%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV401^5 : 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 : n026.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 08:38:35 AM UTC 2026
% Result : Theorem 0.23s 0.38s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV401^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n026.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 15:46:57 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.27 Running higher-order theorem proving
% 0.23/0.28 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
% 0.23/0.38 % (766596)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.38 % (766603)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3237670691:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.38 % (766604)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=539951251: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)
% 0.23/0.38 % (766603)Instruction limit reached!
% 0.23/0.38 % (766603)------------------------------
% 0.23/0.38 % (766603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (766603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (766603)CaDiCaL version: 2.1.3
% 0.23/0.38 % (766603)Termination reason: Instruction limit
% 0.23/0.38 % (766603)Termination phase: Saturation
% 0.23/0.38 % (766603)Time elapsed: 0.003 s
% 0.23/0.38 % (766603)Peak memory usage: 12 MB
% 0.23/0.38 % (766603)Instructions burned: 5 (million)
% 0.23/0.38 % (766601)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1014187578:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.38 % (766602)lrs+10_16_si=on:nwc=1.5:random_seed=1566976026:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.38 % (766607)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.38 % (766607)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
% 0.23/0.38 % (766605)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=186055083:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.38 % (766606)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2374524771:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.38 % (766607)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=1820900487:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.38 % (766610)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1900875913:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.38 % (766610)Instruction limit reached!
% 0.23/0.38 % (766610)------------------------------
% 0.23/0.38 % (766610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (766610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (766610)CaDiCaL version: 2.1.3
% 0.23/0.38 % (766610)Termination reason: Instruction limit
% 0.23/0.38 % (766610)Termination phase: Saturation
% 0.23/0.38 % (766610)Time elapsed: 0.002 s
% 0.23/0.38 % (766610)Peak memory usage: 12 MB
% 0.23/0.38 % (766610)Instructions burned: 3 (million)
% 0.23/0.38 % (766602)Instruction limit reached!
% 0.23/0.38 % (766602)------------------------------
% 0.23/0.38 % (766602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (766602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (766602)CaDiCaL version: 2.1.3
% 0.23/0.38 % (766602)Termination reason: Instruction limit
% 0.23/0.38 % (766602)Termination phase: Saturation
% 0.23/0.38 % (766602)Time elapsed: 0.018 s
% 0.23/0.38 % (766602)Peak memory usage: 12 MB
% 0.23/0.38 % (766602)Instructions burned: 18 (million)
% 0.23/0.38 % (766605)Instruction limit reached!
% 0.23/0.38 % (766605)------------------------------
% 0.23/0.38 % (766605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (766605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (766605)CaDiCaL version: 2.1.3
% 0.23/0.38 % (766605)Termination reason: Instruction limit
% 0.23/0.38 % (766605)Termination phase: Saturation
% 0.23/0.38 % (766605)Time elapsed: 0.022 s
% 0.23/0.38 % (766605)Peak memory usage: 12 MB
% 0.23/0.38 % (766605)Instructions burned: 24 (million)
% 0.23/0.38 % (766617)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1267544680:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.38 % (766617)Instruction limit reached!
% 0.23/0.38 % (766617)------------------------------
% 0.23/0.38 % (766617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (766617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (766617)CaDiCaL version: 2.1.3
% 0.23/0.38 % (766617)Termination reason: Instruction limit
% 0.23/0.38 % (766617)Termination phase: Saturation
% 0.23/0.38 % (766617)Time elapsed: 0.003 s
% 0.23/0.38 % (766617)Peak memory usage: 12 MB
% 0.23/0.38 % (766617)Instructions burned: 6 (million)
% 0.23/0.38 % (766604) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-766596-766604"...
% 0.23/0.38 % (766604)...printing done.
% 0.23/0.38 % (766604)Refutation found. Thanks to Tanya!
% 0.23/0.38 % SZS status Theorem for theBenchmark
% 0.23/0.38 % SZS output start Proof for theBenchmark
% 0.23/0.38 thf(type_def_5, type, a: $tType).
% 0.23/0.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.38 thf(func_def_0, type, cF: ((a > $o) > a > $o)).
% 0.23/0.38 thf(func_def_1, type, cG: ((a > $o) > a > $o)).
% 0.23/0.38 thf(func_def_5, type, sK0: ((a > $o) > (a > $o) > a)).
% 0.23/0.38 thf(func_def_6, type, sK1: a).
% 0.23/0.38 thf(func_def_7, type, sK2: (a > $o)).
% 0.23/0.38 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.23/0.38 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.38 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.38 thf(f1,conjecture,(
% 0.23/0.38 (! [X1 : (a > $o),X0 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cF @ X1 @ X2) => (cF @ X0 @ X2))) & ! [X2 : a,X0 : (a > $o)] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2)) & ! [X2 : a,X0 : (a > $o)] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2))) => ! [X0 : (a > $o),X2 : a] : ((cF @ X0 @ X2) <=> (cF @ (cG @ (cF @ X0)) @ X2))),
% 0.23/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM67_pme)).
% 0.23/0.38 thf(f2,negated_conjecture,(
% 0.23/0.38 ~((! [X1 : (a > $o),X0 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cF @ X1 @ X2) => (cF @ X0 @ X2))) & ! [X2 : a,X0 : (a > $o)] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2)) & ! [X2 : a,X0 : (a > $o)] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2))) => ! [X0 : (a > $o),X2 : a] : ((cF @ X0 @ X2) <=> (cF @ (cG @ (cF @ X0)) @ X2)))),
% 0.23/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.38 thf(f3,plain,(
% 0.23/0.38 ~((! [X0 : (a > $o),X1 : (a > $o)] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) => ! [X3 : a] : ((cF @ X0 @ X3) => (cF @ X1 @ X3))) & ! [X4 : a,X5 : (a > $o)] : ((X5 @ X4) => (cG @ (cF @ X5) @ X4)) & ! [X6 : a,X7 : (a > $o)] : ((X7 @ X6) => (cF @ (cG @ X7) @ X6))) => ! [X8 : (a > $o),X9 : a] : ((cF @ X8 @ X9) <=> (cF @ (cG @ (cF @ X8)) @ X9)))),
% 0.23/0.38 inference(rectify,[],[f2])).
% 0.23/0.38 thf(f4,plain,(
% 0.23/0.38 ~((! [X7 : (a > $o),X6 : a] : (($true = ((X7 @ X6))) => ($true = ((cF @ (cG @ X7) @ X6)))) & ! [X1 : (a > $o),X0 : (a > $o)] : (! [X2 : a] : ((((X1 @ X2)) = $true) => (((X0 @ X2)) = $true)) => ! [X3 : a] : (($true = ((cF @ X0 @ X3))) => ($true = ((cF @ X1 @ X3))))) & ! [X5 : (a > $o),X4 : a] : (($true = ((X5 @ X4))) => (((cG @ (cF @ X5) @ X4)) = $true))) => ! [X9 : a,X8 : (a > $o)] : (((cF @ (cG @ (cF @ X8)) @ X9)) = ((cF @ X8 @ X9))))),
% 0.23/0.38 inference(fool_elimination,[],[f3])).
% 0.23/0.38 thf(f5,plain,(
% 0.23/0.38 ? [X9 : a,X8 : (a > $o)] : (((cF @ (cG @ (cF @ X8)) @ X9)) != ((cF @ X8 @ X9))) & (! [X6 : a,X7 : (a > $o)] : (($true = ((cF @ (cG @ X7) @ X6))) | ($true != ((X7 @ X6)))) & ! [X0 : (a > $o),X1 : (a > $o)] : (? [X2 : a] : ((((X1 @ X2)) = $true) & (((X0 @ X2)) != $true)) | ! [X3 : a] : (($true = ((cF @ X1 @ X3))) | ($true != ((cF @ X0 @ X3))))) & ! [X4 : a,X5 : (a > $o)] : ((((cG @ (cF @ X5) @ X4)) = $true) | ($true != ((X5 @ X4)))))),
% 0.23/0.38 inference(ennf_transformation,[],[f4])).
% 0.23/0.38 thf(f6,plain,(
% 0.23/0.38 ! [X6 : a,X7 : (a > $o)] : (($true = ((cF @ (cG @ X7) @ X6))) | ($true != ((X7 @ X6)))) & ! [X0 : (a > $o),X1 : (a > $o)] : (? [X2 : a] : ((((X1 @ X2)) = $true) & (((X0 @ X2)) != $true)) | ! [X3 : a] : (($true = ((cF @ X1 @ X3))) | ($true != ((cF @ X0 @ X3))))) & ? [X9 : a,X8 : (a > $o)] : (((cF @ (cG @ (cF @ X8)) @ X9)) != ((cF @ X8 @ X9))) & ! [X4 : a,X5 : (a > $o)] : ((((cG @ (cF @ X5) @ X4)) = $true) | ($true != ((X5 @ X4))))),
% 0.23/0.38 inference(flattening,[],[f5])).
% 0.23/0.38 thf(f7,plain,(
% 0.23/0.38 ! [X0 : a,X1 : (a > $o)] : (($true = ((cF @ (cG @ X1) @ X0))) | ($true != ((X1 @ X0)))) & ! [X2 : (a > $o),X3 : (a > $o)] : (? [X4 : a] : (($true = ((X3 @ X4))) & ($true != ((X2 @ X4)))) | ! [X5 : a] : (($true = ((cF @ X3 @ X5))) | ($true != ((cF @ X2 @ X5))))) & ? [X6 : a,X7 : (a > $o)] : (((cF @ (cG @ (cF @ X7)) @ X6)) != ((cF @ X7 @ X6))) & ! [X8 : a,X9 : (a > $o)] : (($true = ((cG @ (cF @ X9) @ X8))) | ($true != ((X9 @ X8))))),
% 0.23/0.38 inference(rectify,[],[f6])).
% 0.23/0.38 thf(f8,plain,(
% 0.23/0.38 ! [X0 : a,X1 : (a > $o)] : (($true = ((cF @ (cG @ X1) @ X0))) | ($true != ((X1 @ X0)))) & ! [X2 : (a > $o),X3 : (a > $o)] : ((($true = ((X3 @ (sK0 @ X3 @ X2)))) & ($true != ((X2 @ (sK0 @ X3 @ X2))))) | ! [X5 : a] : (($true = ((cF @ X3 @ X5))) | ($true != ((cF @ X2 @ X5))))) & (((cF @ (cG @ (cF @ sK2)) @ sK1)) != ((cF @ sK2 @ sK1))) & ! [X8 : a,X9 : (a > $o)] : (($true = ((cG @ (cF @ X9) @ X8))) | ($true != ((X9 @ X8))))),
% 0.23/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X4,sK0 @ X3 @ X2),skolemize(X6,sK1),skolemize(X7,sK2)],[f7])).
% 0.23/0.38 thf(f9,plain,(
% 0.23/0.38 ( ! [X8 : a,X9 : (a > $o)] : (($true = ((cG @ (cF @ X9) @ X8))) | ($true != ((X9 @ X8)))) )),
% 0.23/0.38 inference(cnf_transformation,[],[f8])).
% 0.23/0.38 thf(f10,plain,(
% 0.23/0.38 (((cF @ (cG @ (cF @ sK2)) @ sK1)) != ((cF @ sK2 @ sK1)))),
% 0.23/0.38 inference(cnf_transformation,[],[f8])).
% 0.23/0.38 thf(f11,plain,(
% 0.23/0.38 ( ! [X2 : (a > $o),X3 : (a > $o),X5 : a] : (($true != ((X2 @ (sK0 @ X3 @ X2)))) | ($true = ((cF @ X3 @ X5))) | ($true != ((cF @ X2 @ X5)))) )),
% 0.23/0.38 inference(cnf_transformation,[],[f8])).
% 0.23/0.38 thf(f12,plain,(
% 0.23/0.38 ( ! [X2 : (a > $o),X3 : (a > $o),X5 : a] : (($true = ((X3 @ (sK0 @ X3 @ X2)))) | ($true != ((cF @ X2 @ X5))) | ($true = ((cF @ X3 @ X5)))) )),
% 0.23/0.38 inference(cnf_transformation,[],[f8])).
% 0.23/0.38 thf(f13,plain,(
% 0.23/0.38 ( ! [X0 : a,X1 : (a > $o)] : (($true = ((cF @ (cG @ X1) @ X0))) | ($true != ((X1 @ X0)))) )),
% 0.23/0.38 inference(cnf_transformation,[],[f8])).
% 0.23/0.38 thf(f15,plain,(
% 0.23/0.38 ($true = ((cF @ sK2 @ sK1))) | (((cF @ (cG @ (cF @ sK2)) @ sK1)) = $true)),
% 0.23/0.38 inference(xor_proxy_clausification,[],[f10])).
% 0.23/0.38 thf(f16,plain,(
% 0.23/0.38 (((cF @ sK2 @ sK1)) = $false) | (((cF @ (cG @ (cF @ sK2)) @ sK1)) = $false)),
% 0.23/0.38 inference(xor_proxy_clausification,[],[f10])).
% 0.23/0.38 thf(f18,definition,(
% 0.23/0.38 spl3_1 <=> (((cF @ (cG @ (cF @ sK2)) @ sK1)) = $false)),
% 0.23/0.38 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.23/0.38 thf(f20,plain,(
% 0.23/0.38 (((cF @ (cG @ (cF @ sK2)) @ sK1)) = $false) | ~spl3_1),
% 0.23/0.38 inference(avatar_component_clause,[],[f18])).
% 0.23/0.38 thf(f22,definition,(
% 0.23/0.38 spl3_2 <=> (((cF @ sK2 @ sK1)) = $false)),
% 0.23/0.38 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.23/0.38 thf(f24,plain,(
% 0.23/0.38 (((cF @ sK2 @ sK1)) = $false) | ~spl3_2),
% 0.23/0.38 inference(avatar_component_clause,[],[f22])).
% 0.23/0.38 thf(f25,plain,(
% 0.23/0.38 spl3_1 | spl3_2),
% 0.23/0.38 inference(avatar_split_clause,[],[f16,f22,f18])).
% 0.23/0.38 thf(f27,definition,(
% 0.23/0.38 spl3_3 <=> (((cF @ (cG @ (cF @ sK2)) @ sK1)) = $true)),
% 0.23/0.38 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.23/0.38 thf(f29,plain,(
% 0.23/0.38 (((cF @ (cG @ (cF @ sK2)) @ sK1)) = $true) | ~spl3_3),
% 0.23/0.38 inference(avatar_component_clause,[],[f27])).
% 0.23/0.38 thf(f31,definition,(
% 0.23/0.38 spl3_4 <=> ($true = ((cF @ sK2 @ sK1)))),
% 0.23/0.38 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.23/0.38 thf(f33,plain,(
% 0.23/0.38 ($true = ((cF @ sK2 @ sK1))) | ~spl3_4),
% 0.23/0.38 inference(avatar_component_clause,[],[f31])).
% 0.23/0.38 thf(f34,plain,(
% 0.23/0.38 spl3_3 | spl3_4),
% 0.23/0.38 inference(avatar_split_clause,[],[f15,f31,f27])).
% 0.23/0.38 thf(f40,plain,(
% 0.23/0.38 ( ! [X2 : a,X0 : (a > $o),X1 : (a > $o)] : ((((X0 @ (sK0 @ X1 @ (cG @ (cF @ X0))))) != $true) | (((cF @ (cG @ (cF @ X0)) @ X2)) != $true) | ($true != $true) | (((cF @ X1 @ X2)) = $true)) )),
% 0.23/0.38 inference(superposition,[],[f11,f9])).
% 0.23/0.38 thf(f49,plain,(
% 0.23/0.38 ( ! [X2 : a,X0 : (a > $o),X1 : (a > $o)] : ((((X0 @ (sK0 @ X1 @ (cG @ (cF @ X0))))) != $true) | (((cF @ (cG @ (cF @ X0)) @ X2)) != $true) | (((cF @ X1 @ X2)) = $true)) )),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f40])).
% 0.23/0.38 thf(f296,plain,(
% 0.23/0.38 ( ! [X2 : a,X0 : (a > $o),X1 : a] : (($true = ((cF @ X0 @ X1))) | ($true != $true) | (((cF @ X0 @ X2)) = $true) | ($true != ((cF @ (cG @ (cF @ X0)) @ X1))) | (((cF @ (cG @ (cF @ X0)) @ X2)) != $true)) )),
% 0.23/0.38 inference(superposition,[],[f49,f12])).
% 0.23/0.38 thf(f300,plain,(
% 0.23/0.38 ( ! [X2 : a,X0 : (a > $o),X1 : a] : (($true != ((cF @ (cG @ (cF @ X0)) @ X1))) | (((cF @ (cG @ (cF @ X0)) @ X2)) != $true) | (((cF @ X0 @ X2)) = $true) | ($true = ((cF @ X0 @ X1)))) )),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f296])).
% 0.23/0.38 thf(f328,plain,(
% 0.23/0.38 ( ! [X0 : a] : (($true = ((cF @ sK2 @ sK1))) | ($true != ((cF @ (cG @ (cF @ sK2)) @ X0))) | ($true = ((cF @ sK2 @ X0))) | ($true != $true)) ) | ~spl3_3),
% 0.23/0.38 inference(superposition,[],[f300,f29])).
% 0.23/0.38 thf(f333,plain,(
% 0.23/0.38 ( ! [X0 : a] : (($true = ((cF @ sK2 @ X0))) | ($true != ((cF @ (cG @ (cF @ sK2)) @ X0))) | ($true = ((cF @ sK2 @ sK1)))) ) | ~spl3_3),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f328])).
% 0.23/0.38 thf(f340,plain,(
% 0.23/0.38 ( ! [X0 : a] : (($true = ((cF @ sK2 @ X0))) | ($true != ((cF @ (cG @ (cF @ sK2)) @ X0))) | ($true = $false)) ) | (~spl3_2 | ~spl3_3)),
% 0.23/0.38 inference(forward_demodulation,[],[f333,f24])).
% 0.23/0.38 thf(f341,plain,(
% 0.23/0.38 ( ! [X0 : a] : (($true != ((cF @ (cG @ (cF @ sK2)) @ X0))) | ($true = ((cF @ sK2 @ X0)))) ) | (~spl3_2 | ~spl3_3)),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f340])).
% 0.23/0.38 thf(f348,plain,(
% 0.23/0.38 ($true = ((cF @ sK2 @ sK1))) | ($true != $true) | (~spl3_2 | ~spl3_3)),
% 0.23/0.38 inference(superposition,[],[f341,f29])).
% 0.23/0.38 thf(f356,plain,(
% 0.23/0.38 ($true = ((cF @ sK2 @ sK1))) | (~spl3_2 | ~spl3_3)),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f348])).
% 0.23/0.38 thf(f375,plain,(
% 0.23/0.38 ($true = $false) | (~spl3_2 | ~spl3_3)),
% 0.23/0.38 inference(forward_demodulation,[],[f356,f24])).
% 0.23/0.38 thf(f376,plain,(
% 0.23/0.38 $false | (~spl3_2 | ~spl3_3)),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f375])).
% 0.23/0.38 thf(f377,plain,(
% 0.23/0.38 ~spl3_2 | ~spl3_3),
% 0.23/0.38 inference(avatar_contradiction_clause,[],[f376])).
% 0.23/0.38 thf(f379,plain,(
% 0.23/0.38 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 0.23/0.38 inference(forward_demodulation,[],[f33,f24])).
% 0.23/0.38 thf(f380,plain,(
% 0.23/0.38 $false | (~spl3_2 | ~spl3_4)),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f379])).
% 0.23/0.38 thf(f381,plain,(
% 0.23/0.38 ~spl3_2 | ~spl3_4),
% 0.23/0.38 inference(avatar_contradiction_clause,[],[f380])).
% 0.23/0.38 thf(f382,plain,(
% 0.23/0.38 ($true != ((cF @ sK2 @ sK1))) | ($true = $false) | ~spl3_1),
% 0.23/0.38 inference(superposition,[],[f20,f13])).
% 0.23/0.38 thf(f386,plain,(
% 0.23/0.38 ($true != ((cF @ sK2 @ sK1))) | ~spl3_1),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f382])).
% 0.23/0.38 thf(f391,plain,(
% 0.23/0.38 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 0.23/0.38 inference(forward_demodulation,[],[f29,f20])).
% 0.23/0.38 thf(f392,plain,(
% 0.23/0.38 $false | (~spl3_1 | ~spl3_3)),
% 0.23/0.38 inference(trivial_inequality_removal,[],[f391])).
% 0.23/0.38 thf(f393,plain,(
% 0.23/0.38 ~spl3_1 | ~spl3_3),
% 0.23/0.38 inference(avatar_contradiction_clause,[],[f392])).
% 0.23/0.38 thf(f394,plain,(
% 0.23/0.38 ~spl3_4 | ~spl3_1),
% 0.23/0.38 inference(avatar_split_clause,[],[f386,f18,f31])).
% 0.23/0.38 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f25])).
% 0.23/0.38 cnf(s2, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f34])).
% 0.23/0.38 cnf(s11, plain, ~spl3_2 | ~spl3_3, inference(sat_conversion,[],[f377])).
% 0.23/0.38 cnf(s13, plain, ~spl3_2 | ~spl3_4, inference(sat_conversion,[],[f381])).
% 0.23/0.38 cnf(s16, plain, ~spl3_1 | ~spl3_3, inference(sat_conversion,[],[f393])).
% 0.23/0.38 cnf(s17, plain, ~spl3_1 | ~spl3_4, inference(sat_conversion,[],[f394])).
% 0.23/0.38 cnf(s19, plain, ~spl3_2, inference(rat,[],[s2,s11,s13])).
% 0.23/0.38 cnf(s20, plain, spl3_1, inference(rat,[],[s1,s19])).
% 0.23/0.38 cnf(s21, plain, ~spl3_4, inference(rat,[],[s17,s20])).
% 0.23/0.38 cnf(s22, plain, ~spl3_3, inference(rat,[],[s16,s20])).
% 0.23/0.38 cnf(s23, plain, $false, inference(rat,[],[s2,s21,s22])).
% 0.23/0.38 thf(f395,plain,(
% 0.23/0.38 $false),
% 0.23/0.38 inference(avatar_sat_refutation,[],[s23])).
% 0.23/0.38 % SZS output end Proof for theBenchmark
% 0.23/0.38 % (766604)------------------------------
% 0.23/0.38 % (766604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (766604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (766604)CaDiCaL version: 2.1.3
% 0.23/0.38 % (766604)Termination reason: Refutation
% 0.23/0.38 % (766604)Time elapsed: 0.048 s
% 0.23/0.38 % (766604)Peak memory usage: 13 MB
% 0.23/0.38 % (766604)Instructions burned: 61 (million)
% 0.23/0.38 % (766596)Success in time 0.087 s
% 0.23/0.38 % Vampire exiting
%------------------------------------------------------------------------------