%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV019^5 : 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 08:37:28 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV019^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.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
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:03:12 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.31 % (709870)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (709875)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1927517148:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (709877)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3761458889:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (709876)lrs+10_16_si=on:nwc=1.5:random_seed=2268067731:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (709878)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=1478948854: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)
% 0.23/0.31 % (709880)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2979545119:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.31 % (709879)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=290570424:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (709877)Instruction limit reached!
% 0.23/0.31 % (709877)------------------------------
% 0.23/0.31 % (709877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (709877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (709877)CaDiCaL version: 2.1.3
% 0.23/0.31 % (709877)Termination reason: Instruction limit
% 0.23/0.31 % (709877)Termination phase: Saturation
% 0.23/0.31 % (709877)Time elapsed: 0.003 s
% 0.23/0.31 % (709877)Peak memory usage: 12 MB
% 0.23/0.31 % (709877)Instructions burned: 4 (million)
% 0.23/0.31 % (709881)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (709881)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
% 0.23/0.31 % (709876)Instruction limit reached!
% 0.23/0.31 % (709876)------------------------------
% 0.23/0.31 % (709876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (709876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (709876)CaDiCaL version: 2.1.3
% 0.23/0.31 % (709876)Termination reason: Instruction limit
% 0.23/0.31 % (709876)Termination phase: Saturation
% 0.23/0.31 % (709876)Time elapsed: 0.010 s
% 0.23/0.31 % (709876)Peak memory usage: 12 MB
% 0.23/0.31 % (709876)Instructions burned: 19 (million)
% 0.23/0.31 % (709881)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=2063252948:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.31 % (709878) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-709870-709878"...
% 0.23/0.31 % (709875)Instruction limit reached!
% 0.23/0.31 % (709875)------------------------------
% 0.23/0.31 % (709875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (709875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (709875)CaDiCaL version: 2.1.3
% 0.23/0.31 % (709875)Termination reason: Instruction limit
% 0.23/0.31 % (709875)Termination phase: Saturation
% 0.23/0.31 % (709875)Time elapsed: 0.025 s
% 0.23/0.31 % (709875)Peak memory usage: 12 MB
% 0.23/0.31 % (709875)Instructions burned: 89 (million)
% 0.23/0.31 % (709878)...printing done.
% 0.23/0.31 % (709878)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% 0.23/0.31 thf(type_def_5, type, a: $tType).
% 0.23/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.31 thf(func_def_0, type, cQ: (a > a > $o)).
% 0.23/0.31 thf(func_def_4, type, sK0: a).
% 0.23/0.31 thf(func_def_5, type, sK1: a).
% 0.23/0.31 thf(func_def_6, type, sK2: a).
% 0.23/0.31 thf(func_def_7, type, sK3: a).
% 0.23/0.31 thf(func_def_8, type, sK4: a).
% 0.23/0.31 thf(func_def_9, type, sK5: a).
% 0.23/0.31 thf(func_def_10, type, sK6: (a > a > $o)).
% 0.23/0.31 thf(func_def_11, type, sK7: (a > a)).
% 0.23/0.31 thf(f1,conjecture,(
% 0.23/0.31 ! [X0 : a] : ? [X1 : (a > $o)] : (! [X3 : a] : ((X1 @ X3) => ! [X4 : a] : ((X1 @ X4) <=> (cQ @ X3 @ X4))) & ? [X2 : a] : (X1 @ X2) & (X1 @ X0)) => (! [X0 : a] : (cQ @ X0 @ X0) & ! [X4 : a,X0 : a] : ((cQ @ X0 @ X4) => (cQ @ X4 @ X0)) & ! [X0 : a,X2 : a,X4 : a] : (((cQ @ X4 @ X2) & (cQ @ X0 @ X4)) => (cQ @ X0 @ X2)))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM559_pme)).
% 0.23/0.31 thf(f2,negated_conjecture,(
% 0.23/0.31 ~(! [X0 : a] : ? [X1 : (a > $o)] : (! [X3 : a] : ((X1 @ X3) => ! [X4 : a] : ((X1 @ X4) <=> (cQ @ X3 @ X4))) & ? [X2 : a] : (X1 @ X2) & (X1 @ X0)) => (! [X0 : a] : (cQ @ X0 @ X0) & ! [X4 : a,X0 : a] : ((cQ @ X0 @ X4) => (cQ @ X4 @ X0)) & ! [X0 : a,X2 : a,X4 : a] : (((cQ @ X4 @ X2) & (cQ @ X0 @ X4)) => (cQ @ X0 @ X2))))),
% 0.23/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.31 thf(f3,plain,(
% 0.23/0.31 ~(! [X0 : a] : ? [X1 : (a > $o)] : (! [X2 : a] : ((X1 @ X2) => ! [X3 : a] : ((X1 @ X3) <=> (cQ @ X2 @ X3))) & ? [X4 : a] : (X1 @ X4) & (X1 @ X0)) => (! [X5 : a] : (cQ @ X5 @ X5) & ! [X6 : a,X7 : a] : ((cQ @ X7 @ X6) => (cQ @ X6 @ X7)) & ! [X8 : a,X9 : a,X10 : a] : (((cQ @ X10 @ X9) & (cQ @ X8 @ X10)) => (cQ @ X8 @ X9))))),
% 0.23/0.31 inference(rectify,[],[f2])).
% 0.23/0.31 thf(f4,plain,(
% 0.23/0.31 ~(! [X0 : a] : ? [X1 : (a > $o)] : ((((X1 @ X0)) = $true) & ! [X2 : a] : ((((X1 @ X2)) = $true) => ! [X3 : a] : (((X1 @ X3)) = ((cQ @ X2 @ X3)))) & ? [X4 : a] : (((X1 @ X4)) = $true)) => (! [X7 : a,X6 : a] : (($true = ((cQ @ X7 @ X6))) => (((cQ @ X6 @ X7)) = $true)) & ! [X5 : a] : (((cQ @ X5 @ X5)) = $true) & ! [X9 : a,X10 : a,X8 : a] : ((($true = ((cQ @ X10 @ X9))) & (((cQ @ X8 @ X10)) = $true)) => ($true = ((cQ @ X8 @ X9))))))),
% 0.23/0.31 inference(fool_elimination,[],[f3])).
% 0.23/0.31 thf(f5,plain,(
% 0.23/0.31 (? [X6 : a,X7 : a] : (($true = ((cQ @ X7 @ X6))) & (((cQ @ X6 @ X7)) != $true)) | ? [X5 : a] : (((cQ @ X5 @ X5)) != $true) | ? [X9 : a,X10 : a,X8 : a] : (($true != ((cQ @ X8 @ X9))) & (($true = ((cQ @ X10 @ X9))) & (((cQ @ X8 @ X10)) = $true)))) & ! [X0 : a] : ? [X1 : (a > $o)] : (! [X2 : a] : ((((X1 @ X2)) != $true) | ! [X3 : a] : (((X1 @ X3)) = ((cQ @ X2 @ X3)))) & ? [X4 : a] : (((X1 @ X4)) = $true) & (((X1 @ X0)) = $true))),
% 0.23/0.31 inference(ennf_transformation,[],[f4])).
% 0.23/0.31 thf(f6,plain,(
% 0.23/0.31 (? [X9 : a,X8 : a,X10 : a] : (($true = ((cQ @ X10 @ X9))) & (((cQ @ X8 @ X10)) = $true) & ($true != ((cQ @ X8 @ X9)))) | ? [X5 : a] : (((cQ @ X5 @ X5)) != $true) | ? [X6 : a,X7 : a] : (($true = ((cQ @ X7 @ X6))) & (((cQ @ X6 @ X7)) != $true))) & ! [X0 : a] : ? [X1 : (a > $o)] : (! [X2 : a] : ((((X1 @ X2)) != $true) | ! [X3 : a] : (((X1 @ X3)) = ((cQ @ X2 @ X3)))) & ? [X4 : a] : (((X1 @ X4)) = $true) & (((X1 @ X0)) = $true))),
% 0.23/0.31 inference(flattening,[],[f5])).
% 0.23/0.31 thf(f7,plain,(
% 0.23/0.31 (? [X0 : a,X1 : a,X2 : a] : ((((cQ @ X2 @ X0)) = $true) & (((cQ @ X1 @ X2)) = $true) & (((cQ @ X1 @ X0)) != $true)) | ? [X3 : a] : (((cQ @ X3 @ X3)) != $true) | ? [X4 : a,X5 : a] : ((((cQ @ X5 @ X4)) = $true) & (((cQ @ X4 @ X5)) != $true))) & ! [X6 : a] : ? [X7 : (a > $o)] : (! [X8 : a] : ((((X7 @ X8)) != $true) | ! [X9 : a] : (((X7 @ X9)) = ((cQ @ X8 @ X9)))) & ? [X10 : a] : (((X7 @ X10)) = $true) & (((X7 @ X6)) = $true))),
% 0.23/0.31 inference(rectify,[],[f6])).
% 0.23/0.31 thf(f8,plain,(
% 0.23/0.31 (((((cQ @ sK2 @ sK0)) = $true) & (((cQ @ sK1 @ sK2)) = $true) & (((cQ @ sK1 @ sK0)) != $true)) | (((cQ @ sK3 @ sK3)) != $true) | ((((cQ @ sK5 @ sK4)) = $true) & ($true != ((cQ @ sK4 @ sK5))))) & ! [X6 : a] : (! [X8 : a] : ((((sK6 @ X6 @ X8)) != $true) | ! [X9 : a] : (((sK6 @ X6 @ X9)) = ((cQ @ X8 @ X9)))) & (((sK6 @ X6 @ (sK7 @ X6))) = $true) & (((sK6 @ X6 @ X6)) = $true))),
% 0.23/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X10,sK7 @ X6),skolemize(X10,sK7 @ X6)],[f7])).
% 0.23/0.31 thf(f9,plain,(
% 0.23/0.31 ( ! [X6 : a] : ((((sK6 @ X6 @ X6)) = $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f8])).
% 0.23/0.31 thf(f11,plain,(
% 0.23/0.31 ( ! [X8 : a,X6 : a,X9 : a] : ((((sK6 @ X6 @ X9)) = ((cQ @ X8 @ X9))) | (((sK6 @ X6 @ X8)) != $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f8])).
% 0.23/0.31 thf(f12,plain,(
% 0.23/0.31 (((cQ @ sK1 @ sK0)) != $true) | ($true != ((cQ @ sK4 @ sK5))) | (((cQ @ sK3 @ sK3)) != $true)),
% 0.23/0.31 inference(cnf_transformation,[],[f8])).
% 0.23/0.31 thf(f13,plain,(
% 0.23/0.31 (((cQ @ sK1 @ sK0)) != $true) | (((cQ @ sK3 @ sK3)) != $true) | (((cQ @ sK5 @ sK4)) = $true)),
% 0.23/0.31 inference(cnf_transformation,[],[f8])).
% 0.23/0.31 thf(f14,plain,(
% 0.23/0.31 ($true != ((cQ @ sK4 @ sK5))) | (((cQ @ sK1 @ sK2)) = $true) | (((cQ @ sK3 @ sK3)) != $true)),
% 0.23/0.31 inference(cnf_transformation,[],[f8])).
% 0.23/0.31 thf(f15,plain,(
% 0.23/0.31 (((cQ @ sK5 @ sK4)) = $true) | (((cQ @ sK1 @ sK2)) = $true) | (((cQ @ sK3 @ sK3)) != $true)),
% 0.23/0.31 inference(cnf_transformation,[],[f8])).
% 0.23/0.31 thf(f16,plain,(
% 0.23/0.31 (((cQ @ sK2 @ sK0)) = $true) | (((cQ @ sK3 @ sK3)) != $true) | ($true != ((cQ @ sK4 @ sK5)))),
% 0.23/0.31 inference(cnf_transformation,[],[f8])).
% 0.23/0.31 thf(f17,plain,(
% 0.23/0.31 (((cQ @ sK5 @ sK4)) = $true) | (((cQ @ sK2 @ sK0)) = $true) | (((cQ @ sK3 @ sK3)) != $true)),
% 0.23/0.31 inference(cnf_transformation,[],[f8])).
% 0.23/0.31 thf(f19,plain,(
% 0.23/0.31 ( ! [X8 : a,X6 : a,X9 : a] : (($true = ((sK6 @ X6 @ X9))) | (((sK6 @ X6 @ X8)) != $true) | ($false = ((cQ @ X8 @ X9)))) )),
% 0.23/0.31 inference(iff_proxy_clausification,[],[f11])).
% 0.23/0.31 thf(f20,plain,(
% 0.23/0.31 ( ! [X8 : a,X6 : a,X9 : a] : (($true = ((cQ @ X8 @ X9))) | (((sK6 @ X6 @ X8)) != $true) | ($false = ((sK6 @ X6 @ X9)))) )),
% 0.23/0.31 inference(iff_proxy_clausification,[],[f11])).
% 0.23/0.31 thf(f22,definition,(
% 0.23/0.31 spl8_1 <=> (((cQ @ sK2 @ sK0)) = $true)),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.23/0.31 thf(f24,plain,(
% 0.23/0.31 (((cQ @ sK2 @ sK0)) = $true) | ~spl8_1),
% 0.23/0.31 inference(avatar_component_clause,[],[f22])).
% 0.23/0.31 thf(f26,definition,(
% 0.23/0.31 spl8_2 <=> (((cQ @ sK3 @ sK3)) = $true)),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.23/0.31 thf(f28,plain,(
% 0.23/0.31 (((cQ @ sK3 @ sK3)) != $true) | spl8_2),
% 0.23/0.31 inference(avatar_component_clause,[],[f26])).
% 0.23/0.31 thf(f30,definition,(
% 0.23/0.31 spl8_3 <=> ($true = ((cQ @ sK4 @ sK5)))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.23/0.31 thf(f32,plain,(
% 0.23/0.31 ($true != ((cQ @ sK4 @ sK5))) | spl8_3),
% 0.23/0.31 inference(avatar_component_clause,[],[f30])).
% 0.23/0.31 thf(f33,plain,(
% 0.23/0.31 spl8_1 | ~spl8_2 | ~spl8_3),
% 0.23/0.31 inference(avatar_split_clause,[],[f16,f30,f26,f22])).
% 0.23/0.31 thf(f35,definition,(
% 0.23/0.31 spl8_4 <=> (((cQ @ sK5 @ sK4)) = $true)),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
% 0.23/0.31 thf(f37,plain,(
% 0.23/0.31 (((cQ @ sK5 @ sK4)) = $true) | ~spl8_4),
% 0.23/0.31 inference(avatar_component_clause,[],[f35])).
% 0.23/0.31 thf(f38,plain,(
% 0.23/0.31 spl8_4 | spl8_1 | ~spl8_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f17,f26,f22,f35])).
% 0.23/0.31 thf(f40,definition,(
% 0.23/0.31 spl8_5 <=> (((cQ @ sK1 @ sK2)) = $true)),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.23/0.31 thf(f42,plain,(
% 0.23/0.31 (((cQ @ sK1 @ sK2)) = $true) | ~spl8_5),
% 0.23/0.31 inference(avatar_component_clause,[],[f40])).
% 0.23/0.31 thf(f43,plain,(
% 0.23/0.31 spl8_5 | ~spl8_3 | ~spl8_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f14,f26,f30,f40])).
% 0.23/0.31 thf(f45,definition,(
% 0.23/0.31 spl8_6 <=> (((cQ @ sK1 @ sK0)) = $true)),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 0.23/0.31 thf(f47,plain,(
% 0.23/0.31 (((cQ @ sK1 @ sK0)) != $true) | spl8_6),
% 0.23/0.31 inference(avatar_component_clause,[],[f45])).
% 0.23/0.31 thf(f48,plain,(
% 0.23/0.31 ~spl8_6 | ~spl8_2 | spl8_4),
% 0.23/0.31 inference(avatar_split_clause,[],[f13,f35,f26,f45])).
% 0.23/0.31 thf(f49,plain,(
% 0.23/0.31 ~spl8_2 | spl8_5 | spl8_4),
% 0.23/0.31 inference(avatar_split_clause,[],[f15,f35,f40,f26])).
% 0.23/0.31 thf(f50,plain,(
% 0.23/0.31 ~spl8_6 | ~spl8_3 | ~spl8_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f12,f26,f30,f45])).
% 0.23/0.31 thf(f51,plain,(
% 0.23/0.31 ( ! [X0 : a] : ((((sK6 @ X0 @ sK3)) != $true) | (((sK6 @ X0 @ sK3)) = $false) | ($true != $true)) ) | spl8_2),
% 0.23/0.31 inference(superposition,[],[f28,f20])).
% 0.23/0.31 thf(f52,plain,(
% 0.23/0.31 ( ! [X0 : a] : ((((sK6 @ X0 @ sK3)) = $false) | (((sK6 @ X0 @ sK3)) != $true)) ) | spl8_2),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f51])).
% 0.23/0.31 thf(f55,plain,(
% 0.23/0.31 (((sK6 @ sK3 @ sK3)) != $true) | ($false = $true) | spl8_2),
% 0.23/0.31 inference(superposition,[],[f9,f52])).
% 0.23/0.31 thf(f58,plain,(
% 0.23/0.31 (((sK6 @ sK3 @ sK3)) != $true) | spl8_2),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f55])).
% 0.23/0.31 thf(f63,plain,(
% 0.23/0.31 $false | spl8_2),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f58,f9])).
% 0.23/0.31 thf(f64,plain,(
% 0.23/0.31 spl8_2),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f63])).
% 0.23/0.31 thf(f65,plain,(
% 0.23/0.31 ( ! [X0 : a] : (($false = ((sK6 @ X0 @ sK5))) | ($true != $true) | (((sK6 @ X0 @ sK4)) != $true)) ) | spl8_3),
% 0.23/0.31 inference(superposition,[],[f32,f20])).
% 0.23/0.31 thf(f66,plain,(
% 0.23/0.31 ( ! [X0 : a] : (($false = ((sK6 @ X0 @ sK5))) | (((sK6 @ X0 @ sK4)) != $true)) ) | spl8_3),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f65])).
% 0.23/0.31 thf(f67,plain,(
% 0.23/0.31 ($true != ((sK6 @ sK5 @ sK4))) | ($false = $true) | spl8_3),
% 0.23/0.31 inference(superposition,[],[f66,f9])).
% 0.23/0.31 thf(f71,plain,(
% 0.23/0.31 ($true != ((sK6 @ sK5 @ sK4))) | spl8_3),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f67])).
% 0.23/0.31 thf(f76,definition,(
% 0.23/0.31 spl8_7 <=> ($true = ((sK6 @ sK5 @ sK4)))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition])).
% 0.23/0.31 thf(f78,plain,(
% 0.23/0.31 ($true != ((sK6 @ sK5 @ sK4))) | spl8_7),
% 0.23/0.31 inference(avatar_component_clause,[],[f76])).
% 0.23/0.31 thf(f79,plain,(
% 0.23/0.31 ~spl8_7 | spl8_3),
% 0.23/0.31 inference(avatar_split_clause,[],[f71,f30,f76])).
% 0.23/0.31 thf(f86,plain,(
% 0.23/0.31 ( ! [X0 : a] : (($true != ((sK6 @ sK5 @ X0))) | (((cQ @ X0 @ sK4)) = $false) | ($true != $true)) ) | spl8_7),
% 0.23/0.31 inference(superposition,[],[f78,f19])).
% 0.23/0.31 thf(f87,plain,(
% 0.23/0.31 ( ! [X0 : a] : ((((cQ @ X0 @ sK4)) = $false) | ($true != ((sK6 @ sK5 @ X0)))) ) | spl8_7),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f86])).
% 0.23/0.31 thf(f89,plain,(
% 0.23/0.31 ($false = $true) | ($true != ((sK6 @ sK5 @ sK5))) | (~spl8_4 | spl8_7)),
% 0.23/0.31 inference(superposition,[],[f87,f37])).
% 0.23/0.31 thf(f95,plain,(
% 0.23/0.31 ($true != ((sK6 @ sK5 @ sK5))) | (~spl8_4 | spl8_7)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f89])).
% 0.23/0.31 thf(f98,plain,(
% 0.23/0.31 $false | (~spl8_4 | spl8_7)),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f95,f9])).
% 0.23/0.31 thf(f99,plain,(
% 0.23/0.31 ~spl8_4 | spl8_7),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f98])).
% 0.23/0.31 thf(f100,plain,(
% 0.23/0.31 ( ! [X0 : a] : (($false = ((sK6 @ X0 @ sK0))) | (((sK6 @ X0 @ sK1)) != $true) | ($true != $true)) ) | spl8_6),
% 0.23/0.31 inference(superposition,[],[f47,f20])).
% 0.23/0.31 thf(f101,plain,(
% 0.23/0.31 ( ! [X0 : a] : (($false = ((sK6 @ X0 @ sK0))) | (((sK6 @ X0 @ sK1)) != $true)) ) | spl8_6),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f100])).
% 0.23/0.31 thf(f105,plain,(
% 0.23/0.31 ( ! [X0 : a,X1 : a] : ((((sK6 @ X0 @ X1)) != $true) | ($false = $true) | (((sK6 @ X0 @ sK1)) != $true) | (((cQ @ X1 @ sK0)) = $false)) ) | spl8_6),
% 0.23/0.31 inference(superposition,[],[f19,f101])).
% 0.23/0.31 thf(f106,plain,(
% 0.23/0.31 ( ! [X0 : a,X1 : a] : ((((cQ @ X1 @ sK0)) = $false) | (((sK6 @ X0 @ sK1)) != $true) | (((sK6 @ X0 @ X1)) != $true)) ) | spl8_6),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f105])).
% 0.23/0.31 thf(f118,plain,(
% 0.23/0.31 ( ! [X0 : a] : (($false = $true) | (((sK6 @ X0 @ sK1)) != $true) | (((sK6 @ X0 @ sK2)) != $true)) ) | (~spl8_1 | spl8_6)),
% 0.23/0.31 inference(superposition,[],[f106,f24])).
% 0.23/0.31 thf(f122,plain,(
% 0.23/0.31 ( ! [X0 : a] : ((((sK6 @ X0 @ sK2)) != $true) | (((sK6 @ X0 @ sK1)) != $true)) ) | (~spl8_1 | spl8_6)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f118])).
% 0.23/0.31 thf(f128,plain,(
% 0.23/0.31 ( ! [X0 : a,X1 : a] : (($true != $true) | (((sK6 @ X0 @ sK1)) != $true) | (((cQ @ X1 @ sK2)) = $false) | (((sK6 @ X0 @ X1)) != $true)) ) | (~spl8_1 | spl8_6)),
% 0.23/0.31 inference(superposition,[],[f122,f19])).
% 0.23/0.31 thf(f129,plain,(
% 0.23/0.31 ( ! [X0 : a,X1 : a] : ((((cQ @ X1 @ sK2)) = $false) | (((sK6 @ X0 @ X1)) != $true) | (((sK6 @ X0 @ sK1)) != $true)) ) | (~spl8_1 | spl8_6)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f128])).
% 0.23/0.31 thf(f187,plain,(
% 0.23/0.31 ( ! [X0 : a] : ((((sK6 @ X0 @ sK1)) != $true) | ($false = $true) | (((sK6 @ X0 @ sK1)) != $true)) ) | (~spl8_1 | ~spl8_5 | spl8_6)),
% 0.23/0.31 inference(superposition,[],[f42,f129])).
% 0.23/0.31 thf(f190,plain,(
% 0.23/0.31 ( ! [X0 : a] : (($false = $true) | (((sK6 @ X0 @ sK1)) != $true)) ) | (~spl8_1 | ~spl8_5 | spl8_6)),
% 0.23/0.31 inference(duplicate_literal_removal,[],[f187])).
% 0.23/0.31 thf(f191,plain,(
% 0.23/0.31 ( ! [X0 : a] : ((((sK6 @ X0 @ sK1)) != $true)) ) | (~spl8_1 | ~spl8_5 | spl8_6)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f190])).
% 0.23/0.31 thf(f346,plain,(
% 0.23/0.31 ($true != $true) | (~spl8_1 | ~spl8_5 | spl8_6)),
% 0.23/0.31 inference(superposition,[],[f191,f9])).
% 0.23/0.31 thf(f349,plain,(
% 0.23/0.31 $false | (~spl8_1 | ~spl8_5 | spl8_6)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f346])).
% 0.23/0.31 thf(f350,plain,(
% 0.23/0.31 ~spl8_1 | ~spl8_5 | spl8_6),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f349])).
% 0.23/0.31 cnf(s1, plain, spl8_1 | ~spl8_2 | ~spl8_3, inference(sat_conversion,[],[f33])).
% 0.23/0.31 cnf(s2, plain, spl8_1 | ~spl8_2 | spl8_4, inference(sat_conversion,[],[f38])).
% 0.23/0.31 cnf(s3, plain, ~spl8_2 | ~spl8_3 | spl8_5, inference(sat_conversion,[],[f43])).
% 0.23/0.31 cnf(s4, plain, ~spl8_2 | spl8_4 | ~spl8_6, inference(sat_conversion,[],[f48])).
% 0.23/0.31 cnf(s5, plain, ~spl8_2 | spl8_4 | spl8_5, inference(sat_conversion,[],[f49])).
% 0.23/0.31 cnf(s6, plain, ~spl8_2 | ~spl8_3 | ~spl8_6, inference(sat_conversion,[],[f50])).
% 0.23/0.31 cnf(s8, plain, spl8_2, inference(sat_conversion,[],[f64])).
% 0.23/0.31 cnf(s9, plain, spl8_3 | ~spl8_7, inference(sat_conversion,[],[f79])).
% 0.23/0.31 cnf(s12, plain, ~spl8_4 | spl8_7, inference(sat_conversion,[],[f99])).
% 0.23/0.31 cnf(s30, plain, ~spl8_1 | ~spl8_5 | spl8_6, inference(sat_conversion,[],[f350])).
% 0.23/0.31 cnf(s31, plain, ~spl8_3 | ~spl8_6, inference(rat,[],[s6,s8])).
% 0.23/0.31 cnf(s32, plain, spl8_4 | spl8_5, inference(rat,[],[s5,s8])).
% 0.23/0.31 cnf(s33, plain, spl8_4 | ~spl8_6, inference(rat,[],[s4,s8])).
% 0.23/0.31 cnf(s34, plain, ~spl8_3 | spl8_5, inference(rat,[],[s3,s8])).
% 0.23/0.31 cnf(s35, plain, spl8_1 | spl8_4, inference(rat,[],[s2,s8])).
% 0.23/0.31 cnf(s36, plain, spl8_1 | ~spl8_3, inference(rat,[],[s1,s8])).
% 0.23/0.31 cnf(s37, plain, spl8_1, inference(rat,[],[s9,s12,s36,s35])).
% 0.23/0.31 cnf(s38, plain, spl8_4, inference(rat,[],[s30,s33,s32,s37])).
% 0.23/0.31 cnf(s39, plain, spl8_7, inference(rat,[],[s12,s38])).
% 0.23/0.31 cnf(s40, plain, spl8_3, inference(rat,[],[s9,s39])).
% 0.23/0.31 cnf(s41, plain, ~spl8_6, inference(rat,[],[s31,s40])).
% 0.23/0.31 cnf(s42, plain, spl8_5, inference(rat,[],[s34,s40])).
% 0.23/0.31 cnf(s45, plain, $false, inference(rat,[],[s30,s37,s41,s42])).
% 0.23/0.31 thf(f351,plain,(
% 0.23/0.31 $false),
% 0.23/0.31 inference(avatar_sat_refutation,[],[s45])).
% 0.23/0.31 % SZS output end Proof for theBenchmark
% 0.23/0.31 % (709878)------------------------------
% 0.23/0.31 % (709878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (709878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (709878)CaDiCaL version: 2.1.3
% 0.23/0.31 % (709878)Termination reason: Refutation
% 0.23/0.31 % (709878)Time elapsed: 0.016 s
% 0.23/0.31 % (709878)Peak memory usage: 13 MB
% 0.23/0.31 % (709878)Instructions burned: 26 (million)
% 0.23/0.31 % (709870)Success in time 0.056 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------