%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU499^2 : 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 : n012.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 08:32:12 AM UTC 2026
% Result : Theorem 0.07s 0.17s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU499^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.12 % Computer : n012.cluster.edu
% 0.07/0.12 % Model : x86_64 x86_64
% 0.07/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.12 % Memory : 8046.5625MB
% 0.07/0.12 % OS : Linux 6.8.0-71-generic
% 0.07/0.12 % CPULimit : 300
% 0.07/0.12 % WCLimit : 300
% 0.07/0.12 % DateTime : Tue Sep 29 13:46:04 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.13 Running first-order model finding
% 0.07/0.13 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
% 0.07/0.17 % (123833)Will run a generic schedule for satisfiability detection.
% 0.07/0.17 % (123839)% WARNING: option uhcvi not known.
% 0.07/0.17 % (123839)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3265271912:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.17 % (123840)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1719697922:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.17 % (123838)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3761103707_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.17 % (123841)dis+10_1_sil=32000:sp=arity:random_seed=2516256440:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.17 % (123839)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.17 % Exception at run slice level
% 0.07/0.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.17 % (123839)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.17 % (123841) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-123833-123841"...
% 0.07/0.17 % (123840) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-123833-123840"...
% 0.07/0.17 % (123839) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-123833-123839"...
% 0.07/0.17 % (123841)...printing done.
% 0.07/0.17 % (123840)...printing done.
% 0.07/0.17 % (123841)Refutation found. Thanks to Tanya!
% 0.07/0.17 % SZS status Theorem for theBenchmark
% 0.07/0.17 % SZS output start Proof for theBenchmark
% 0.07/0.17 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.17 thf(func_def_0, type, exu: (($i > $o) > $o)).
% 0.07/0.17 thf(func_def_2, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.17 thf(func_def_3, type, vAND: ($o > $o > $o)).
% 0.07/0.17 thf(func_def_4, type, db1: !>[X0: $tType]:(X0)).
% 0.07/0.17 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.17 thf(func_def_6, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.17 thf(func_def_7, type, vIMP: ($o > $o > $o)).
% 0.07/0.17 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.07/0.17 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.07/0.17 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.17 thf(func_def_13, type, sK0: ($i > $o)).
% 0.07/0.17 thf(func_def_14, type, sK1: ($i > $i)).
% 0.07/0.17 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.07/0.17 thf(f1,axiom,(
% 0.07/0.17 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.07/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu)).
% 0.07/0.17 thf(f2,conjecture,(
% 0.07/0.17 ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))),
% 0.07/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1)).
% 0.07/0.17 thf(f3,negated_conjecture,(
% 0.07/0.17 ~ ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))),
% 0.07/0.17 inference(negated_conjecture,[status(cth)],[f2])).
% 0.07/0.17 thf(f4,plain,(
% 0.07/0.17 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.07/0.17 inference(rectify,[],[f1])).
% 0.07/0.17 thf(f5,plain,(
% 0.07/0.17 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.07/0.17 inference(fool_elimination,[],[f4])).
% 0.07/0.17 thf(f6,plain,(
% 0.07/0.17 ~ ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : (! [X3 : $i] : ((X0 @ X3) => (X2 = X3)) & (X0 @ X2)))),
% 0.07/0.17 inference(rectify,[],[f3])).
% 0.07/0.17 thf(f7,plain,(
% 0.07/0.17 ~ ! [X0 : ($i > $o)] : ((((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ? [X2 : $i] : (! [X3 : $i] : ((((X0 @ X3)) = $true) => (X2 = X3)) & (((X0 @ X2)) = $true)))),
% 0.07/0.17 inference(fool_elimination,[],[f6])).
% 0.07/0.17 thf(f8,plain,(
% 0.07/0.17 ~ ! [X0 : ($i > $o)] : ((((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ? [X1 : $i] : (! [X2 : $i] : ((((X0 @ X2)) = $true) => (X1 = X2)) & (((X0 @ X1)) = $true)))),
% 0.07/0.17 inference(rectify,[],[f7])).
% 0.07/0.17 thf(f9,plain,(
% 0.07/0.17 ? [X0 : ($i > $o)] : (! [X1 : $i] : (? [X2 : $i] : ((X1 != X2) & (((X0 @ X2)) = $true)) | (((X0 @ X1)) != $true)) & (((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true))),
% 0.07/0.17 inference(ennf_transformation,[],[f8])).
% 0.07/0.17 thf(f10,plain,(
% 0.07/0.17 ! [X1 : $i] : (((((sK1 @ X1)) != X1) & ($true = ((sK0 @ (sK1 @ X1))))) | ($true != ((sK0 @ X1)))) & ($true = ((exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.07/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X2,sK1 @ X1)],[f9])).
% 0.07/0.17 thf(f11,plain,(
% 0.07/0.17 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.07/0.17 inference(cnf_transformation,[],[f5])).
% 0.07/0.17 thf(f12,plain,(
% 0.07/0.17 ($true = ((exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.07/0.17 inference(cnf_transformation,[],[f10])).
% 0.07/0.17 thf(f13,plain,(
% 0.07/0.17 ( ! [X1 : $i] : (($true != ((sK0 @ X1))) | ($true = ((sK0 @ (sK1 @ X1))))) )),
% 0.07/0.17 inference(cnf_transformation,[],[f10])).
% 0.07/0.17 thf(f14,plain,(
% 0.07/0.17 ( ! [X1 : $i] : (($true != ((sK0 @ X1))) | (((sK1 @ X1)) != X1)) )),
% 0.07/0.17 inference(cnf_transformation,[],[f10])).
% 0.07/0.17 thf(f17,plain,(
% 0.07/0.17 ($true = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.07/0.17 inference(definition_unfolding,[],[f12,f11])).
% 0.07/0.17 thf(f18,plain,(
% 0.07/0.17 ($true = ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))))))),
% 0.07/0.17 inference(beta-eta_normalization,[],[f17])).
% 0.07/0.17 thf(f19,plain,(
% 0.07/0.17 ($true = (((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ sK2)))),
% 0.07/0.17 inference(sigma_proxy_clausification,[],[f18])).
% 0.07/0.17 thf(f20,plain,(
% 0.07/0.17 ($true = (((sK0 @ sK2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0)))))))),
% 0.07/0.17 inference(beta-eta_normalization,[],[f19])).
% 0.07/0.17 thf(f21,plain,(
% 0.07/0.17 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0))))))),
% 0.07/0.17 inference(and_proxy_clausification,[],[f20])).
% 0.07/0.17 thf(f22,plain,(
% 0.07/0.17 ($true = ((sK0 @ sK2)))),
% 0.07/0.17 inference(and_proxy_clausification,[],[f20])).
% 0.07/0.17 thf(f23,plain,(
% 0.07/0.17 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0))) @ X1)))) )),
% 0.07/0.17 inference(pi_proxy_clausification,[],[f21])).
% 0.07/0.17 thf(f24,plain,(
% 0.07/0.17 ( ! [X1 : $i] : (($true = (((sK0 @ X1) => (sK2 = X1))))) )),
% 0.07/0.17 inference(beta-eta_normalization,[],[f23])).
% 0.07/0.17 thf(f25,plain,(
% 0.07/0.17 ( ! [X1 : $i] : ((((sK0 @ X1)) = $false) | ($true = ((sK2 = X1)))) )),
% 0.07/0.17 inference(imp_proxy_clausification,[],[f24])).
% 0.07/0.17 thf(f26,plain,(
% 0.07/0.17 ( ! [X1 : $i] : ((((sK0 @ X1)) = $false) | (sK2 = X1)) )),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f25])).
% 0.07/0.17 thf(f27,plain,(
% 0.07/0.17 ($true != $true) | (sK2 != ((sK1 @ sK2)))),
% 0.07/0.17 inference(constrained_superposition,[],[f14,f22])).
% 0.07/0.17 thf(f28,plain,(
% 0.07/0.17 (sK2 != ((sK1 @ sK2)))),
% 0.07/0.17 inference(trivial_inequality_removal,[],[f27])).
% 0.07/0.17 thf(f29,plain,(
% 0.07/0.17 ($true != $true) | ($true = ((sK0 @ (sK1 @ sK2))))),
% 0.07/0.17 inference(constrained_superposition,[],[f13,f22])).
% 0.07/0.17 thf(f30,plain,(
% 0.07/0.17 ($true = ((sK0 @ (sK1 @ sK2))))),
% 0.07/0.17 inference(trivial_inequality_removal,[],[f29])).
% 0.07/0.17 thf(f60,plain,(
% 0.07/0.17 ($true = $false) | (sK2 = ((sK1 @ sK2)))),
% 0.07/0.17 inference(constrained_superposition,[],[f26,f30])).
% 0.07/0.17 thf(f65,plain,(
% 0.07/0.17 (sK2 = ((sK1 @ sK2)))),
% 0.07/0.17 inference(trivial_inequality_removal,[],[f60])).
% 0.07/0.17 thf(f67,plain,(
% 0.07/0.17 $false),
% 0.07/0.17 inference(forward_subsumption_resolution,[],[f65,f28])).
% 0.07/0.17 % SZS output end Proof for theBenchmark
% 0.07/0.17 % (123841)------------------------------
% 0.07/0.17 % (123841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.17 % (123841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.17 % (123841)CaDiCaL version: 2.1.3
% 0.07/0.17 % (123841)Termination reason: Refutation
% 0.07/0.17 % (123841)Time elapsed: 0.002 s
% 0.07/0.17 % (123841)Peak memory usage: 12 MB
% 0.07/0.17 % (123841)Instructions burned: 4 (million)
% 0.07/0.17 % (123833)Success in time 0.029 s
% 0.07/0.17 % Vampire exiting
%------------------------------------------------------------------------------