%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM760^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:18:48 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM760^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n008.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 12:54:00 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (3101702)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3101719)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1616793200:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (3101720)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (3101720)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.28 % (3101716)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2625214803:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (3101715)lrs+10_16_si=on:nwc=1.5:random_seed=814414610:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (3101713)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=12314339:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (3101717)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4269107835:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.28 % (3101718)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1283359128:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (3101720)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=4266962286:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (3101716)Instruction limit reached!
% 0.21/0.28 % (3101716)------------------------------
% 0.21/0.28 % (3101716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3101716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3101716)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3101716)Termination reason: Instruction limit
% 0.21/0.28 % (3101716)Termination phase: Saturation
% 0.21/0.28 % (3101716)Time elapsed: 0.003 s
% 0.21/0.28 % (3101716)Peak memory usage: 12 MB
% 0.21/0.28 % (3101716)Instructions burned: 4 (million)
% 0.21/0.28 % (3101719) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3101702-3101719"...
% 0.21/0.28 % (3101719)...printing done.
% 0.21/0.28 % (3101719)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, frac: $tType).
% 0.21/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, x: frac).
% 0.21/0.28 thf(func_def_1, type, y: frac).
% 0.21/0.28 thf(func_def_2, type, z: frac).
% 0.21/0.28 thf(func_def_3, type, u: frac).
% 0.21/0.28 thf(func_def_4, type, moref: (frac > frac > $o)).
% 0.21/0.28 thf(func_def_6, type, pf: (frac > frac > frac)).
% 0.21/0.28 thf(func_def_7, type, lessf: (frac > frac > $o)).
% 0.21/0.28 thf(func_def_8, type, eq: (frac > frac > $o)).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 (moref @ x @ y)),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',m)).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 (moref @ z @ u)),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n)).
% 0.21/0.28 thf(f3,axiom,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ((lessf @ X0 @ X1) => (moref @ X1 @ X0))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz43)).
% 0.21/0.28 thf(f4,axiom,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X0 @ X1) => ((lessf @ X1 @ X2) => (lessf @ X0 @ X2)))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz50)).
% 0.21/0.28 thf(f5,axiom,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ((moref @ X0 @ X1) => (lessf @ X1 @ X0))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz42)).
% 0.21/0.28 thf(f6,axiom,(
% 0.21/0.28 ! [X0 : frac,X2 : frac,X3 : frac,X1 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44)).
% 0.21/0.28 thf(f7,axiom,(
% 0.21/0.28 ! [X2 : frac,X1 : frac,X0 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz61)).
% 0.21/0.28 thf(f8,axiom,(
% 0.21/0.28 ! [X1 : frac,X0 : frac] : (eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz58)).
% 0.21/0.28 thf(f9,conjecture,(
% 0.21/0.28 (moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz64)).
% 0.21/0.28 thf(f10,negated_conjecture,(
% 0.21/0.28 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f9])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X2 @ X1) => (moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0)))),
% 0.21/0.28 inference(rectify,[],[f7])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ! [X0 : frac,X2 : frac,X1 : frac] : ((((moref @ X2 @ X1)) = $true) => ($true = ((moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0)))))),
% 0.21/0.28 inference(fool_elimination,[],[f11])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 (moref @ x @ y)),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 (((moref @ x @ y)) = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f13])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 (moref @ z @ u)),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 (((moref @ z @ u)) = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f15])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : (eq @ (pf @ X1 @ X0) @ (pf @ X0 @ X1))),
% 0.21/0.28 inference(rectify,[],[f8])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ($true = ((eq @ (pf @ X1 @ X0) @ (pf @ X0 @ X1))))),
% 0.21/0.28 inference(fool_elimination,[],[f17])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X0 @ X1) => ((lessf @ X1 @ X2) => (lessf @ X0 @ X2)))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((((lessf @ X0 @ X1)) = $true) => ((((lessf @ X1 @ X2)) = $true) => (((lessf @ X0 @ X2)) = $true)))),
% 0.21/0.28 inference(fool_elimination,[],[f19])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ((moref @ X0 @ X1) => (lessf @ X1 @ X0))),
% 0.21/0.28 inference(rectify,[],[f5])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) = $true) => (((lessf @ X1 @ X0)) = $true))),
% 0.21/0.28 inference(fool_elimination,[],[f21])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ((lessf @ X0 @ X1) => (moref @ X1 @ X0))),
% 0.21/0.28 inference(rectify,[],[f3])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ((((lessf @ X0 @ X1)) = $true) => (((moref @ X1 @ X0)) = $true))),
% 0.21/0.28 inference(fool_elimination,[],[f23])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X3) => ((eq @ X0 @ X1) => ((eq @ X3 @ X2) => (moref @ X1 @ X2))))),
% 0.21/0.28 inference(rectify,[],[f6])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 ! [X3 : frac,X1 : frac,X0 : frac,X2 : frac] : (($true = ((moref @ X0 @ X3))) => ((((eq @ X0 @ X1)) = $true) => (($true = ((eq @ X3 @ X2))) => ($true = ((moref @ X1 @ X2))))))),
% 0.21/0.28 inference(fool_elimination,[],[f25])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.21/0.28 inference(rectify,[],[f10])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ~ (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f27])).
% 0.21/0.28 thf(f29,plain,(
% 0.21/0.28 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) != $true)),
% 0.21/0.28 inference(flattening,[],[f28])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac] : (((((lessf @ X0 @ X2)) = $true) | (((lessf @ X1 @ X2)) != $true)) | (((lessf @ X0 @ X1)) != $true))),
% 0.21/0.28 inference(ennf_transformation,[],[f20])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 ! [X1 : frac,X2 : frac,X0 : frac] : ((((lessf @ X1 @ X2)) != $true) | (((lessf @ X0 @ X2)) = $true) | (((lessf @ X0 @ X1)) != $true))),
% 0.21/0.28 inference(flattening,[],[f30])).
% 0.21/0.28 thf(f32,plain,(
% 0.21/0.28 ! [X1 : frac,X0 : frac] : ((((lessf @ X0 @ X1)) != $true) | (((moref @ X1 @ X0)) = $true))),
% 0.21/0.28 inference(ennf_transformation,[],[f24])).
% 0.21/0.28 thf(f33,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ((((lessf @ X1 @ X0)) = $true) | (((moref @ X0 @ X1)) != $true))),
% 0.21/0.28 inference(ennf_transformation,[],[f22])).
% 0.21/0.28 thf(f34,plain,(
% 0.21/0.28 ! [X2 : frac,X1 : frac,X0 : frac] : (($true = ((moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0)))) | (((moref @ X2 @ X1)) != $true))),
% 0.21/0.28 inference(ennf_transformation,[],[f12])).
% 0.21/0.28 thf(f35,plain,(
% 0.21/0.28 ! [X3 : frac,X1 : frac,X0 : frac,X2 : frac] : (((($true = ((moref @ X1 @ X2))) | ($true != ((eq @ X3 @ X2)))) | (((eq @ X0 @ X1)) != $true)) | ($true != ((moref @ X0 @ X3))))),
% 0.21/0.28 inference(ennf_transformation,[],[f26])).
% 0.21/0.28 thf(f36,plain,(
% 0.21/0.28 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((eq @ X0 @ X1)) != $true) | ($true != ((moref @ X0 @ X3))) | ($true != ((eq @ X3 @ X2))) | ($true = ((moref @ X1 @ X2))))),
% 0.21/0.28 inference(flattening,[],[f35])).
% 0.21/0.28 thf(f37,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true) | (((moref @ X0 @ X1)) != $true))),
% 0.21/0.28 inference(rectify,[],[f34])).
% 0.21/0.28 thf(f38,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != ((eq @ X2 @ X3))) | (((moref @ X2 @ X1)) != $true) | (((eq @ X1 @ X0)) != $true) | ($true = ((moref @ X3 @ X0))))),
% 0.21/0.28 inference(rectify,[],[f36])).
% 0.21/0.28 thf(f39,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((((lessf @ X0 @ X1)) != $true) | ($true = ((lessf @ X2 @ X1))) | ($true != ((lessf @ X2 @ X0))))),
% 0.21/0.28 inference(rectify,[],[f31])).
% 0.21/0.28 thf(f40,plain,(
% 0.21/0.28 ! [X0 : frac,X1 : frac] : ((((lessf @ X1 @ X0)) != $true) | (((moref @ X0 @ X1)) = $true))),
% 0.21/0.28 inference(rectify,[],[f32])).
% 0.21/0.28 thf(f41,plain,(
% 0.21/0.28 (((moref @ z @ u)) = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f16])).
% 0.21/0.28 thf(f42,plain,(
% 0.21/0.28 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f37])).
% 0.21/0.28 thf(f43,plain,(
% 0.21/0.28 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) != $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f29])).
% 0.21/0.28 thf(f44,plain,(
% 0.21/0.28 (((moref @ x @ y)) = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f14])).
% 0.21/0.28 thf(f45,plain,(
% 0.21/0.28 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X2 @ X3))) | (((moref @ X2 @ X1)) != $true) | (((eq @ X1 @ X0)) != $true) | ($true = ((moref @ X3 @ X0)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f38])).
% 0.21/0.28 thf(f46,plain,(
% 0.21/0.28 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != ((lessf @ X2 @ X0))) | (((lessf @ X0 @ X1)) != $true) | ($true = ((lessf @ X2 @ X1)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f39])).
% 0.21/0.28 thf(f47,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((lessf @ X1 @ X0)) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f33])).
% 0.21/0.28 thf(f48,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : (($true = ((eq @ (pf @ X1 @ X0) @ (pf @ X0 @ X1))))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f18])).
% 0.21/0.28 thf(f49,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : ((((lessf @ X1 @ X0)) != $true) | (((moref @ X0 @ X1)) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f40])).
% 0.21/0.28 thf(f51,definition,(
% 0.21/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.28 thf(f54,plain,(
% 0.21/0.28 ($true != $true) | (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $false)),
% 0.21/0.28 inference(constrained_superposition,[],[f43,f51])).
% 0.21/0.28 thf(f60,plain,(
% 0.21/0.28 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $false)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f54])).
% 0.21/0.28 thf(f71,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : ((((moref @ X1 @ X0)) = $true) | (((lessf @ X0 @ X1)) = $false) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f49,f51])).
% 0.21/0.28 thf(f72,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : ((((lessf @ X0 @ X1)) = $false) | (((moref @ X1 @ X0)) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f71])).
% 0.21/0.28 thf(f86,plain,(
% 0.21/0.28 ( ! [X0 : frac] : ((((moref @ (pf @ z @ X0) @ (pf @ u @ X0))) = $true) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f42,f41])).
% 0.21/0.28 thf(f88,plain,(
% 0.21/0.28 ( ! [X0 : frac] : (($true != $true) | ($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f42,f44])).
% 0.21/0.28 thf(f90,plain,(
% 0.21/0.28 ( ! [X0 : frac] : (($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f88])).
% 0.21/0.28 thf(f91,plain,(
% 0.21/0.28 ( ! [X0 : frac] : ((((moref @ (pf @ z @ X0) @ (pf @ u @ X0))) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f86])).
% 0.21/0.28 thf(f95,plain,(
% 0.21/0.28 ( ! [X0 : frac] : ((((lessf @ (pf @ y @ X0) @ (pf @ x @ X0))) = $true) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f47,f90])).
% 0.21/0.28 thf(f97,plain,(
% 0.21/0.28 ( ! [X0 : frac] : ((((lessf @ (pf @ y @ X0) @ (pf @ x @ X0))) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f95])).
% 0.21/0.28 thf(f143,plain,(
% 0.21/0.28 (((lessf @ (pf @ y @ u) @ (pf @ x @ z))) = $false) | ($true = $false)),
% 0.21/0.28 inference(constrained_superposition,[],[f60,f72])).
% 0.21/0.28 thf(f145,plain,(
% 0.21/0.28 (((lessf @ (pf @ y @ u) @ (pf @ x @ z))) = $false)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f143])).
% 0.21/0.28 thf(f155,plain,(
% 0.21/0.28 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X2 @ X3))) | ($true != ((moref @ (pf @ X0 @ X1) @ X2))) | ($true != $true) | ($true = ((moref @ (pf @ X1 @ X0) @ X3)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f45,f48])).
% 0.21/0.28 thf(f156,plain,(
% 0.21/0.28 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != ((moref @ (pf @ X0 @ X1) @ X2))) | ($true = ((moref @ (pf @ X1 @ X0) @ X3))) | ($true != ((eq @ X2 @ X3)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f155])).
% 0.21/0.28 thf(f164,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : (($true = ((lessf @ (pf @ y @ X0) @ X1))) | (((lessf @ (pf @ x @ X0) @ X1)) != $true) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f46,f97])).
% 0.21/0.28 thf(f166,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : ((((lessf @ (pf @ x @ X0) @ X1)) != $true) | ($true = ((lessf @ (pf @ y @ X0) @ X1)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f164])).
% 0.21/0.28 thf(f228,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ($true = ((moref @ (pf @ X0 @ z) @ X1))) | ($true != ((eq @ (pf @ u @ X0) @ X1)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f156,f91])).
% 0.21/0.28 thf(f231,plain,(
% 0.21/0.28 ( ! [X0 : frac,X1 : frac] : (($true != ((eq @ (pf @ u @ X0) @ X1))) | ($true = ((moref @ (pf @ X0 @ z) @ X1)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f228])).
% 0.21/0.28 thf(f269,plain,(
% 0.21/0.28 ( ! [X0 : frac] : (($true != $true) | ($true = ((moref @ (pf @ X0 @ z) @ (pf @ X0 @ u))))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f231,f48])).
% 0.21/0.28 thf(f270,plain,(
% 0.21/0.28 ( ! [X0 : frac] : (($true = ((moref @ (pf @ X0 @ z) @ (pf @ X0 @ u))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f269])).
% 0.21/0.28 thf(f334,plain,(
% 0.21/0.28 ( ! [X0 : frac] : (($true = ((lessf @ (pf @ X0 @ u) @ (pf @ X0 @ z)))) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f47,f270])).
% 0.21/0.28 thf(f337,plain,(
% 0.21/0.28 ( ! [X0 : frac] : (($true = ((lessf @ (pf @ X0 @ u) @ (pf @ X0 @ z))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f334])).
% 0.21/0.28 thf(f375,plain,(
% 0.21/0.28 ($true = ((lessf @ (pf @ y @ u) @ (pf @ x @ z)))) | ($true != $true)),
% 0.21/0.28 inference(constrained_superposition,[],[f166,f337])).
% 0.21/0.28 thf(f379,plain,(
% 0.21/0.28 ($true = ((lessf @ (pf @ y @ u) @ (pf @ x @ z))))),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f375])).
% 0.21/0.28 thf(f381,plain,(
% 0.21/0.28 ($true = $false)),
% 0.21/0.28 inference(forward_demodulation,[],[f379,f145])).
% 0.21/0.28 thf(f382,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f381])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (3101719)------------------------------
% 0.21/0.28 % (3101719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3101719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3101719)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3101719)Termination reason: Refutation
% 0.21/0.28 % (3101719)Time elapsed: 0.013 s
% 0.21/0.28 % (3101719)Peak memory usage: 12 MB
% 0.21/0.28 % (3101719)Instructions burned: 40 (million)
% 0.21/0.28 % (3101702)Success in time 0.03 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------