK0 @ X0)))) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.09/0.28 inference(equality_resolution,[],[f45])).
% 0.09/0.28 thf(f82,plain,(
% 0.09/0.28 ($true = $false) | ($true = $false)),
% 0.09/0.28 inference(constrained_superposition,[],[f47,f19])).
% 0.09/0.28 thf(f136,plain,(
% 0.09/0.28 ($true = $false)),
% 0.09/0.28 inference(duplicate_literal_removal,[],[f82])).
% 0.09/0.28 thf(f137,plain,(
% 0.09/0.28 $false),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f136])).
% 0.09/0.28 % SZS output end Proof for theBenchmark
% 0.09/0.28 % (1527423)------------------------------
% 0.09/0.28 % (1527423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1527423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1527423)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1527423)Termination reason: Refutation
% 0.09/0.28 % (1527423)Time elapsed: 0.004 s
% 0.09/0.28 % (1527423)Peak memory usage: 12 MB
% 0.09/0.28 % (1527423)Instructions burned: 9 (million)
% 0.09/0.28 % (1527415)Success in time 0.035 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------