%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV074^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 08:37:35 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV074^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:06:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.32 % (898829)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (898840)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (898840)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
% 0.22/0.32 % (898840)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=3593088699:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (898838)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2732773010:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (898835)lrs+10_16_si=on:nwc=1.5:random_seed=2287801577:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (898837)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=2155798814: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)
% 0.22/0.32 % (898834)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1173128185:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (898836)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1851175738:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (898839)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=675404539:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (898836)Instruction limit reached!
% 0.22/0.32 % (898836)------------------------------
% 0.22/0.32 % (898836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (898836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (898836)CaDiCaL version: 2.1.3
% 0.22/0.32 % (898836)Termination reason: Instruction limit
% 0.22/0.32 % (898836)Termination phase: Saturation
% 0.22/0.32 % (898836)Time elapsed: 0.004 s
% 0.22/0.32 % (898836)Peak memory usage: 12 MB
% 0.22/0.32 % (898836)Instructions burned: 3 (million)
% 0.22/0.32 % (898837)Refutation not found, incomplete strategy
% 0.22/0.32 % (898837)------------------------------
% 0.22/0.32 % (898837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (898837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (898837)CaDiCaL version: 2.1.3
% 0.22/0.32 % (898837)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.32 % (898837)Time elapsed: 0.008 s
% 0.22/0.32 % (898837)Peak memory usage: 12 MB
% 0.22/0.32 % (898837)Instructions burned: 7 (million)
% 0.22/0.32 % (898840) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-898829-898840"...
% 0.22/0.32 % (898838)Refutation not found, incomplete strategy
% 0.22/0.32 % (898838)------------------------------
% 0.22/0.32 % (898838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (898838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (898838)CaDiCaL version: 2.1.3
% 0.22/0.32 % (898838)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.32 % (898838)Time elapsed: 0.013 s
% 0.22/0.32 % (898838)Peak memory usage: 12 MB
% 0.22/0.32 % (898838)Instructions burned: 13 (million)
% 0.22/0.32 % (898837)------------------------------
% 0.22/0.32 % (898837)------------------------------
% 0.22/0.32 % (898838)------------------------------
% 0.22/0.32 % (898838)------------------------------
% 0.22/0.32 % (898840)...printing done.
% 0.22/0.32 % (898840)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% 0.22/0.32 thf(type_def_5, type, a: $tType).
% 0.22/0.32 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.32 thf(func_def_3, type, sP0: (a > a > (a > a > $o) > $o)).
% 0.22/0.32 thf(func_def_4, type, sP1: ((a > a > $o) > a > a > $o)).
% 0.22/0.32 thf(func_def_5, type, sK2: (a > a > (a > a > $o) > a > a > $o)).
% 0.22/0.32 thf(func_def_6, type, sK3: ((a > a > $o) > a)).
% 0.22/0.32 thf(func_def_7, type, sK4: ((a > a > $o) > (a > a > $o) > a)).
% 0.22/0.32 thf(func_def_8, type, sK5: ((a > a > $o) > (a > a > $o) > a)).
% 0.22/0.32 thf(func_def_9, type, sK6: a).
% 0.22/0.32 thf(func_def_10, type, sK7: a).
% 0.22/0.32 thf(func_def_11, type, sK8: (a > a > $o)).
% 0.22/0.32 thf(func_def_12, type, sF9: $o).
% 0.22/0.32 thf(func_def_13, type, sF10: $o).
% 0.22/0.32 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.32 thf(f1,conjecture,(
% 0.22/0.32 ! [X1 : a,X2 : a,X0 : (a > a > $o)] : (! [X3 : (a > a > $o)] : ((! [X4 : a] : (X3 @ X4 @ X4) & ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)) <=> ((X0 @ X1 @ X2) | (X1 = X2)))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM523_pme)).
% 0.22/0.32 thf(f2,negated_conjecture,(
% 0.22/0.32 ~ ! [X1 : a,X2 : a,X0 : (a > a > $o)] : (! [X3 : (a > a > $o)] : ((! [X4 : a] : (X3 @ X4 @ X4) & ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)) <=> ((X0 @ X1 @ X2) | (X1 = X2)))),
% 0.22/0.32 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.32 thf(f3,plain,(
% 0.22/0.32 ~ ! [X0 : a,X1 : a,X2 : (a > a > $o)] : (! [X3 : (a > a > $o)] : ((! [X4 : a] : (X3 @ X4 @ X4) & ! [X5 : a,X6 : a] : ((X2 @ X5 @ X6) => (X3 @ X5 @ X6))) => (X3 @ X0 @ X1)) <=> ((X2 @ X0 @ X1) | (X0 = X1)))),
% 0.22/0.32 inference(rectify,[],[f2])).
% 0.22/0.32 thf(f4,plain,(
% 0.22/0.32 ~ ! [X0 : a,X1 : a,X2 : (a > a > $o)] : (((X0 = X1) | ($true = ((X2 @ X0 @ X1)))) <=> ! [X3 : (a > a > $o)] : ((! [X5 : a,X6 : a] : (($true = ((X2 @ X5 @ X6))) => ($true = ((X3 @ X5 @ X6)))) & ! [X4 : a] : (((X3 @ X4 @ X4)) = $true)) => ($true = ((X3 @ X0 @ X1)))))),
% 0.22/0.32 inference(fool_elimination,[],[f3])).
% 0.22/0.32 thf(f5,plain,(
% 0.22/0.32 ? [X0 : a,X1 : a,X2 : (a > a > $o)] : (((X0 = X1) | ($true = ((X2 @ X0 @ X1)))) <~> ! [X3 : (a > a > $o)] : (($true = ((X3 @ X0 @ X1))) | (? [X6 : a,X5 : a] : (($true = ((X2 @ X5 @ X6))) & ($true != ((X3 @ X5 @ X6)))) | ? [X4 : a] : (((X3 @ X4 @ X4)) != $true))))),
% 0.22/0.32 inference(ennf_transformation,[],[f4])).
% 0.22/0.32 thf(f6,plain,(
% 0.22/0.32 ? [X0 : a,X1 : a,X2 : (a > a > $o)] : (! [X3 : (a > a > $o)] : (? [X4 : a] : (((X3 @ X4 @ X4)) != $true) | ? [X6 : a,X5 : a] : (($true = ((X2 @ X5 @ X6))) & ($true != ((X3 @ X5 @ X6)))) | ($true = ((X3 @ X0 @ X1)))) <~> ((X0 = X1) | ($true = ((X2 @ X0 @ X1)))))),
% 0.22/0.32 inference(flattening,[],[f5])).
% 0.22/0.32 thf(f7,definition,(
% 0.22/0.32 ! [X2 : (a > a > $o),X1 : a,X0 : a] : (($true = ((sP0 @ X0 @ X1 @ X2))) <=> ! [X3 : (a > a > $o)] : (? [X4 : a] : (((X3 @ X4 @ X4)) != $true) | ? [X6 : a,X5 : a] : (($true = ((X2 @ X5 @ X6))) & ($true != ((X3 @ X5 @ X6)))) | ($true = ((X3 @ X0 @ X1)))))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.32 thf(f8,definition,(
% 0.22/0.32 ! [X1 : a,X0 : a,X2 : (a > a > $o)] : (($true = ((sP1 @ X2 @ X0 @ X1))) <=> ((X0 = X1) | ($true = ((X2 @ X0 @ X1)))))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.32 thf(f9,plain,(
% 0.22/0.32 ? [X0 : a,X1 : a,X2 : (a > a > $o)] : (($true = ((sP0 @ X0 @ X1 @ X2))) <~> ($true = ((sP1 @ X2 @ X0 @ X1))))),
% 0.22/0.32 inference(definition_folding,[],[f6,f8,f7])).
% 0.22/0.32 thf(f10,plain,(
% 0.22/0.32 ! [X1 : a,X0 : a,X2 : (a > a > $o)] : ((($true = ((sP1 @ X2 @ X0 @ X1))) | ((X0 != X1) & ($true != ((X2 @ X0 @ X1))))) & (((X0 = X1) | ($true = ((X2 @ X0 @ X1)))) | ($true != ((sP1 @ X2 @ X0 @ X1)))))),
% 0.22/0.32 inference(nnf_transformation,[],[f8])).
% 0.22/0.32 thf(f11,plain,(
% 0.22/0.32 ! [X1 : a,X0 : a,X2 : (a > a > $o)] : ((($true = ((sP1 @ X2 @ X0 @ X1))) | ((X0 != X1) & ($true != ((X2 @ X0 @ X1))))) & ((X0 = X1) | ($true = ((X2 @ X0 @ X1))) | ($true != ((sP1 @ X2 @ X0 @ X1)))))),
% 0.22/0.32 inference(flattening,[],[f10])).
% 0.22/0.32 thf(f12,plain,(
% 0.22/0.32 ! [X0 : a,X1 : a,X2 : (a > a > $o)] : ((($true = ((sP1 @ X2 @ X1 @ X0))) | ((X0 != X1) & ($true != ((X2 @ X1 @ X0))))) & ((X0 = X1) | ($true = ((X2 @ X1 @ X0))) | ($true != ((sP1 @ X2 @ X1 @ X0)))))),
% 0.22/0.32 inference(rectify,[],[f11])).
% 0.22/0.32 thf(f13,plain,(
% 0.22/0.32 ! [X2 : (a > a > $o),X1 : a,X0 : a] : ((($true = ((sP0 @ X0 @ X1 @ X2))) | ? [X3 : (a > a > $o)] : (! [X4 : a] : (((X3 @ X4 @ X4)) = $true) & ! [X6 : a,X5 : a] : (($true != ((X2 @ X5 @ X6))) | ($true = ((X3 @ X5 @ X6)))) & ($true != ((X3 @ X0 @ X1))))) & (! [X3 : (a > a > $o)] : (? [X4 : a] : (((X3 @ X4 @ X4)) != $true) | ? [X6 : a,X5 : a] : (($true = ((X2 @ X5 @ X6))) & ($true != ((X3 @ X5 @ X6)))) | ($true = ((X3 @ X0 @ X1)))) | ($true != ((sP0 @ X0 @ X1 @ X2)))))),
% 0.22/0.32 inference(nnf_transformation,[],[f7])).
% 0.22/0.32 thf(f14,plain,(
% 0.22/0.32 ! [X0 : (a > a > $o),X1 : a,X2 : a] : ((($true = ((sP0 @ X2 @ X1 @ X0))) | ? [X3 : (a > a > $o)] : (! [X4 : a] : (((X3 @ X4 @ X4)) = $true) & ! [X5 : a,X6 : a] : (($true != ((X0 @ X6 @ X5))) | (((X3 @ X6 @ X5)) = $true)) & ($true != ((X3 @ X2 @ X1))))) & (! [X7 : (a > a > $o)] : (? [X8 : a] : ($true != ((X7 @ X8 @ X8))) | ? [X9 : a,X10 : a] : (($true = ((X0 @ X10 @ X9))) & ($true != ((X7 @ X10 @ X9)))) | ($true = ((X7 @ X2 @ X1)))) | ($true != ((sP0 @ X2 @ X1 @ X0)))))),
% 0.22/0.32 inference(rectify,[],[f13])).
% 0.22/0.32 thf(f15,plain,(
% 0.22/0.32 ! [X0 : (a > a > $o),X1 : a,X2 : a] : ((($true = ((sP0 @ X2 @ X1 @ X0))) | (! [X4 : a] : ($true = ((sK2 @ X2 @ X1 @ X0 @ X4 @ X4))) & ! [X5 : a,X6 : a] : (($true != ((X0 @ X6 @ X5))) | (((sK2 @ X2 @ X1 @ X0 @ X6 @ X5)) = $true)) & ($true != ((sK2 @ X2 @ X1 @ X0 @ X2 @ X1))))) & (! [X7 : (a > a > $o)] : (($true != ((X7 @ (sK3 @ X7) @ (sK3 @ X7)))) | (($true = ((X0 @ (sK5 @ X7 @ X0) @ (sK4 @ X7 @ X0)))) & ($true != ((X7 @ (sK5 @ X7 @ X0) @ (sK4 @ X7 @ X0))))) | ($true = ((X7 @ X2 @ X1)))) | ($true != ((sP0 @ X2 @ X1 @ X0)))))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X10,sK5 @ X7 @ X0),skolemize(X10,sK5 @ X7 @ X0),skolemize(X10,sK5 @ X7 @ X0),skolemize(X10,sK5 @ X7 @ X0)],[f14])).
% 0.22/0.32 thf(f16,plain,(
% 0.22/0.32 ? [X0 : a,X1 : a,X2 : (a > a > $o)] : ((($true != ((sP1 @ X2 @ X0 @ X1))) | ($true != ((sP0 @ X0 @ X1 @ X2)))) & (($true = ((sP1 @ X2 @ X0 @ X1))) | ($true = ((sP0 @ X0 @ X1 @ X2)))))),
% 0.22/0.32 inference(nnf_transformation,[],[f9])).
% 0.22/0.32 thf(f17,plain,(
% 0.22/0.32 (($true != ((sP1 @ sK8 @ sK6 @ sK7))) | (((sP0 @ sK6 @ sK7 @ sK8)) != $true)) & (($true = ((sP1 @ sK8 @ sK6 @ sK7))) | (((sP0 @ sK6 @ sK7 @ sK8)) = $true))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f16])).
% 0.22/0.32 thf(f18,plain,(
% 0.22/0.32 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : (($true != ((sP1 @ X2 @ X1 @ X0))) | ($true = ((X2 @ X1 @ X0))) | (X0 = X1)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f12])).
% 0.22/0.32 thf(f19,plain,(
% 0.22/0.32 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : (($true = ((sP1 @ X2 @ X1 @ X0))) | ($true != ((X2 @ X1 @ X0)))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f12])).
% 0.22/0.32 thf(f20,plain,(
% 0.22/0.32 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : (($true = ((sP1 @ X2 @ X1 @ X0))) | (X0 != X1)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f12])).
% 0.22/0.32 thf(f21,plain,(
% 0.22/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a,X7 : (a > a > $o)] : (($true != ((X7 @ (sK5 @ X7 @ X0) @ (sK4 @ X7 @ X0)))) | ($true != ((sP0 @ X2 @ X1 @ X0))) | ($true = ((X7 @ X2 @ X1))) | ($true != ((X7 @ (sK3 @ X7) @ (sK3 @ X7))))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f15])).
% 0.22/0.32 thf(f22,plain,(
% 0.22/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a,X7 : (a > a > $o)] : (($true = ((X0 @ (sK5 @ X7 @ X0) @ (sK4 @ X7 @ X0)))) | ($true != ((sP0 @ X2 @ X1 @ X0))) | ($true = ((X7 @ X2 @ X1))) | ($true != ((X7 @ (sK3 @ X7) @ (sK3 @ X7))))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f15])).
% 0.22/0.32 thf(f23,plain,(
% 0.22/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true != ((sK2 @ X2 @ X1 @ X0 @ X2 @ X1))) | ($true = ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f15])).
% 0.22/0.32 thf(f24,plain,(
% 0.22/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a,X6 : a,X5 : a] : ((((sK2 @ X2 @ X1 @ X0 @ X6 @ X5)) = $true) | ($true = ((sP0 @ X2 @ X1 @ X0))) | ($true != ((X0 @ X6 @ X5)))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f15])).
% 0.22/0.32 thf(f25,plain,(
% 0.22/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true = ((sK2 @ X2 @ X1 @ X0 @ X4 @ X4))) | ($true = ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f15])).
% 0.22/0.32 thf(f26,plain,(
% 0.22/0.32 ($true = ((sP1 @ sK8 @ sK6 @ sK7))) | (((sP0 @ sK6 @ sK7 @ sK8)) = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f17])).
% 0.22/0.32 thf(f27,plain,(
% 0.22/0.32 ($true != ((sP1 @ sK8 @ sK6 @ sK7))) | (((sP0 @ sK6 @ sK7 @ sK8)) != $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f17])).
% 0.22/0.32 thf(f30,plain,(
% 0.22/0.32 ( ! [X2 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X2 @ X1 @ X1)))) )),
% 0.22/0.32 inference(equality_resolution,[],[f20])).
% 0.22/0.32 thf(f31,definition,(
% 0.22/0.32 (sF9 = ((sP1 @ sK8 @ sK6 @ sK7)))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
% 0.22/0.32 thf(f32,definition,(
% 0.22/0.32 (sF10 = ((sP0 @ sK6 @ sK7 @ sK8)))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
% 0.22/0.32 thf(f33,plain,(
% 0.22/0.32 (sF10 != $true) | ($true != sF9)),
% 0.22/0.32 inference(definition_folding,[],[f27,f32,f31])).
% 0.22/0.32 thf(f34,plain,(
% 0.22/0.32 (sF10 = $true) | ($true = sF9)),
% 0.22/0.32 inference(definition_folding,[],[f26,f32,f31])).
% 0.22/0.32 thf(f35,plain,(
% 0.22/0.32 ($false = ((sP1 @ sK8 @ sK6 @ sK7))) | ($true = sF9)),
% 0.22/0.32 inference(iff_proxy_clausification,[],[f31])).
% 0.22/0.32 thf(f36,plain,(
% 0.22/0.32 (sF9 = $false) | ($true = ((sP1 @ sK8 @ sK6 @ sK7)))),
% 0.22/0.32 inference(iff_proxy_clausification,[],[f31])).
% 0.22/0.32 thf(f37,plain,(
% 0.22/0.32 (sF10 = $true) | (((sP0 @ sK6 @ sK7 @ sK8)) = $false)),
% 0.22/0.32 inference(iff_proxy_clausification,[],[f32])).
% 0.22/0.32 thf(f38,plain,(
% 0.22/0.32 (sF10 = $false) | (((sP0 @ sK6 @ sK7 @ sK8)) = $true)),
% 0.22/0.32 inference(iff_proxy_clausification,[],[f32])).
% 0.22/0.32 thf(f40,definition,(
% 0.22/0.32 spl11_1 <=> (sF10 = $true)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition])).
% 0.22/0.32 thf(f41,plain,(
% 0.22/0.32 (sF10 = $true) | ~spl11_1),
% 0.22/0.32 inference(avatar_component_clause,[],[f40])).
% 0.22/0.32 thf(f44,definition,(
% 0.22/0.32 spl11_2 <=> ($true = sF9)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition])).
% 0.22/0.32 thf(f45,plain,(
% 0.22/0.32 ($true = sF9) | ~spl11_2),
% 0.22/0.32 inference(avatar_component_clause,[],[f44])).
% 0.22/0.32 thf(f47,plain,(
% 0.22/0.32 ~spl11_1 | ~spl11_2),
% 0.22/0.32 inference(avatar_split_clause,[],[f33,f44,f40])).
% 0.22/0.32 thf(f49,definition,(
% 0.22/0.32 spl11_3 <=> (sF9 = $false)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition])).
% 0.22/0.32 thf(f51,plain,(
% 0.22/0.32 (sF9 = $false) | ~spl11_3),
% 0.22/0.32 inference(avatar_component_clause,[],[f49])).
% 0.22/0.32 thf(f53,definition,(
% 0.22/0.32 spl11_4 <=> ($true = ((sP1 @ sK8 @ sK6 @ sK7)))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition])).
% 0.22/0.32 thf(f55,plain,(
% 0.22/0.32 ($true = ((sP1 @ sK8 @ sK6 @ sK7))) | ~spl11_4),
% 0.22/0.32 inference(avatar_component_clause,[],[f53])).
% 0.22/0.32 thf(f56,plain,(
% 0.22/0.32 spl11_3 | spl11_4),
% 0.22/0.32 inference(avatar_split_clause,[],[f36,f53,f49])).
% 0.22/0.32 thf(f58,definition,(
% 0.22/0.32 spl11_5 <=> ($false = ((sP1 @ sK8 @ sK6 @ sK7)))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition])).
% 0.22/0.32 thf(f60,plain,(
% 0.22/0.32 ($false = ((sP1 @ sK8 @ sK6 @ sK7))) | ~spl11_5),
% 0.22/0.32 inference(avatar_component_clause,[],[f58])).
% 0.22/0.32 thf(f61,plain,(
% 0.22/0.32 spl11_5 | spl11_2),
% 0.22/0.32 inference(avatar_split_clause,[],[f35,f44,f58])).
% 0.22/0.32 thf(f62,plain,(
% 0.22/0.32 spl11_1 | spl11_2),
% 0.22/0.32 inference(avatar_split_clause,[],[f34,f44,f40])).
% 0.22/0.32 thf(f64,definition,(
% 0.22/0.32 spl11_6 <=> (sF10 = $false)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition])).
% 0.22/0.32 thf(f66,plain,(
% 0.22/0.32 (sF10 = $false) | ~spl11_6),
% 0.22/0.32 inference(avatar_component_clause,[],[f64])).
% 0.22/0.32 thf(f68,definition,(
% 0.22/0.32 spl11_7 <=> (((sP0 @ sK6 @ sK7 @ sK8)) = $true)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition])).
% 0.22/0.32 thf(f69,plain,(
% 0.22/0.32 (((sP0 @ sK6 @ sK7 @ sK8)) != $true) | spl11_7),
% 0.22/0.32 inference(avatar_component_clause,[],[f68])).
% 0.22/0.32 thf(f70,plain,(
% 0.22/0.32 (((sP0 @ sK6 @ sK7 @ sK8)) = $true) | ~spl11_7),
% 0.22/0.32 inference(avatar_component_clause,[],[f68])).
% 0.22/0.32 thf(f71,plain,(
% 0.22/0.32 spl11_6 | spl11_7),
% 0.22/0.32 inference(avatar_split_clause,[],[f38,f68,f64])).
% 0.22/0.32 thf(f73,definition,(
% 0.22/0.32 spl11_8 <=> (((sP0 @ sK6 @ sK7 @ sK8)) = $false)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition])).
% 0.22/0.32 thf(f75,plain,(
% 0.22/0.32 (((sP0 @ sK6 @ sK7 @ sK8)) = $false) | ~spl11_8),
% 0.22/0.32 inference(avatar_component_clause,[],[f73])).
% 0.22/0.32 thf(f76,plain,(
% 0.22/0.32 spl11_8 | spl11_1),
% 0.22/0.32 inference(avatar_split_clause,[],[f37,f40,f73])).
% 0.22/0.32 thf(f77,plain,(
% 0.22/0.32 ($true = $false) | (~spl11_2 | ~spl11_3)),
% 0.22/0.32 inference(forward_demodulation,[],[f51,f45])).
% 0.22/0.32 thf(f78,plain,(
% 0.22/0.32 $false | (~spl11_2 | ~spl11_3)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f77])).
% 0.22/0.32 thf(f79,plain,(
% 0.22/0.32 ~spl11_2 | ~spl11_3),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f78])).
% 0.22/0.32 thf(f81,plain,(
% 0.22/0.32 ($true = $false) | (~spl11_1 | ~spl11_6)),
% 0.22/0.32 inference(forward_demodulation,[],[f66,f41])).
% 0.22/0.32 thf(f82,plain,(
% 0.22/0.32 $false | (~spl11_1 | ~spl11_6)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f81])).
% 0.22/0.32 thf(f83,plain,(
% 0.22/0.32 ~spl11_1 | ~spl11_6),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f82])).
% 0.22/0.32 thf(f107,plain,(
% 0.22/0.32 ($true = $false) | (~spl11_7 | ~spl11_8)),
% 0.22/0.32 inference(forward_demodulation,[],[f75,f70])).
% 0.22/0.32 thf(f108,plain,(
% 0.22/0.32 $false | (~spl11_7 | ~spl11_8)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f107])).
% 0.22/0.32 thf(f109,plain,(
% 0.22/0.32 ~spl11_7 | ~spl11_8),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f108])).
% 0.22/0.32 thf(f134,plain,(
% 0.22/0.32 ( ! [X0 : a,X1 : (a > a > $o)] : (($true != $true) | ($true = ((sP0 @ X0 @ X0 @ X1))) | ($true = ((sP0 @ X0 @ X0 @ X1)))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f23,f25])).
% 0.22/0.32 thf(f135,plain,(
% 0.22/0.32 ( ! [X0 : a,X1 : (a > a > $o)] : (($true = ((sP0 @ X0 @ X0 @ X1))) | ($true != $true)) )),
% 0.22/0.32 inference(duplicate_literal_removal,[],[f134])).
% 0.22/0.32 thf(f136,plain,(
% 0.22/0.32 ( ! [X0 : a,X1 : (a > a > $o)] : (($true = ((sP0 @ X0 @ X0 @ X1)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f135])).
% 0.22/0.32 thf(f137,plain,(
% 0.22/0.32 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : (($true != ((X2 @ X0 @ X1))) | ($true = ((sP0 @ X0 @ X1 @ X2))) | ($true != $true) | ($true = ((sP0 @ X0 @ X1 @ X2)))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f23,f24])).
% 0.22/0.32 thf(f138,plain,(
% 0.22/0.32 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : (($true != $true) | ($true = ((sP0 @ X0 @ X1 @ X2))) | ($true != ((X2 @ X0 @ X1)))) )),
% 0.22/0.32 inference(duplicate_literal_removal,[],[f137])).
% 0.22/0.32 thf(f139,plain,(
% 0.22/0.32 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : (($true = ((sP0 @ X0 @ X1 @ X2))) | ($true != ((X2 @ X0 @ X1)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f138])).
% 0.22/0.32 thf(f158,plain,(
% 0.22/0.32 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : (($true != ((X0 @ (sK5 @ (sP1 @ X0) @ X1) @ (sK4 @ (sP1 @ X0) @ X1)))) | ($true != ((sP1 @ X0 @ (sK3 @ (sP1 @ X0)) @ (sK3 @ (sP1 @ X0))))) | ($true = ((sP1 @ X0 @ X2 @ X3))) | ($true != ((sP0 @ X2 @ X3 @ X1))) | ($true != $true)) )),
% 0.22/0.32 inference(constrained_superposition,[],[f21,f19])).
% 0.22/0.32 thf(f162,plain,(
% 0.22/0.32 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : (($true != ((X0 @ (sK5 @ (sP1 @ X0) @ X1) @ (sK4 @ (sP1 @ X0) @ X1)))) | ($true != ((sP0 @ X2 @ X3 @ X1))) | ($true != ((sP1 @ X0 @ (sK3 @ (sP1 @ X0)) @ (sK3 @ (sP1 @ X0))))) | ($true = ((sP1 @ X0 @ X2 @ X3)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f158])).
% 0.22/0.32 thf(f166,plain,(
% 0.22/0.32 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : (($true != ((X0 @ (sK5 @ (sP1 @ X0) @ X1) @ (sK4 @ (sP1 @ X0) @ X1)))) | ($true != ((sP0 @ X2 @ X3 @ X1))) | ($true = ((sP1 @ X0 @ X2 @ X3)))) )),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f162,f30])).
% 0.22/0.32 thf(f303,plain,(
% 0.22/0.32 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true != ((sP0 @ X3 @ X4 @ X0))) | ($true != $true) | ($true = ((sP1 @ X0 @ X3 @ X4))) | ($true != ((sP1 @ X0 @ (sK3 @ (sP1 @ X0)) @ (sK3 @ (sP1 @ X0))))) | ($true != ((sP0 @ X1 @ X2 @ X0))) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f166,f22])).
% 0.22/0.32 thf(f310,plain,(
% 0.22/0.32 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true = ((sP1 @ X0 @ X3 @ X4))) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($true != ((sP1 @ X0 @ (sK3 @ (sP1 @ X0)) @ (sK3 @ (sP1 @ X0))))) | ($true != ((sP0 @ X1 @ X2 @ X0))) | ($true != ((sP0 @ X3 @ X4 @ X0)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f303])).
% 0.22/0.32 thf(f311,plain,(
% 0.22/0.32 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true != ((sP0 @ X3 @ X4 @ X0))) | ($true = ((sP1 @ X0 @ X3 @ X4))) | ($true != ((sP0 @ X1 @ X2 @ X0))) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f310,f30])).
% 0.22/0.32 thf(f335,plain,(
% 0.22/0.32 ( ! [X0 : a,X1 : a] : (($true != ((sP0 @ X0 @ X1 @ sK8))) | ($true = ((sP1 @ sK8 @ sK6 @ sK7))) | ($true != $true) | ($true = ((sP1 @ sK8 @ X0 @ X1)))) ) | ~spl11_7),
% 0.22/0.32 inference(constrained_superposition,[],[f311,f70])).
% 0.22/0.32 thf(f342,plain,(
% 0.22/0.32 ( ! [X0 : a,X1 : a] : (($true != ((sP0 @ X0 @ X1 @ sK8))) | ($true = ((sP1 @ sK8 @ sK6 @ sK7))) | ($true = ((sP1 @ sK8 @ X0 @ X1)))) ) | ~spl11_7),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f335])).
% 0.22/0.32 thf(f345,plain,(
% 0.22/0.32 ( ! [X0 : a,X1 : a] : (($true = ((sP1 @ sK8 @ X0 @ X1))) | ($true = $false) | ($true != ((sP0 @ X0 @ X1 @ sK8)))) ) | (~spl11_5 | ~spl11_7)),
% 0.22/0.32 inference(forward_demodulation,[],[f342,f60])).
% 0.22/0.32 thf(f346,plain,(
% 0.22/0.32 ( ! [X0 : a,X1 : a] : (($true != ((sP0 @ X0 @ X1 @ sK8))) | ($true = ((sP1 @ sK8 @ X0 @ X1)))) ) | (~spl11_5 | ~spl11_7)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f345])).
% 0.22/0.32 thf(f347,plain,(
% 0.22/0.32 ($true != $true) | ($true = ((sP1 @ sK8 @ sK6 @ sK7))) | (~spl11_5 | ~spl11_7)),
% 0.22/0.32 inference(constrained_superposition,[],[f346,f70])).
% 0.22/0.32 thf(f356,plain,(
% 0.22/0.32 ($true = ((sP1 @ sK8 @ sK6 @ sK7))) | (~spl11_5 | ~spl11_7)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f347])).
% 0.22/0.32 thf(f357,plain,(
% 0.22/0.32 ($true = $false) | (~spl11_5 | ~spl11_7)),
% 0.22/0.32 inference(forward_demodulation,[],[f356,f60])).
% 0.22/0.32 thf(f358,plain,(
% 0.22/0.32 $false | (~spl11_5 | ~spl11_7)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f357])).
% 0.22/0.32 thf(f359,plain,(
% 0.22/0.32 ~spl11_5 | ~spl11_7),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f358])).
% 0.22/0.32 thf(f369,plain,(
% 0.22/0.32 (((sK8 @ sK6 @ sK7)) = $true) | ($true != $true) | (sK7 = sK6) | ~spl11_4),
% 0.22/0.32 inference(constrained_superposition,[],[f18,f55])).
% 0.22/0.32 thf(f372,plain,(
% 0.22/0.32 (((sK8 @ sK6 @ sK7)) = $true) | (sK7 = sK6) | ~spl11_4),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f369])).
% 0.22/0.32 thf(f374,definition,(
% 0.22/0.32 spl11_11 <=> (sK7 = sK6)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition])).
% 0.22/0.32 thf(f376,plain,(
% 0.22/0.32 (sK7 = sK6) | ~spl11_11),
% 0.22/0.32 inference(avatar_component_clause,[],[f374])).
% 0.22/0.32 thf(f378,definition,(
% 0.22/0.32 spl11_12 <=> (((sK8 @ sK6 @ sK7)) = $true)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition])).
% 0.22/0.32 thf(f383,plain,(
% 0.22/0.32 spl11_11 | spl11_12 | ~spl11_4),
% 0.22/0.32 inference(avatar_split_clause,[],[f372,f53,f378,f374])).
% 0.22/0.32 thf(f386,plain,(
% 0.22/0.32 (((sP0 @ sK7 @ sK7 @ sK8)) != $true) | (spl11_7 | ~spl11_11)),
% 0.22/0.32 inference(forward_demodulation,[],[f69,f376])).
% 0.22/0.32 thf(f387,plain,(
% 0.22/0.32 $false | (spl11_7 | ~spl11_11)),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f386,f136])).
% 0.22/0.32 thf(f388,plain,(
% 0.22/0.32 spl11_7 | ~spl11_11),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f387])).
% 0.22/0.32 thf(f391,plain,(
% 0.22/0.32 ($true != $true) | (((sK8 @ sK6 @ sK7)) != $true) | spl11_7),
% 0.22/0.32 inference(constrained_superposition,[],[f69,f139])).
% 0.22/0.32 thf(f394,plain,(
% 0.22/0.32 (((sK8 @ sK6 @ sK7)) != $true) | spl11_7),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f391])).
% 0.22/0.32 thf(f396,plain,(
% 0.22/0.32 ~spl11_12 | spl11_7),
% 0.22/0.32 inference(avatar_split_clause,[],[f394,f68,f378])).
% 0.22/0.32 cnf(s1, plain, ~spl11_1 | ~spl11_2, inference(sat_conversion,[],[f47])).
% 0.22/0.32 cnf(s2, plain, spl11_3 | spl11_4, inference(sat_conversion,[],[f56])).
% 0.22/0.32 cnf(s3, plain, spl11_2 | spl11_5, inference(sat_conversion,[],[f61])).
% 0.22/0.32 cnf(s4, plain, spl11_1 | spl11_2, inference(sat_conversion,[],[f62])).
% 0.22/0.32 cnf(s5, plain, spl11_6 | spl11_7, inference(sat_conversion,[],[f71])).
% 0.22/0.32 cnf(s6, plain, spl11_1 | spl11_8, inference(sat_conversion,[],[f76])).
% 0.22/0.32 cnf(s7, plain, ~spl11_2 | ~spl11_3, inference(sat_conversion,[],[f79])).
% 0.22/0.32 cnf(s8, plain, ~spl11_1 | ~spl11_6, inference(sat_conversion,[],[f83])).
% 0.22/0.32 cnf(s9, plain, ~spl11_7 | ~spl11_8, inference(sat_conversion,[],[f109])).
% 0.22/0.32 cnf(s13, plain, ~spl11_5 | ~spl11_7, inference(sat_conversion,[],[f359])).
% 0.22/0.32 cnf(s17, plain, ~spl11_4 | spl11_11 | spl11_12, inference(sat_conversion,[],[f383])).
% 0.22/0.32 cnf(s18, plain, spl11_7 | ~spl11_11, inference(sat_conversion,[],[f388])).
% 0.22/0.32 cnf(s20, plain, spl11_7 | ~spl11_12, inference(sat_conversion,[],[f396])).
% 0.22/0.32 cnf(s21, plain, spl11_1, inference(rat,[],[s17,s2,s18,s20,s7,s9,s4,s6])).
% 0.22/0.32 cnf(s22, plain, ~spl11_6, inference(rat,[],[s8,s21])).
% 0.22/0.32 cnf(s23, plain, ~spl11_2, inference(rat,[],[s1,s21])).
% 0.22/0.32 cnf(s24, plain, spl11_7, inference(rat,[],[s5,s22])).
% 0.22/0.32 cnf(s26, plain, spl11_5, inference(rat,[],[s3,s23])).
% 0.22/0.32 cnf(s27, plain, $false, inference(rat,[],[s13,s24,s26])).
% 0.22/0.32 thf(f397,plain,(
% 0.22/0.32 $false),
% 0.22/0.32 inference(avatar_sat_refutation,[],[s27])).
% 0.22/0.32 % SZS output end Proof for theBenchmark
% 0.22/0.32 % (898840)------------------------------
% 0.22/0.32 % (898840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (898840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (898840)CaDiCaL version: 2.1.3
% 0.22/0.32 % (898840)Termination reason: Refutation
% 0.22/0.32 % (898840)Time elapsed: 0.019 s
% 0.22/0.32 % (898840)Peak memory usage: 13 MB
% 0.22/0.32 % (898840)Instructions burned: 34 (million)
% 0.22/0.32 % (898829)Success in time 0.072 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------