%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM753^1 : 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 : n019.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 08:19:27 AM UTC 2026
% Result : Theorem 0.21s 0.33s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM753^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n019.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 12:50:48 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.22 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
% 0.21/0.33 % (710311)Will run a generic schedule for satisfiability detection.
% 0.21/0.33 % (710326)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1760305173:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.33 % (710324)% WARNING: option uhcvi not known.
% 0.21/0.33 % (710323)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2932781101_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.33 % (710327)dis+10_1_sil=32000:sp=arity:random_seed=2629091965:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.33 % (710324)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4127004616:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.33 % (710328)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2077891860:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.33 % Exception at run slice level
% 0.21/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.33 % (710324)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.33 % (710329)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2415726505:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.33 % (710330)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3622926116:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.33 % (710324)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.33 % (710328)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.33 % (710342)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1987134623:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.33 % Exception at run slice level
% 0.21/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.33 % (710329) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-710311-710329"...
% 0.21/0.33 % (710350)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1172025178:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.33 % (710328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-710311-710328"...
% 0.21/0.33 % (710329)...printing done.
% 0.21/0.33 % (710329)Refutation found. Thanks to Tanya!
% 0.21/0.33 % SZS status Theorem for theBenchmark
% 0.21/0.33 % SZS output start Proof for theBenchmark
% 0.21/0.33 thf(type_def_5, type, frac: $tType).
% 0.21/0.33 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.33 thf(func_def_0, type, x: frac).
% 0.21/0.33 thf(func_def_1, type, y: frac).
% 0.21/0.33 thf(func_def_2, type, z: frac).
% 0.21/0.33 thf(func_def_3, type, u: frac).
% 0.21/0.33 thf(func_def_4, type, eq: (frac > frac > $o)).
% 0.21/0.33 thf(func_def_6, type, moref: (frac > frac > $o)).
% 0.21/0.33 thf(func_def_7, type, pf: (frac > frac > frac)).
% 0.21/0.33 thf(f1,axiom,(
% 0.21/0.33 (eq @ x @ y)),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',e)).
% 0.21/0.33 thf(f2,axiom,(
% 0.21/0.33 (moref @ z @ u)),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',m)).
% 0.21/0.33 thf(f3,axiom,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44)).
% 0.21/0.33 thf(f4,axiom,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X2 @ X0) @ (pf @ X2 @ X1)))),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62d)).
% 0.21/0.33 thf(f5,axiom,(
% 0.21/0.33 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37)).
% 0.21/0.33 thf(f6,axiom,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56)).
% 0.21/0.33 thf(f7,conjecture,(
% 0.21/0.33 (moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62g)).
% 0.21/0.33 thf(f8,negated_conjecture,(
% 0.21/0.33 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.21/0.33 inference(negated_conjecture,[status(cth)],[f7])).
% 0.21/0.33 thf(f9,plain,(
% 0.21/0.33 (eq @ x @ y)),
% 0.21/0.33 inference(rectify,[],[f1])).
% 0.21/0.33 thf(f10,plain,(
% 0.21/0.33 (((eq @ x @ y)) = $true)),
% 0.21/0.33 inference(fool_elimination,[],[f9])).
% 0.21/0.33 thf(f11,plain,(
% 0.21/0.33 (moref @ z @ u)),
% 0.21/0.33 inference(rectify,[],[f2])).
% 0.21/0.33 thf(f12,plain,(
% 0.21/0.33 (((moref @ z @ u)) = $true)),
% 0.21/0.33 inference(fool_elimination,[],[f11])).
% 0.21/0.33 thf(f13,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.21/0.33 inference(rectify,[],[f3])).
% 0.21/0.33 thf(f14,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X0 @ X1)) = $true) => ((((eq @ X0 @ X2)) = $true) => ((((eq @ X1 @ X3)) = $true) => (((moref @ X2 @ X3)) = $true))))),
% 0.21/0.33 inference(fool_elimination,[],[f13])).
% 0.21/0.33 thf(f15,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X2 @ X0) @ (pf @ X2 @ X1)))),
% 0.21/0.33 inference(rectify,[],[f4])).
% 0.21/0.33 thf(f16,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac] : ((((moref @ X0 @ X1)) = $true) => (((moref @ (pf @ X2 @ X0) @ (pf @ X2 @ X1))) = $true))),
% 0.21/0.33 inference(fool_elimination,[],[f15])).
% 0.21/0.33 thf(f17,plain,(
% 0.21/0.33 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.21/0.33 inference(rectify,[],[f5])).
% 0.21/0.33 thf(f18,plain,(
% 0.21/0.33 ! [X0 : frac] : (((eq @ X0 @ X0)) = $true)),
% 0.21/0.33 inference(fool_elimination,[],[f17])).
% 0.21/0.33 thf(f19,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.21/0.33 inference(rectify,[],[f6])).
% 0.21/0.33 thf(f20,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ X0 @ X1)) = $true) => ((((eq @ X2 @ X3)) = $true) => (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)))),
% 0.21/0.33 inference(fool_elimination,[],[f19])).
% 0.21/0.33 thf(f21,plain,(
% 0.21/0.33 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.21/0.33 inference(rectify,[],[f8])).
% 0.21/0.33 thf(f22,plain,(
% 0.21/0.33 ~ (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $true)),
% 0.21/0.33 inference(fool_elimination,[],[f21])).
% 0.21/0.33 thf(f23,plain,(
% 0.21/0.33 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) != $true)),
% 0.21/0.33 inference(flattening,[],[f22])).
% 0.21/0.33 thf(f24,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((((moref @ X2 @ X3)) = $true) | (((eq @ X1 @ X3)) != $true)) | (((eq @ X0 @ X2)) != $true)) | (((moref @ X0 @ X1)) != $true))),
% 0.21/0.33 inference(ennf_transformation,[],[f14])).
% 0.21/0.33 thf(f25,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X2 @ X3)) = $true) | (((eq @ X1 @ X3)) != $true) | (((eq @ X0 @ X2)) != $true) | (((moref @ X0 @ X1)) != $true))),
% 0.21/0.33 inference(flattening,[],[f24])).
% 0.21/0.33 thf(f26,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac] : ((((moref @ (pf @ X2 @ X0) @ (pf @ X2 @ X1))) = $true) | (((moref @ X0 @ X1)) != $true))),
% 0.21/0.33 inference(ennf_transformation,[],[f16])).
% 0.21/0.33 thf(f27,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X2 @ X3)) != $true)) | (((eq @ X0 @ X1)) != $true))),
% 0.21/0.33 inference(ennf_transformation,[],[f20])).
% 0.21/0.33 thf(f28,plain,(
% 0.21/0.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X2 @ X3)) != $true) | (((eq @ X0 @ X1)) != $true))),
% 0.21/0.33 inference(flattening,[],[f27])).
% 0.21/0.33 thf(f29,plain,(
% 0.21/0.33 (((eq @ x @ y)) = $true)),
% 0.21/0.33 inference(cnf_transformation,[],[f10])).
% 0.21/0.33 thf(f30,plain,(
% 0.21/0.33 (((moref @ z @ u)) = $true)),
% 0.21/0.33 inference(cnf_transformation,[],[f12])).
% 0.21/0.33 thf(f31,plain,(
% 0.21/0.33 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((eq @ X1 @ X3)) != $true) | (((moref @ X2 @ X3)) = $true) | (((eq @ X0 @ X2)) != $true) | (((moref @ X0 @ X1)) != $true)) )),
% 0.21/0.33 inference(cnf_transformation,[],[f25])).
% 0.21/0.33 thf(f32,plain,(
% 0.21/0.33 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((moref @ (pf @ X2 @ X0) @ (pf @ X2 @ X1))) = $true)) )),
% 0.21/0.33 inference(cnf_transformation,[],[f26])).
% 0.21/0.33 thf(f33,plain,(
% 0.21/0.33 ( ! [X0 : frac] : ((((eq @ X0 @ X0)) = $true)) )),
% 0.21/0.33 inference(cnf_transformation,[],[f18])).
% 0.21/0.33 thf(f34,plain,(
% 0.21/0.33 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((eq @ X2 @ X3)) != $true) | (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X0 @ X1)) != $true)) )),
% 0.21/0.33 inference(cnf_transformation,[],[f28])).
% 0.21/0.33 thf(f35,plain,(
% 0.21/0.33 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) != $true)),
% 0.21/0.33 inference(cnf_transformation,[],[f23])).
% 0.21/0.33 thf(f37,definition,(
% 0.21/0.33 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.33 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.33 thf(f52,plain,(
% 0.21/0.33 ( ! [X0 : frac] : (($true != $true) | ($true = ((moref @ (pf @ X0 @ z) @ (pf @ X0 @ u))))) )),
% 0.21/0.33 inference(constrained_superposition,[],[f32,f30])).
% 0.21/0.33 thf(f53,plain,(
% 0.21/0.33 ( ! [X0 : frac] : (($true = ((moref @ (pf @ X0 @ z) @ (pf @ X0 @ u))))) )),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f52])).
% 0.21/0.33 thf(f57,plain,(
% 0.21/0.33 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true = ((moref @ X2 @ X1))) | ($true != ((eq @ X3 @ X2))) | ($true != ((moref @ X3 @ X0))) | (((eq @ X0 @ X1)) = $false)) )),
% 0.21/0.33 inference(constrained_superposition,[],[f31,f37])).
% 0.21/0.33 thf(f62,plain,(
% 0.21/0.33 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X3 @ X2))) | ($true = ((moref @ X2 @ X1))) | ($true != ((moref @ X3 @ X0))) | (((eq @ X0 @ X1)) = $false)) )),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f57])).
% 0.21/0.33 thf(f70,plain,(
% 0.21/0.33 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true = ((eq @ (pf @ X1 @ X0) @ (pf @ X2 @ X0)))) | ($true != ((eq @ X1 @ X2)))) )),
% 0.21/0.33 inference(constrained_superposition,[],[f34,f33])).
% 0.21/0.33 thf(f71,plain,(
% 0.21/0.33 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X1 @ X2))) | ($true = ((eq @ (pf @ X1 @ X0) @ (pf @ X2 @ X0))))) )),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f70])).
% 0.21/0.33 thf(f101,plain,(
% 0.21/0.33 ( ! [X0 : frac] : (($true != $true) | ($true = ((eq @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.21/0.33 inference(constrained_superposition,[],[f71,f29])).
% 0.21/0.33 thf(f104,plain,(
% 0.21/0.33 ( ! [X0 : frac] : (($true = ((eq @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f101])).
% 0.21/0.33 thf(f121,plain,(
% 0.21/0.33 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | (((moref @ X0 @ X1)) = $true) | ($true != ((moref @ X0 @ X2))) | ($false = ((eq @ X2 @ X1)))) )),
% 0.21/0.33 inference(constrained_superposition,[],[f62,f33])).
% 0.21/0.33 thf(f122,plain,(
% 0.21/0.33 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != ((moref @ X0 @ X2))) | (((moref @ X0 @ X1)) = $true) | ($false = ((eq @ X2 @ X1)))) )),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f121])).
% 0.21/0.33 thf(f220,plain,(
% 0.21/0.33 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true = ((moref @ X0 @ X2))) | ($false = ((eq @ X1 @ X2))) | (((moref @ X0 @ X1)) = $false)) )),
% 0.21/0.33 inference(constrained_superposition,[],[f122,f37])).
% 0.21/0.33 thf(f234,plain,(
% 0.21/0.33 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = ((moref @ X0 @ X2))) | ($false = ((eq @ X1 @ X2))) | (((moref @ X0 @ X1)) = $false)) )),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f220])).
% 0.21/0.33 thf(f675,plain,(
% 0.21/0.33 ( ! [X0 : frac] : (($true != $true) | ($false = ((eq @ X0 @ (pf @ y @ u)))) | ($false = ((moref @ (pf @ x @ z) @ X0)))) )),
% 0.21/0.33 inference(constrained_superposition,[],[f35,f234])).
% 0.21/0.33 thf(f737,plain,(
% 0.21/0.33 ( ! [X0 : frac] : (($false = ((eq @ X0 @ (pf @ y @ u)))) | ($false = ((moref @ (pf @ x @ z) @ X0)))) )),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f675])).
% 0.21/0.33 thf(f799,plain,(
% 0.21/0.33 ($true = $false) | ($false = ((moref @ (pf @ x @ z) @ (pf @ x @ u))))),
% 0.21/0.33 inference(constrained_superposition,[],[f104,f737])).
% 0.21/0.33 thf(f818,plain,(
% 0.21/0.33 ($false = ((moref @ (pf @ x @ z) @ (pf @ x @ u))))),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f799])).
% 0.21/0.33 thf(f831,plain,(
% 0.21/0.33 ($true = $false)),
% 0.21/0.33 inference(forward_demodulation,[],[f818,f53])).
% 0.21/0.33 thf(f832,plain,(
% 0.21/0.33 $false),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f831])).
% 0.21/0.33 % SZS output end Proof for theBenchmark
% 0.21/0.33 % (710329)------------------------------
% 0.21/0.33 % (710329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (710329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (710329)CaDiCaL version: 2.1.3
% 0.21/0.33 % (710329)Termination reason: Refutation
% 0.21/0.33 % (710329)Time elapsed: 0.038 s
% 0.21/0.33 % (710329)Peak memory usage: 12 MB
% 0.21/0.33 % (710329)Instructions burned: 74 (million)
% 0.21/0.33 % (710311)Success in time 0.075 s
% 0.21/0.33 % Vampire exiting
%------------------------------------------------------------------------------