%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM755^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM755^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:51:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.25 % (43291)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (43299)dis+10_1_sil=32000:sp=arity:random_seed=657259020:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (43297)% WARNING: option uhcvi not known.
% 0.08/0.25 % (43299) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-43291-43299"...
% 0.08/0.25 % (43299)...printing done.
% 0.08/0.25 % (43296)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=430548025_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.25 % (43297)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=510322459:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (43298)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1565548797:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.25 % (43300)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=989532469:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (43299)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% 0.08/0.25 thf(type_def_5, type, frac: $tType).
% 0.08/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.25 thf(func_def_0, type, x: frac).
% 0.08/0.25 thf(func_def_1, type, y: frac).
% 0.08/0.25 thf(func_def_2, type, z: frac).
% 0.08/0.25 thf(func_def_3, type, moref: (frac > frac > $o)).
% 0.08/0.25 thf(func_def_4, type, pf: (frac > frac > frac)).
% 0.08/0.25 thf(func_def_6, type, eq: (frac > frac > $o)).
% 0.08/0.25 thf(func_def_7, type, lessf: (frac > frac > $o)).
% 0.08/0.25 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.08/0.25 thf(f1,axiom,(
% 0.08/0.25 (moref @ (pf @ x @ z) @ (pf @ y @ z))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m)).
% 0.08/0.25 thf(f3,axiom,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : ~(((eq @ X0 @ X1) => ~(moref @ X0 @ X1)) => ~ ~(((moref @ X0 @ X1) => ~(lessf @ X0 @ X1)) => ~((lessf @ X0 @ X1) => ~(eq @ X0 @ X1))))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41b)).
% 0.08/0.25 thf(f4,axiom,(
% 0.08/0.25 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62b)).
% 0.08/0.25 thf(f5,axiom,(
% 0.08/0.25 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X0 @ X1) => (lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62c)).
% 0.08/0.25 thf(f6,axiom,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : (~(eq @ X0 @ X1) => (~(moref @ X0 @ X1) => (lessf @ X0 @ X1)))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41a)).
% 0.08/0.25 thf(f7,conjecture,(
% 0.08/0.25 (moref @ x @ y)),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63a)).
% 0.08/0.25 thf(f8,negated_conjecture,(
% 0.08/0.25 ~(moref @ x @ y)),
% 0.08/0.25 inference(negated_conjecture,[status(cth)],[f7])).
% 0.08/0.25 thf(f9,plain,(
% 0.08/0.25 (moref @ (pf @ x @ z) @ (pf @ y @ z))),
% 0.08/0.25 inference(rectify,[],[f1])).
% 0.08/0.25 thf(f10,plain,(
% 0.08/0.25 (((moref @ (pf @ x @ z) @ (pf @ y @ z))) = $true)),
% 0.08/0.25 inference(fool_elimination,[],[f9])).
% 0.08/0.25 thf(f13,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : ~(((eq @ X0 @ X1) => ~(moref @ X0 @ X1)) => ~ ~(((moref @ X0 @ X1) => ~(lessf @ X0 @ X1)) => ~((lessf @ X0 @ X1) => ~(eq @ X0 @ X1))))),
% 0.08/0.25 inference(rectify,[],[f3])).
% 0.08/0.25 thf(f14,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : ~(((((eq @ X0 @ X1)) = $true) => ~ (((moref @ X0 @ X1)) = $true)) => ~ ~(((((moref @ X0 @ X1)) = $true) => ~ (((lessf @ X0 @ X1)) = $true)) => ~((((lessf @ X0 @ X1)) = $true) => ~ (((eq @ X0 @ X1)) = $true))))),
% 0.08/0.25 inference(fool_elimination,[],[f13])).
% 0.08/0.25 thf(f15,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.08/0.25 inference(rectify,[],[f4])).
% 0.08/0.25 thf(f16,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac,X2 : frac] : ((((eq @ X0 @ X1)) = $true) => (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true))),
% 0.08/0.25 inference(fool_elimination,[],[f15])).
% 0.08/0.25 thf(f17,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X0 @ X1) => (lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.08/0.25 inference(rectify,[],[f5])).
% 0.08/0.25 thf(f18,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac,X2 : frac] : ((((lessf @ X0 @ X1)) = $true) => (((lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true))),
% 0.08/0.25 inference(fool_elimination,[],[f17])).
% 0.08/0.25 thf(f19,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : (~(eq @ X0 @ X1) => (~(moref @ X0 @ X1) => (lessf @ X0 @ X1)))),
% 0.08/0.25 inference(rectify,[],[f6])).
% 0.08/0.25 thf(f20,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : (~ (((eq @ X0 @ X1)) = $true) => (~ (((moref @ X0 @ X1)) = $true) => (((lessf @ X0 @ X1)) = $true)))),
% 0.08/0.25 inference(fool_elimination,[],[f19])).
% 0.08/0.25 thf(f21,plain,(
% 0.08/0.25 ~(moref @ x @ y)),
% 0.08/0.25 inference(rectify,[],[f8])).
% 0.08/0.25 thf(f22,plain,(
% 0.08/0.25 ~ (((moref @ x @ y)) = $true)),
% 0.08/0.25 inference(fool_elimination,[],[f21])).
% 0.08/0.25 thf(f24,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : ~(((((eq @ X0 @ X1)) = $true) => (((moref @ X0 @ X1)) != $true)) => (((((moref @ X0 @ X1)) = $true) => (((lessf @ X0 @ X1)) != $true)) => ~((((lessf @ X0 @ X1)) = $true) => (((eq @ X0 @ X1)) != $true))))),
% 0.08/0.25 inference(flattening,[],[f14])).
% 0.08/0.25 thf(f25,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : ((((eq @ X0 @ X1)) != $true) => ((((moref @ X0 @ X1)) != $true) => (((lessf @ X0 @ X1)) = $true)))),
% 0.08/0.25 inference(flattening,[],[f20])).
% 0.08/0.25 thf(f26,plain,(
% 0.08/0.25 (((moref @ x @ y)) != $true)),
% 0.08/0.25 inference(flattening,[],[f22])).
% 0.08/0.25 thf(f28,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : ((((((eq @ X0 @ X1)) != $true) | (((lessf @ X0 @ X1)) != $true)) & ((((lessf @ X0 @ X1)) != $true) | (((moref @ X0 @ X1)) != $true))) & ((((moref @ X0 @ X1)) != $true) | (((eq @ X0 @ X1)) != $true)))),
% 0.08/0.25 inference(ennf_transformation,[],[f24])).
% 0.08/0.25 thf(f29,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : (((((eq @ X0 @ X1)) != $true) | (((lessf @ X0 @ X1)) != $true)) & ((((lessf @ X0 @ X1)) != $true) | (((moref @ X0 @ X1)) != $true)) & ((((moref @ X0 @ X1)) != $true) | (((eq @ X0 @ X1)) != $true)))),
% 0.08/0.25 inference(flattening,[],[f28])).
% 0.08/0.25 thf(f30,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac,X2 : frac] : ((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true) | (((eq @ X0 @ X1)) != $true))),
% 0.08/0.25 inference(ennf_transformation,[],[f16])).
% 0.08/0.25 thf(f31,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac,X2 : frac] : ((((lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true) | (((lessf @ X0 @ X1)) != $true))),
% 0.08/0.25 inference(ennf_transformation,[],[f18])).
% 0.08/0.25 thf(f32,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : (((((lessf @ X0 @ X1)) = $true) | (((moref @ X0 @ X1)) = $true)) | (((eq @ X0 @ X1)) = $true))),
% 0.08/0.25 inference(ennf_transformation,[],[f25])).
% 0.08/0.25 thf(f33,plain,(
% 0.08/0.25 ! [X0 : frac,X1 : frac] : ((((lessf @ X0 @ X1)) = $true) | (((moref @ X0 @ X1)) = $true) | (((eq @ X0 @ X1)) = $true))),
% 0.08/0.25 inference(flattening,[],[f32])).
% 0.08/0.25 thf(f34,plain,(
% 0.08/0.25 (((moref @ (pf @ x @ z) @ (pf @ y @ z))) = $true)),
% 0.08/0.25 inference(cnf_transformation,[],[f10])).
% 0.08/0.25 thf(f36,plain,(
% 0.08/0.25 ( ! [X0 : frac,X1 : frac] : ((((eq @ X0 @ X1)) != $true) | (((moref @ X0 @ X1)) != $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f29])).
% 0.08/0.25 thf(f37,plain,(
% 0.08/0.25 ( ! [X0 : frac,X1 : frac] : ((((lessf @ X0 @ X1)) != $true) | (((moref @ X0 @ X1)) != $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f29])).
% 0.08/0.25 thf(f39,plain,(
% 0.08/0.25 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((eq @ X0 @ X1)) != $true) | (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f30])).
% 0.08/0.25 thf(f40,plain,(
% 0.08/0.25 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((lessf @ X0 @ X1)) != $true) | (((lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f31])).
% 0.08/0.25 thf(f41,plain,(
% 0.08/0.25 ( ! [X0 : frac,X1 : frac] : ((((lessf @ X0 @ X1)) = $true) | (((moref @ X0 @ X1)) = $true) | (((eq @ X0 @ X1)) = $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f33])).
% 0.08/0.25 thf(f42,plain,(
% 0.08/0.25 (((moref @ x @ y)) != $true)),
% 0.08/0.25 inference(cnf_transformation,[],[f26])).
% 0.08/0.25 thf(f44,definition,(
% 0.08/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.25 thf(f55,plain,(
% 0.08/0.25 ( ! [X0 : frac,X1 : frac] : (($true != $true) | (((moref @ X0 @ X1)) != $true) | (((eq @ X0 @ X1)) = $false)) )),
% 0.08/0.25 inference(constrained_superposition,[],[f36,f44])).
% 0.08/0.25 thf(f56,plain,(
% 0.08/0.25 ( ! [X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((eq @ X0 @ X1)) = $false)) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f55])).
% 0.08/0.25 thf(f60,plain,(
% 0.08/0.25 ( ! [X0 : frac,X1 : frac] : (($true != $true) | (((moref @ X0 @ X1)) != $true) | (((lessf @ X0 @ X1)) = $false)) )),
% 0.08/0.25 inference(constrained_superposition,[],[f37,f44])).
% 0.08/0.25 thf(f61,plain,(
% 0.08/0.25 ( ! [X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((lessf @ X0 @ X1)) = $false)) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f60])).
% 0.08/0.25 thf(f66,plain,(
% 0.08/0.25 ($true != $true) | ($false = ((eq @ (pf @ x @ z) @ (pf @ y @ z))))),
% 0.08/0.25 inference(constrained_superposition,[],[f56,f34])).
% 0.08/0.25 thf(f67,plain,(
% 0.08/0.25 ($false = ((eq @ (pf @ x @ z) @ (pf @ y @ z))))),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f66])).
% 0.08/0.25 thf(f73,plain,(
% 0.08/0.25 ($true != $true) | ($false = ((lessf @ (pf @ x @ z) @ (pf @ y @ z))))),
% 0.08/0.25 inference(constrained_superposition,[],[f61,f34])).
% 0.08/0.25 thf(f74,plain,(
% 0.08/0.25 ($false = ((lessf @ (pf @ x @ z) @ (pf @ y @ z))))),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f73])).
% 0.08/0.25 thf(f81,plain,(
% 0.08/0.25 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | (((lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true) | (((moref @ X0 @ X1)) = $true) | (((eq @ X0 @ X1)) = $true)) )),
% 0.08/0.25 inference(constrained_superposition,[],[f40,f41])).
% 0.08/0.25 thf(f82,plain,(
% 0.08/0.25 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true) | (((moref @ X0 @ X1)) = $true) | (((eq @ X0 @ X1)) = $true)) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f81])).
% 0.08/0.25 thf(f162,plain,(
% 0.08/0.25 ($true = $false) | (((moref @ x @ y)) = $true) | ($true = ((eq @ x @ y)))),
% 0.08/0.25 inference(constrained_superposition,[],[f82,f74])).
% 0.08/0.25 thf(f165,plain,(
% 0.08/0.25 (((moref @ x @ y)) = $true) | ($true = ((eq @ x @ y)))),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f162])).
% 0.08/0.25 thf(f171,plain,(
% 0.08/0.25 ($true = ((eq @ x @ y)))),
% 0.08/0.25 inference(forward_subsumption_resolution,[],[f165,f42])).
% 0.08/0.25 thf(f176,plain,(
% 0.08/0.25 ( ! [X0 : frac] : (($true != $true) | ($true = ((eq @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.08/0.25 inference(constrained_superposition,[],[f39,f171])).
% 0.08/0.25 thf(f179,plain,(
% 0.08/0.25 ( ! [X0 : frac] : (($true = ((eq @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f176])).
% 0.08/0.25 thf(f224,plain,(
% 0.08/0.25 ($true = $false)),
% 0.08/0.25 inference(constrained_superposition,[],[f67,f179])).
% 0.08/0.25 thf(f225,plain,(
% 0.08/0.25 $false),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f224])).
% 0.08/0.25 % SZS output end Proof for theBenchmark
% 0.08/0.25 % (43299)------------------------------
% 0.08/0.25 % (43299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (43299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (43299)CaDiCaL version: 2.1.3
% 0.08/0.25 % (43299)Termination reason: Refutation
% 0.08/0.25 % (43299)Time elapsed: 0.005 s
% 0.08/0.25 % (43299)Peak memory usage: 12 MB
% 0.08/0.25 % (43299)Instructions burned: 17 (million)
% 0.08/0.25 % (43291)Success in time 0.03 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------