%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO263^5 : 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 : n001.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 08:47:18 AM UTC 2026
% Result : Theorem 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO263^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:47:51 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.32 % (1486668)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (1486678)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1546654192:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (1486679)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.32 % (1486679)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
% 0.21/0.32 % (1486673)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=269400771:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (1486674)lrs+10_16_si=on:nwc=1.5:random_seed=4141697073:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (1486675)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=279247872:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (1486677)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1972234471:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (1486676)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=2618991058: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)
% 0.21/0.32 % (1486679)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=2364460346:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.32 % (1486675)Refutation not found, incomplete strategy
% 0.21/0.32 % (1486675)------------------------------
% 0.21/0.32 % (1486675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1486675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1486675)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1486675)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.32 % (1486675)Time elapsed: 0.003 s
% 0.21/0.32 % (1486675)Peak memory usage: 12 MB
% 0.21/0.32 % (1486675)Instructions burned: 4 (million)
% 0.21/0.32 % (1486675)------------------------------
% 0.21/0.32 % (1486675)------------------------------
% 0.21/0.32 % (1486676)Refutation not found, incomplete strategy
% 0.21/0.32 % (1486676)------------------------------
% 0.21/0.32 % (1486676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1486676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1486676)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1486676)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.32 % (1486676)Time elapsed: 0.007 s
% 0.21/0.32 % (1486676)Peak memory usage: 12 MB
% 0.21/0.32 % (1486676)Instructions burned: 9 (million)
% 0.21/0.32 % (1486676)------------------------------
% 0.21/0.32 % (1486676)------------------------------
% 0.21/0.32 % (1486674)Instruction limit reached!
% 0.21/0.32 % (1486674)------------------------------
% 0.21/0.32 % (1486674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1486674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1486674)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1486674)Termination reason: Instruction limit
% 0.21/0.32 % (1486674)Termination phase: Saturation
% 0.21/0.32 % (1486674)Time elapsed: 0.012 s
% 0.21/0.32 % (1486674)Peak memory usage: 12 MB
% 0.21/0.32 % (1486674)Instructions burned: 18 (million)
% 0.21/0.32 % (1486677)Instruction limit reached!
% 0.21/0.32 % (1486677)------------------------------
% 0.21/0.32 % (1486677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1486677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1486677)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1486677)Termination reason: Instruction limit
% 0.21/0.32 % (1486677)Termination phase: Saturation
% 0.21/0.32 % (1486677)Time elapsed: 0.013 s
% 0.21/0.32 % (1486677)Peak memory usage: 11 MB
% 0.21/0.32 % (1486677)Instructions burned: 24 (million)
% 0.21/0.32 % (1486678)Instruction limit reached!
% 0.21/0.32 % (1486678)------------------------------
% 0.21/0.32 % (1486678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1486678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1486678)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1486678)Termination reason: Instruction limit
% 0.21/0.32 % (1486678)Termination phase: Saturation
% 0.21/0.32 % (1486678)Time elapsed: 0.023 s
% 0.21/0.32 % (1486678)Peak memory usage: 12 MB
% 0.21/0.32 % (1486678)Instructions burned: 75 (million)
% 0.21/0.32 % (1486673) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1486668-1486673"...
% 0.21/0.32 % (1486673)...printing done.
% 0.21/0.32 % (1486673)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Theorem for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% 0.21/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.32 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.32 thf(func_def_4, type, sK1: ($i > $o)).
% 0.21/0.32 thf(func_def_8, type, sK5: (($i > $o) > $i)).
% 0.21/0.32 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.21/0.32 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.32 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.32 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.32 thf(f1,conjecture,(
% 0.21/0.32 ! [X3 : ($i > $o),X2 : $i,X0 : $i,X1 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : ((~(X3 @ X2) | (X4 @ X2)) & ((X5 @ X0) | (X4 @ X0)) & ! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & ((X3 @ X1) | (X5 @ X1)))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM125D)).
% 0.21/0.32 thf(f2,negated_conjecture,(
% 0.21/0.32 ~ ! [X3 : ($i > $o),X2 : $i,X0 : $i,X1 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : ((~(X3 @ X2) | (X4 @ X2)) & ((X5 @ X0) | (X4 @ X0)) & ! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & ((X3 @ X1) | (X5 @ X1)))),
% 0.21/0.32 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.32 thf(f3,plain,(
% 0.21/0.32 ~ ! [X0 : ($i > $o),X1 : $i,X2 : $i,X3 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : ((~(X0 @ X1) | (X4 @ X1)) & ((X5 @ X2) | (X4 @ X2)) & ! [X6 : $i] : ((X5 @ X6) <=> ~(X0 @ X6)) & ((X0 @ X3) | (X5 @ X3)))),
% 0.21/0.32 inference(rectify,[],[f2])).
% 0.21/0.32 thf(f4,plain,(
% 0.21/0.32 ~ ! [X0 : ($i > $o),X1 : $i,X2 : $i,X3 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : ((~ (((X0 @ X1)) = $true) | (((X4 @ X1)) = $true)) & ((((X4 @ X2)) = $true) | (((X5 @ X2)) = $true)) & ! [X6 : $i] : ((((X5 @ X6)) = $true) <=> ~ ($true = ((X0 @ X6)))) & ((((X0 @ X3)) = $true) | (((X5 @ X3)) = $true)))),
% 0.21/0.32 inference(fool_elimination,[],[f3])).
% 0.21/0.32 thf(f5,plain,(
% 0.21/0.32 ~ ! [X1 : $i,X2 : $i,X0 : ($i > $o),X3 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (((((X4 @ X1)) = $true) | (((X0 @ X1)) != $true)) & ((((X0 @ X3)) = $true) | (((X5 @ X3)) = $true)) & ((((X4 @ X2)) = $true) | (((X5 @ X2)) = $true)) & ! [X6 : $i] : ((((X5 @ X6)) = $true) <=> ($true != ((X0 @ X6)))))),
% 0.21/0.32 inference(flattening,[],[f4])).
% 0.21/0.32 thf(f6,plain,(
% 0.21/0.32 ? [X0 : ($i > $o),X1 : $i,X3 : $i,X2 : $i] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X3)) != $true) & (((X5 @ X3)) != $true)) | ? [X6 : $i] : ((((X5 @ X6)) = $true) <~> ($true != ((X0 @ X6)))) | ((((X4 @ X1)) != $true) & (((X0 @ X1)) = $true)) | ((((X5 @ X2)) != $true) & (((X4 @ X2)) != $true)))),
% 0.21/0.32 inference(ennf_transformation,[],[f5])).
% 0.21/0.32 thf(f7,definition,(
% 0.21/0.32 ! [X2 : $i,X5 : ($i > $o),X4 : ($i > $o)] : (((((X5 @ X2)) != $true) & (((X4 @ X2)) != $true)) | ~ (((sP0 @ X4 @ X5 @ X2)) = $true))),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.21/0.32 thf(f8,plain,(
% 0.21/0.32 ? [X0 : ($i > $o),X1 : $i,X3 : $i,X2 : $i] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X3)) != $true) & (((X5 @ X3)) != $true)) | ? [X6 : $i] : ((((X5 @ X6)) = $true) <~> ($true != ((X0 @ X6)))) | ((((X4 @ X1)) != $true) & (((X0 @ X1)) = $true)) | (((sP0 @ X4 @ X5 @ X2)) = $true))),
% 0.21/0.32 inference(definition_folding,[],[f6,f7])).
% 0.21/0.32 thf(f9,plain,(
% 0.21/0.32 ! [X2 : $i,X5 : ($i > $o),X4 : ($i > $o)] : (((((X5 @ X2)) != $true) & (((X4 @ X2)) != $true)) | (((sP0 @ X4 @ X5 @ X2)) != $true))),
% 0.21/0.32 inference(nnf_transformation,[],[f7])).
% 0.21/0.32 thf(f10,plain,(
% 0.21/0.32 ! [X0 : $i,X1 : ($i > $o),X2 : ($i > $o)] : (((((X1 @ X0)) != $true) & (((X2 @ X0)) != $true)) | (((sP0 @ X2 @ X1 @ X0)) != $true))),
% 0.21/0.32 inference(rectify,[],[f9])).
% 0.21/0.32 thf(f11,plain,(
% 0.21/0.32 ? [X0 : ($i > $o),X1 : $i,X3 : $i,X2 : $i] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X3)) != $true) & (((X5 @ X3)) != $true)) | ? [X6 : $i] : ((($true = ((X0 @ X6))) | (((X5 @ X6)) != $true)) & (($true != ((X0 @ X6))) | (((X5 @ X6)) = $true))) | ((((X4 @ X1)) != $true) & (((X0 @ X1)) = $true)) | (((sP0 @ X4 @ X5 @ X2)) = $true))),
% 0.21/0.32 inference(nnf_transformation,[],[f8])).
% 0.21/0.32 thf(f12,plain,(
% 0.21/0.32 ? [X0 : ($i > $o),X1 : $i,X2 : $i,X3 : $i] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X2)) != $true) & (((X5 @ X2)) != $true)) | ? [X6 : $i] : ((($true = ((X0 @ X6))) | (((X5 @ X6)) != $true)) & (($true != ((X0 @ X6))) | (((X5 @ X6)) = $true))) | ((((X4 @ X1)) != $true) & (((X0 @ X1)) = $true)) | (((sP0 @ X4 @ X5 @ X3)) = $true))),
% 0.21/0.32 inference(rectify,[],[f11])).
% 0.21/0.32 thf(f13,plain,(
% 0.21/0.32 ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((sK1 @ sK3)) != $true) & (((X5 @ sK3)) != $true)) | (((((sK1 @ (sK5 @ X5))) = $true) | (((X5 @ (sK5 @ X5))) != $true)) & ((((sK1 @ (sK5 @ X5))) != $true) | (((X5 @ (sK5 @ X5))) = $true))) | ((((X4 @ sK2)) != $true) & (((sK1 @ sK2)) = $true)) | (((sP0 @ X4 @ X5 @ sK4)) = $true))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,vAPP]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X6,sK5 @ X5)],[f12])).
% 0.21/0.32 thf(f14,plain,(
% 0.21/0.32 ( ! [X2 : ($i > $o),X0 : $i,X1 : ($i > $o)] : ((((sP0 @ X2 @ X1 @ X0)) != $true) | (((X2 @ X0)) != $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f10])).
% 0.21/0.32 thf(f17,plain,(
% 0.21/0.32 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((sK1 @ (sK5 @ X5))) != $true) | (((sP0 @ X4 @ X5 @ sK4)) = $true) | (((X4 @ sK2)) != $true) | (((X5 @ sK3)) != $true) | (((X5 @ (sK5 @ X5))) = $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f13])).
% 0.21/0.32 thf(f19,plain,(
% 0.21/0.32 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((X5 @ (sK5 @ X5))) != $true) | (((sK1 @ (sK5 @ X5))) = $true) | (((sP0 @ X4 @ X5 @ sK4)) = $true) | (((X4 @ sK2)) != $true) | (((X5 @ sK3)) != $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f13])).
% 0.21/0.32 thf(f21,plain,(
% 0.21/0.32 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((sP0 @ X4 @ X5 @ sK4)) = $true) | (((X5 @ (sK5 @ X5))) = $true) | (((sK1 @ (sK5 @ X5))) != $true) | (((sK1 @ sK3)) != $true) | (((X4 @ sK2)) != $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f13])).
% 0.21/0.32 thf(f23,plain,(
% 0.21/0.32 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((X4 @ sK2)) != $true) | (((sK1 @ (sK5 @ X5))) = $true) | (((sK1 @ sK3)) != $true) | (((sP0 @ X4 @ X5 @ sK4)) = $true) | (((X5 @ (sK5 @ X5))) != $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f13])).
% 0.21/0.32 thf(f27,definition,(
% 0.21/0.32 spl6_1 <=> ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((X4 @ sK2)) != $true) | (((X5 @ (sK5 @ X5))) != $true) | (((sP0 @ X4 @ X5 @ sK4)) = $true) | (((sK1 @ (sK5 @ X5))) = $true))),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.21/0.32 thf(f28,plain,(
% 0.21/0.32 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((X5 @ (sK5 @ X5))) != $true) | (((X4 @ sK2)) != $true) | (((sK1 @ (sK5 @ X5))) = $true) | (((sP0 @ X4 @ X5 @ sK4)) = $true)) ) | ~spl6_1),
% 0.21/0.32 inference(avatar_component_clause,[],[f27])).
% 0.21/0.32 thf(f30,definition,(
% 0.21/0.32 spl6_2 <=> (((sK1 @ sK3)) = $true)),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.21/0.32 thf(f32,plain,(
% 0.21/0.32 (((sK1 @ sK3)) != $true) | spl6_2),
% 0.21/0.32 inference(avatar_component_clause,[],[f30])).
% 0.21/0.32 thf(f33,plain,(
% 0.21/0.32 spl6_1 | ~spl6_2),
% 0.21/0.32 inference(avatar_split_clause,[],[f23,f30,f27])).
% 0.21/0.32 thf(f47,definition,(
% 0.21/0.32 spl6_6 <=> ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((sP0 @ X4 @ X5 @ sK4)) = $true) | (((X4 @ sK2)) != $true) | (((sK1 @ (sK5 @ X5))) != $true) | (((X5 @ (sK5 @ X5))) = $true))),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition])).
% 0.21/0.32 thf(f48,plain,(
% 0.21/0.32 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((sK1 @ (sK5 @ X5))) != $true) | (((X4 @ sK2)) != $true) | (((X5 @ (sK5 @ X5))) = $true) | (((sP0 @ X4 @ X5 @ sK4)) = $true)) ) | ~spl6_6),
% 0.21/0.32 inference(avatar_component_clause,[],[f47])).
% 0.21/0.32 thf(f49,plain,(
% 0.21/0.32 ~spl6_2 | spl6_6),
% 0.21/0.32 inference(avatar_split_clause,[],[f21,f47,f30])).
% 0.21/0.32 thf(f73,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : ((((X4 @ sK2)) != $true) | (((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | ((((^[Y0 : $i]: (~ (X6 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) != $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | ((((^[Y0 : $i]: (~ (X6 @ Y0))) @ sK3)) != $true)) )),
% 0.21/0.32 inference(primitive_instantiation,[],[f19])).
% 0.21/0.32 thf(f81,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : ((((~ (X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) != $true) | (((X4 @ sK2)) != $true) | (((~ (X6 @ sK3))) != $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true)) )),
% 0.21/0.32 inference(beta-eta_normalization,[],[f73])).
% 0.21/0.32 thf(f82,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : ((((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((~ (X6 @ sK3))) != $true) | (((X4 @ sK2)) != $true) | (((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | (((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true)) )),
% 0.21/0.32 inference(not_proxy_clausification,[],[f81])).
% 0.21/0.32 thf(f83,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : ((((X4 @ sK2)) != $true) | (((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | (((X6 @ sK3)) = $true)) )),
% 0.21/0.32 inference(not_proxy_clausification,[],[f82])).
% 0.21/0.32 thf(f108,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o)] : ((((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((X6 @ sK3)) = $true) | (((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | ((((^[Y0 : $i]: ($true)) @ sK2)) != $true) | (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true)) )),
% 0.21/0.32 inference(primitive_instantiation,[],[f83])).
% 0.21/0.32 thf(f115,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o)] : ((((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | (((X6 @ sK3)) = $true) | (((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | ($true != $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true)) )),
% 0.21/0.32 inference(beta-eta_normalization,[],[f108])).
% 0.21/0.32 thf(f116,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o)] : ((((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | (((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((X6 @ sK3)) = $true)) )),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f115])).
% 0.21/0.32 thf(f221,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : (($true != $true) | (((X0 @ sK3)) = $true) | ((((^[Y0 : $i]: ($true)) @ sK4)) != $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) )),
% 0.21/0.32 inference(constrained_superposition,[],[f14,f116])).
% 0.21/0.32 thf(f241,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ sK3)) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ((((^[Y0 : $i]: ($true)) @ sK4)) != $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) )),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f221])).
% 0.21/0.32 thf(f242,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != $true) | (((X0 @ sK3)) = $true)) )),
% 0.21/0.32 inference(beta-eta_normalization,[],[f241])).
% 0.21/0.32 thf(f243,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ sK3)) = $true)) )),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f242])).
% 0.21/0.32 thf(f308,plain,(
% 0.21/0.32 (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true) | ($true != $true) | (((sK1 @ sK3)) = $true)),
% 0.21/0.32 inference(equality_factoring,[],[f243])).
% 0.21/0.32 thf(f309,plain,(
% 0.21/0.32 (((sK1 @ sK3)) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f308])).
% 0.21/0.32 thf(f330,plain,(
% 0.21/0.32 (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true) | spl6_2),
% 0.21/0.32 inference(forward_subsumption_resolution,[],[f309,f32])).
% 0.21/0.32 thf(f332,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : (($true != $true) | (((X0 @ sK2)) != $true) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | ((((^[Y0 : $i]: (~ (sK1 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true) | ((((^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK3)) != $true)) ) | spl6_2),
% 0.21/0.32 inference(constrained_superposition,[],[f17,f330])).
% 0.21/0.32 thf(f333,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : (((((^[Y0 : $i]: (~ (sK1 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | ((((^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK3)) != $true) | (((X0 @ sK2)) != $true)) ) | spl6_2),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f332])).
% 0.21/0.32 thf(f334,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ sK2)) != $true) | (((~ (sK1 @ sK3))) != $true) | (((~ (sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0))))))) = $true) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true)) ) | spl6_2),
% 0.21/0.32 inference(beta-eta_normalization,[],[f333])).
% 0.21/0.32 thf(f335,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ sK2)) != $true) | (((sK1 @ sK3)) = $true) | (((~ (sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0))))))) = $true) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true)) ) | spl6_2),
% 0.21/0.32 inference(not_proxy_clausification,[],[f334])).
% 0.21/0.32 thf(f336,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | (((sK1 @ sK3)) = $true) | (((X0 @ sK2)) != $true) | ($false = ((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))))) ) | spl6_2),
% 0.21/0.32 inference(not_proxy_clausification,[],[f335])).
% 0.21/0.32 thf(f337,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ sK2)) != $true) | ($false = ((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0))))))) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true)) ) | spl6_2),
% 0.21/0.32 inference(forward_subsumption_resolution,[],[f336,f32])).
% 0.21/0.32 thf(f338,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | (((X0 @ sK2)) != $true) | ($false = $true)) ) | spl6_2),
% 0.21/0.32 inference(forward_demodulation,[],[f337,f330])).
% 0.21/0.32 thf(f339,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ sK2)) != $true) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true)) ) | spl6_2),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f338])).
% 0.21/0.32 thf(f343,plain,(
% 0.21/0.32 (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | ((((^[Y0 : $i]: ($true)) @ sK2)) != $true) | spl6_2),
% 0.21/0.32 inference(imitation,[],[f339])).
% 0.21/0.32 thf(f349,plain,(
% 0.21/0.32 ($true != $true) | (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | spl6_2),
% 0.21/0.32 inference(beta-eta_normalization,[],[f343])).
% 0.21/0.32 thf(f350,plain,(
% 0.21/0.32 (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | spl6_2),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f349])).
% 0.21/0.32 thf(f356,plain,(
% 0.21/0.32 ((((^[Y0 : $i]: ($true)) @ sK4)) != $true) | ($true != $true) | spl6_2),
% 0.21/0.32 inference(constrained_superposition,[],[f14,f350])).
% 0.21/0.32 thf(f357,plain,(
% 0.21/0.32 ((((^[Y0 : $i]: ($true)) @ sK4)) != $true) | spl6_2),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f356])).
% 0.21/0.32 thf(f358,plain,(
% 0.21/0.32 ($true != $true) | spl6_2),
% 0.21/0.32 inference(beta-eta_normalization,[],[f357])).
% 0.21/0.32 thf(f359,plain,(
% 0.21/0.32 $false | spl6_2),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f358])).
% 0.21/0.32 thf(f360,plain,(
% 0.21/0.32 spl6_2),
% 0.21/0.32 inference(avatar_contradiction_clause,[],[f359])).
% 0.21/0.32 thf(f362,definition,(
% 0.21/0.32 spl6_19 <=> (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true)),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl6_19])],[avatar_definition])).
% 0.21/0.32 thf(f364,plain,(
% 0.21/0.32 (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true) | ~spl6_19),
% 0.21/0.32 inference(avatar_component_clause,[],[f362])).
% 0.21/0.32 thf(f368,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : ((((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | (((X4 @ sK2)) != $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | ((((^[Y0 : $i]: (~ (X6 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) != $true)) ) | ~spl6_1),
% 0.21/0.32 inference(primitive_instantiation,[],[f28])).
% 0.21/0.32 thf(f380,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : ((((X4 @ sK2)) != $true) | (((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | (((~ (X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) != $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true)) ) | ~spl6_1),
% 0.21/0.32 inference(beta-eta_normalization,[],[f368])).
% 0.21/0.32 thf(f381,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : ((((X4 @ sK2)) != $true) | (((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true)) ) | ~spl6_1),
% 0.21/0.32 inference(not_proxy_clausification,[],[f380])).
% 0.21/0.32 thf(f393,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o)] : ((((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | ((((^[Y0 : $i]: ($true)) @ sK2)) != $true)) ) | ~spl6_1),
% 0.21/0.32 inference(primitive_instantiation,[],[f381])).
% 0.21/0.32 thf(f400,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o)] : (($true != $true) | (((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true)) ) | ~spl6_1),
% 0.21/0.32 inference(beta-eta_normalization,[],[f393])).
% 0.21/0.32 thf(f401,plain,(
% 0.21/0.32 ( ! [X6 : ($i > $o)] : ((((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK4)) = $true) | (((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))) = $true)) ) | ~spl6_1),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f400])).
% 0.21/0.32 thf(f444,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != $true) | ((((^[Y0 : $i]: ($true)) @ sK4)) != $true)) ) | ~spl6_1),
% 0.21/0.32 inference(constrained_superposition,[],[f14,f401])).
% 0.21/0.32 thf(f446,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ((((^[Y0 : $i]: ($true)) @ sK4)) != $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_1),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f444])).
% 0.21/0.32 thf(f447,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : (($true != $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_1),
% 0.21/0.32 inference(beta-eta_normalization,[],[f446])).
% 0.21/0.32 thf(f448,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_1),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f447])).
% 0.21/0.32 thf(f470,plain,(
% 0.21/0.32 ($true != $true) | (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true) | ~spl6_1),
% 0.21/0.32 inference(equality_factoring,[],[f448])).
% 0.21/0.32 thf(f478,plain,(
% 0.21/0.32 (((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true) | ~spl6_1),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f470])).
% 0.21/0.32 thf(f491,plain,(
% 0.21/0.32 spl6_19 | ~spl6_1),
% 0.21/0.32 inference(avatar_split_clause,[],[f478,f27,f362])).
% 0.21/0.32 thf(f492,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | ($true != $true) | (((X0 @ sK2)) != $true) | ((((^[Y0 : $i]: (~ (sK1 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true)) ) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(constrained_superposition,[],[f48,f364])).
% 0.21/0.32 thf(f498,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ sK2)) != $true) | ((((^[Y0 : $i]: (~ (sK1 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0)))))) = $true) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true)) ) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f492])).
% 0.21/0.32 thf(f499,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | (((~ (sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0))))))) = $true) | (((X0 @ sK2)) != $true)) ) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(beta-eta_normalization,[],[f498])).
% 0.21/0.32 thf(f500,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : (($false = ((sK1 @ (sK5 @ (^[Y0 : $i]: (~ (sK1 @ Y0))))))) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | (((X0 @ sK2)) != $true)) ) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(not_proxy_clausification,[],[f499])).
% 0.21/0.32 thf(f501,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ sK2)) != $true) | ($false = $true) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true)) ) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(forward_demodulation,[],[f500,f364])).
% 0.21/0.32 thf(f502,plain,(
% 0.21/0.32 ( ! [X0 : ($i > $o)] : ((((X0 @ sK2)) != $true) | (((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true)) ) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f501])).
% 0.21/0.32 thf(f522,plain,(
% 0.21/0.32 ((((^[Y0 : $i]: ($true)) @ sK2)) != $true) | (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(imitation,[],[f502])).
% 0.21/0.32 thf(f524,plain,(
% 0.21/0.32 ($true != $true) | (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(beta-eta_normalization,[],[f522])).
% 0.21/0.32 thf(f525,plain,(
% 0.21/0.32 (((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK1 @ Y0))) @ sK4)) = $true) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f524])).
% 0.21/0.32 thf(f534,plain,(
% 0.21/0.32 ((((^[Y0 : $i]: ($true)) @ sK4)) != $true) | ($true != $true) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(constrained_superposition,[],[f14,f525])).
% 0.21/0.32 thf(f535,plain,(
% 0.21/0.32 ((((^[Y0 : $i]: ($true)) @ sK4)) != $true) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f534])).
% 0.21/0.32 thf(f536,plain,(
% 0.21/0.32 ($true != $true) | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(beta-eta_normalization,[],[f535])).
% 0.21/0.32 thf(f537,plain,(
% 0.21/0.32 $false | (~spl6_6 | ~spl6_19)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f536])).
% 0.21/0.32 thf(f538,plain,(
% 0.21/0.32 ~spl6_6 | ~spl6_19),
% 0.21/0.32 inference(avatar_contradiction_clause,[],[f537])).
% 0.21/0.32 cnf(s1, plain, spl6_1 | ~spl6_2, inference(sat_conversion,[],[f33])).
% 0.21/0.32 cnf(s4, plain, ~spl6_2 | spl6_6, inference(sat_conversion,[],[f49])).
% 0.21/0.32 cnf(s20, plain, spl6_2, inference(sat_conversion,[],[f360])).
% 0.21/0.32 cnf(s22, plain, ~spl6_1 | spl6_19, inference(sat_conversion,[],[f491])).
% 0.21/0.32 cnf(s24, plain, ~spl6_6 | ~spl6_19, inference(sat_conversion,[],[f538])).
% 0.21/0.32 cnf(s27, plain, spl6_6, inference(rat,[],[s4,s20])).
% 0.21/0.32 cnf(s28, plain, ~spl6_19, inference(rat,[],[s24,s27])).
% 0.21/0.32 cnf(s29, plain, ~spl6_1, inference(rat,[],[s22,s28])).
% 0.21/0.32 cnf(s31, plain, $false, inference(rat,[],[s1,s20,s29])).
% 0.21/0.32 thf(f539,plain,(
% 0.21/0.32 $false),
% 0.21/0.32 inference(avatar_sat_refutation,[],[s31])).
% 0.21/0.32 % SZS output end Proof for theBenchmark
% 0.21/0.32 % (1486673)------------------------------
% 0.21/0.32 % (1486673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1486673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1486673)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1486673)Termination reason: Refutation
% 0.21/0.32 % (1486673)Time elapsed: 0.021 s
% 0.21/0.32 % (1486673)Peak memory usage: 13 MB
% 0.21/0.32 % (1486673)Instructions burned: 35 (million)
% 0.21/0.32 % (1486668)Success in time 0.069 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------