%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO264^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO264^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.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 16:42:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.31 % (1537677)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (1537686)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=302045962:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (1537682)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3189189287:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (1537684)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=238389833:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (1537683)lrs+10_16_si=on:nwc=1.5:random_seed=535400007:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (1537685)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=329076480: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)
% 0.22/0.31 % (1537684)Instruction limit reached!
% 0.22/0.31 % (1537684)------------------------------
% 0.22/0.31 % (1537684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1537684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1537684)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1537684)Termination reason: Instruction limit
% 0.22/0.31 % (1537684)Termination phase: Saturation
% 0.22/0.31 % (1537684)Time elapsed: 0.003 s
% 0.22/0.31 % (1537684)Peak memory usage: 12 MB
% 0.22/0.31 % (1537684)Instructions burned: 4 (million)
% 0.22/0.31 % (1537686)Instruction limit reached!
% 0.22/0.31 % (1537686)------------------------------
% 0.22/0.31 % (1537686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1537686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1537686)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1537686)Termination reason: Instruction limit
% 0.22/0.31 % (1537686)Termination phase: Saturation
% 0.22/0.31 % (1537686)Time elapsed: 0.008 s
% 0.22/0.31 % (1537686)Peak memory usage: 12 MB
% 0.22/0.31 % (1537686)Instructions burned: 27 (million)
% 0.22/0.31 % (1537688)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (1537688)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
% 0.22/0.31 % (1537685)Refutation not found, incomplete strategy
% 0.22/0.31 % (1537685)------------------------------
% 0.22/0.31 % (1537685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1537685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1537685)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1537685)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (1537685)Time elapsed: 0.006 s
% 0.22/0.31 % (1537685)Peak memory usage: 12 MB
% 0.22/0.31 % (1537685)Instructions burned: 8 (million)
% 0.22/0.31 % (1537685)------------------------------
% 0.22/0.31 % (1537685)------------------------------
% 0.22/0.31 % (1537688)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=266227004:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (1537683)Instruction limit reached!
% 0.22/0.31 % (1537683)------------------------------
% 0.22/0.31 % (1537683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1537683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1537683)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1537683)Termination reason: Instruction limit
% 0.22/0.31 % (1537683)Termination phase: Saturation
% 0.22/0.31 % (1537683)Time elapsed: 0.011 s
% 0.22/0.31 % (1537683)Peak memory usage: 12 MB
% 0.22/0.31 % (1537683)Instructions burned: 18 (million)
% 0.22/0.31 % (1537694)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4149064739:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (1537694)Instruction limit reached!
% 0.22/0.31 % (1537694)------------------------------
% 0.22/0.31 % (1537694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1537694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1537694)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1537694)Termination reason: Instruction limit
% 0.22/0.31 % (1537694)Termination phase: Saturation
% 0.22/0.31 % (1537694)Time elapsed: 0.001 s
% 0.22/0.31 % (1537694)Peak memory usage: 12 MB
% 0.22/0.31 % (1537694)Instructions burned: 2 (million)
% 0.22/0.31 % (1537687)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2320976175:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (1537682) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1537677-1537682"...
% 0.22/0.31 % (1537695)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=898261590:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.31 % (1537697)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.31 % (1537700)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
% 0.22/0.31 % (1537700)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.31 % (1537682)...printing done.
% 0.22/0.31 % (1537682)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% 0.22/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.31 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $i > $o)).
% 0.22/0.31 thf(func_def_6, type, sK3: ($i > $o)).
% 0.22/0.31 thf(func_def_8, type, sK5: (($i > $o) > $i)).
% 0.22/0.31 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.22/0.31 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.31 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.31 thf(f1,conjecture,(
% 0.22/0.31 ! [X3 : ($i > $o),X1 : $i,X2 : $i,X0 : $i] : ? [X5 : ($i > $o),X4 : ($i > $o)] : (((X4 @ X2) | ~(X3 @ X2)) & ((X4 @ X0) | (X5 @ X0)) & ! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & ((X3 @ X1) | (X5 @ X1)))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM125C)).
% 0.22/0.31 thf(f2,negated_conjecture,(
% 0.22/0.31 ~ ! [X3 : ($i > $o),X1 : $i,X2 : $i,X0 : $i] : ? [X5 : ($i > $o),X4 : ($i > $o)] : (((X4 @ X2) | ~(X3 @ X2)) & ((X4 @ X0) | (X5 @ X0)) & ! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & ((X3 @ X1) | (X5 @ X1)))),
% 0.22/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.31 thf(f3,plain,(
% 0.22/0.31 ~ ! [X0 : ($i > $o),X1 : $i,X2 : $i,X3 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (((X5 @ X2) | ~(X0 @ X2)) & ((X5 @ X3) | (X4 @ X3)) & ! [X6 : $i] : ((X4 @ X6) <=> ~(X0 @ X6)) & ((X0 @ X1) | (X4 @ X1)))),
% 0.22/0.31 inference(rectify,[],[f2])).
% 0.22/0.31 thf(f4,plain,(
% 0.22/0.31 ~ ! [X0 : ($i > $o),X1 : $i,X2 : $i,X3 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (((((X5 @ X2)) = $true) | ~ (((X0 @ X2)) = $true)) & ((((X5 @ X3)) = $true) | ($true = ((X4 @ X3)))) & ! [X6 : $i] : ((((X4 @ X6)) = $true) <=> ~ (((X0 @ X6)) = $true)) & ((((X4 @ X1)) = $true) | (((X0 @ X1)) = $true)))),
% 0.22/0.31 inference(fool_elimination,[],[f3])).
% 0.22/0.31 thf(f5,plain,(
% 0.22/0.31 ~ ! [X1 : $i,X3 : $i,X2 : $i,X0 : ($i > $o)] : ? [X5 : ($i > $o),X4 : ($i > $o)] : (((((X4 @ X1)) = $true) | (((X0 @ X1)) = $true)) & ((((X0 @ X2)) != $true) | (((X5 @ X2)) = $true)) & ((((X5 @ X3)) = $true) | ($true = ((X4 @ X3)))) & ! [X6 : $i] : ((((X0 @ X6)) != $true) <=> (((X4 @ X6)) = $true)))),
% 0.22/0.31 inference(flattening,[],[f4])).
% 0.22/0.31 thf(f6,plain,(
% 0.22/0.31 ? [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X2)) = $true) & (((X5 @ X2)) != $true)) | ((((X5 @ X3)) != $true) & ($true != ((X4 @ X3)))) | ? [X6 : $i] : ((((X0 @ X6)) != $true) <~> (((X4 @ X6)) = $true)) | ((((X4 @ X1)) != $true) & (((X0 @ X1)) != $true)))),
% 0.22/0.31 inference(ennf_transformation,[],[f5])).
% 0.22/0.31 thf(f7,definition,(
% 0.22/0.31 ! [X1 : $i,X4 : ($i > $o),X0 : ($i > $o)] : (((((X4 @ X1)) != $true) & (((X0 @ X1)) != $true)) | ~ (((sP0 @ X0 @ X4 @ X1)) = $true))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.31 thf(f8,plain,(
% 0.22/0.31 ? [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X2)) = $true) & (((X5 @ X2)) != $true)) | ((((X5 @ X3)) != $true) & ($true != ((X4 @ X3)))) | ? [X6 : $i] : ((((X0 @ X6)) != $true) <~> (((X4 @ X6)) = $true)) | (((sP0 @ X0 @ X4 @ X1)) = $true))),
% 0.22/0.31 inference(definition_folding,[],[f6,f7])).
% 0.22/0.31 thf(f9,plain,(
% 0.22/0.31 ! [X1 : $i,X4 : ($i > $o),X0 : ($i > $o)] : (((((X4 @ X1)) != $true) & (((X0 @ X1)) != $true)) | (((sP0 @ X0 @ X4 @ X1)) != $true))),
% 0.22/0.31 inference(nnf_transformation,[],[f7])).
% 0.22/0.31 thf(f10,plain,(
% 0.22/0.31 ! [X0 : $i,X1 : ($i > $o),X2 : ($i > $o)] : (((((X1 @ X0)) != $true) & (((X2 @ X0)) != $true)) | (((sP0 @ X2 @ X1 @ X0)) != $true))),
% 0.22/0.31 inference(rectify,[],[f9])).
% 0.22/0.31 thf(f11,plain,(
% 0.22/0.31 ? [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X2)) = $true) & (((X5 @ X2)) != $true)) | ((((X5 @ X3)) != $true) & ($true != ((X4 @ X3)))) | ? [X6 : $i] : (((((X4 @ X6)) != $true) | (((X0 @ X6)) = $true)) & ((((X4 @ X6)) = $true) | (((X0 @ X6)) != $true))) | (((sP0 @ X0 @ X4 @ X1)) = $true))),
% 0.22/0.31 inference(nnf_transformation,[],[f8])).
% 0.22/0.31 thf(f12,plain,(
% 0.22/0.31 ? [X0 : $i,X1 : $i,X2 : ($i > $o),X3 : $i] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((X2 @ X0)) = $true) & (((X5 @ X0)) != $true)) | ((((X5 @ X1)) != $true) & (((X4 @ X1)) != $true)) | ? [X6 : $i] : (((((X4 @ X6)) != $true) | (((X2 @ X6)) = $true)) & ((((X4 @ X6)) = $true) | (((X2 @ X6)) != $true))) | (((sP0 @ X2 @ X4 @ X3)) = $true))),
% 0.22/0.31 inference(rectify,[],[f11])).
% 0.22/0.31 thf(f13,plain,(
% 0.22/0.31 ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((sK3 @ sK1)) = $true) & (((X5 @ sK1)) != $true)) | ((((X5 @ sK2)) != $true) & (((X4 @ sK2)) != $true)) | (((((X4 @ (sK5 @ X4))) != $true) | (((sK3 @ (sK5 @ X4))) = $true)) & ((((X4 @ (sK5 @ X4))) = $true) | (((sK3 @ (sK5 @ X4))) != $true))) | (((sP0 @ sK3 @ X4 @ sK4)) = $true))),
% 0.22/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,vAPP]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X6,sK5 @ X4)],[f12])).
% 0.22/0.31 thf(f14,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : ($i > $o)] : ((((sP0 @ X2 @ X1 @ X0)) != $true) | (((X2 @ X0)) != $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f10])).
% 0.22/0.31 thf(f15,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : ($i > $o)] : ((((sP0 @ X2 @ X1 @ X0)) != $true) | (((X1 @ X0)) != $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f10])).
% 0.22/0.31 thf(f18,plain,(
% 0.22/0.31 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((X5 @ sK1)) != $true) | (((sK3 @ (sK5 @ X4))) != $true) | (((sP0 @ sK3 @ X4 @ sK4)) = $true) | (((X5 @ sK2)) != $true) | (((X4 @ (sK5 @ X4))) = $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f13])).
% 0.22/0.31 thf(f19,plain,(
% 0.22/0.31 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ (sK5 @ X4))) = $true) | (((X5 @ sK2)) != $true) | (((sP0 @ sK3 @ X4 @ sK4)) = $true) | (((X4 @ (sK5 @ X4))) != $true) | (((X5 @ sK1)) != $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f13])).
% 0.22/0.31 thf(f34,definition,(
% 0.22/0.31 spl6_3 <=> ! [X4 : ($i > $o)] : ((((X4 @ (sK5 @ X4))) = $true) | (((sK3 @ (sK5 @ X4))) != $true) | (((sP0 @ sK3 @ X4 @ sK4)) = $true))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.22/0.31 thf(f35,plain,(
% 0.22/0.31 ( ! [X4 : ($i > $o)] : ((((sK3 @ (sK5 @ X4))) != $true) | (((X4 @ (sK5 @ X4))) = $true) | (((sP0 @ sK3 @ X4 @ sK4)) = $true)) ) | ~spl6_3),
% 0.22/0.31 inference(avatar_component_clause,[],[f34])).
% 0.22/0.31 thf(f51,definition,(
% 0.22/0.31 spl6_7 <=> ! [X4 : ($i > $o)] : ((((sP0 @ sK3 @ X4 @ sK4)) = $true) | (((sK3 @ (sK5 @ X4))) = $true) | (((X4 @ (sK5 @ X4))) != $true))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
% 0.22/0.31 thf(f52,plain,(
% 0.22/0.31 ( ! [X4 : ($i > $o)] : ((((X4 @ (sK5 @ X4))) != $true) | (((sK3 @ (sK5 @ X4))) = $true) | (((sP0 @ sK3 @ X4 @ sK4)) = $true)) ) | ~spl6_7),
% 0.22/0.31 inference(avatar_component_clause,[],[f51])).
% 0.22/0.31 thf(f55,definition,(
% 0.22/0.31 spl6_8 <=> ! [X5 : ($i > $o)] : ((((X5 @ sK1)) != $true) | (((X5 @ sK2)) != $true))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 0.22/0.31 thf(f56,plain,(
% 0.22/0.31 ( ! [X5 : ($i > $o)] : ((((X5 @ sK2)) != $true) | (((X5 @ sK1)) != $true)) ) | ~spl6_8),
% 0.22/0.31 inference(avatar_component_clause,[],[f55])).
% 0.22/0.31 thf(f57,plain,(
% 0.22/0.31 spl6_8 | spl6_3),
% 0.22/0.31 inference(avatar_split_clause,[],[f18,f34,f55])).
% 0.22/0.31 thf(f58,plain,(
% 0.22/0.31 spl6_8 | spl6_7),
% 0.22/0.31 inference(avatar_split_clause,[],[f19,f51,f55])).
% 0.22/0.31 thf(f80,plain,(
% 0.22/0.31 ((((^[Y0 : $i]: ($true)) @ sK1)) != $true) | ((((^[Y0 : $i]: ($true)) @ sK2)) != $true) | ~spl6_8),
% 0.22/0.31 inference(primitive_instantiation,[],[f56])).
% 0.22/0.31 thf(f93,plain,(
% 0.22/0.31 ($true != $true) | ($true != $true) | ~spl6_8),
% 0.22/0.31 inference(beta-eta_normalization,[],[f80])).
% 0.22/0.31 thf(f94,plain,(
% 0.22/0.31 ($true != $true) | ~spl6_8),
% 0.22/0.31 inference(duplicate_literal_removal,[],[f93])).
% 0.22/0.31 thf(f95,plain,(
% 0.22/0.31 $false | ~spl6_8),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f94])).
% 0.22/0.31 thf(f96,plain,(
% 0.22/0.31 ~spl6_8),
% 0.22/0.31 inference(avatar_contradiction_clause,[],[f95])).
% 0.22/0.31 thf(f103,plain,(
% 0.22/0.31 ( ! [X5 : ($i > $o)] : ((((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))) = $true) | ((((^[Y0 : $i]: (~ (X5 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))) != $true) | (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (X5 @ Y0))) @ sK4)) = $true)) ) | ~spl6_7),
% 0.22/0.31 inference(primitive_instantiation,[],[f52])).
% 0.22/0.31 thf(f108,plain,(
% 0.22/0.31 ( ! [X5 : ($i > $o)] : ((((sP0 @ sK3 @ (^[Y0 : $i]: (~ (X5 @ Y0))) @ sK4)) = $true) | (((~ (X5 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0))))))) != $true) | (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))) = $true)) ) | ~spl6_7),
% 0.22/0.31 inference(beta-eta_normalization,[],[f103])).
% 0.22/0.31 thf(f109,plain,(
% 0.22/0.31 ( ! [X5 : ($i > $o)] : ((((sP0 @ sK3 @ (^[Y0 : $i]: (~ (X5 @ Y0))) @ sK4)) = $true) | ($true = ((X5 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0))))))) | (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))) = $true)) ) | ~spl6_7),
% 0.22/0.31 inference(not_proxy_clausification,[],[f108])).
% 0.22/0.31 thf(f156,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true != $true) | (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((sK3 @ sK4)) != $true)) ) | ~spl6_7),
% 0.22/0.31 inference(constrained_superposition,[],[f14,f109])).
% 0.22/0.31 thf(f160,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | (((sK3 @ sK4)) != $true)) ) | ~spl6_7),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f156])).
% 0.22/0.31 thf(f165,definition,(
% 0.22/0.31 spl6_11 <=> (((sK3 @ sK4)) = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.22/0.31 thf(f166,plain,(
% 0.22/0.31 (((sK3 @ sK4)) = $true) | ~spl6_11),
% 0.22/0.31 inference(avatar_component_clause,[],[f165])).
% 0.22/0.31 thf(f167,plain,(
% 0.22/0.31 (((sK3 @ sK4)) != $true) | spl6_11),
% 0.22/0.31 inference(avatar_component_clause,[],[f165])).
% 0.22/0.31 thf(f169,definition,(
% 0.22/0.31 spl6_12 <=> ! [X0 : ($i > $o)] : ((((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 0.22/0.31 thf(f170,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_12),
% 0.22/0.31 inference(avatar_component_clause,[],[f169])).
% 0.22/0.31 thf(f171,plain,(
% 0.22/0.31 ~spl6_11 | spl6_12 | ~spl6_7),
% 0.22/0.31 inference(avatar_split_clause,[],[f160,f51,f169,f165])).
% 0.22/0.31 thf(f266,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ((((^[Y0 : $i]: (~ (X0 @ Y0))) @ sK4)) != $true) | (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_7),
% 0.22/0.31 inference(constrained_superposition,[],[f15,f109])).
% 0.22/0.31 thf(f299,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ((((^[Y0 : $i]: (~ (X0 @ Y0))) @ sK4)) != $true)) ) | ~spl6_7),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f266])).
% 0.22/0.31 thf(f300,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != ((~ (X0 @ sK4)))) | ($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))))) ) | ~spl6_7),
% 0.22/0.31 inference(beta-eta_normalization,[],[f299])).
% 0.22/0.31 thf(f301,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ sK4)) = $true)) ) | ~spl6_7),
% 0.22/0.31 inference(not_proxy_clausification,[],[f300])).
% 0.22/0.31 thf(f353,plain,(
% 0.22/0.31 (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | (((sK3 @ sK4)) = $true) | ($true != $true) | ~spl6_7),
% 0.22/0.31 inference(equality_factoring,[],[f301])).
% 0.22/0.31 thf(f359,plain,(
% 0.22/0.31 (((sK3 @ sK4)) = $true) | (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | ~spl6_7),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f353])).
% 0.22/0.31 thf(f374,plain,(
% 0.22/0.31 (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | (~spl6_7 | spl6_11)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f359,f167])).
% 0.22/0.31 thf(f376,plain,(
% 0.22/0.31 (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | ((((^[Y0 : $i]: (~ (sK3 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | ($true != $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(constrained_superposition,[],[f35,f374])).
% 0.22/0.31 thf(f377,plain,(
% 0.22/0.31 ((((^[Y0 : $i]: (~ (sK3 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f376])).
% 0.22/0.31 thf(f378,plain,(
% 0.22/0.31 (((~ (sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0))))))) = $true) | (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(beta-eta_normalization,[],[f377])).
% 0.22/0.31 thf(f379,plain,(
% 0.22/0.31 ($false = ((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0))))))) | (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(not_proxy_clausification,[],[f378])).
% 0.22/0.31 thf(f380,plain,(
% 0.22/0.31 (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | ($false = $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(forward_demodulation,[],[f379,f374])).
% 0.22/0.31 thf(f381,plain,(
% 0.22/0.31 (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f380])).
% 0.22/0.31 thf(f401,plain,(
% 0.22/0.31 ((((^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) != $true) | ($true != $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(constrained_superposition,[],[f15,f381])).
% 0.22/0.31 thf(f405,plain,(
% 0.22/0.31 ((((^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) != $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f401])).
% 0.22/0.31 thf(f406,plain,(
% 0.22/0.31 (((~ (sK3 @ sK4))) != $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(beta-eta_normalization,[],[f405])).
% 0.22/0.31 thf(f407,plain,(
% 0.22/0.31 (((sK3 @ sK4)) = $true) | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(not_proxy_clausification,[],[f406])).
% 0.22/0.31 thf(f409,plain,(
% 0.22/0.31 $false | (~spl6_3 | ~spl6_7 | spl6_11)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f407,f167])).
% 0.22/0.31 thf(f410,plain,(
% 0.22/0.31 ~spl6_3 | ~spl6_7 | spl6_11),
% 0.22/0.31 inference(avatar_contradiction_clause,[],[f409])).
% 0.22/0.31 thf(f425,definition,(
% 0.22/0.31 spl6_17 <=> (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl6_17])],[avatar_definition])).
% 0.22/0.31 thf(f427,plain,(
% 0.22/0.31 (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | ~spl6_17),
% 0.22/0.31 inference(avatar_component_clause,[],[f425])).
% 0.22/0.31 thf(f469,plain,(
% 0.22/0.31 (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | ($true != $true) | ~spl6_12),
% 0.22/0.31 inference(equality_factoring,[],[f170])).
% 0.22/0.31 thf(f475,plain,(
% 0.22/0.31 (((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | ~spl6_12),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f469])).
% 0.22/0.31 thf(f487,plain,(
% 0.22/0.31 spl6_17 | ~spl6_12),
% 0.22/0.31 inference(avatar_split_clause,[],[f475,f169,f425])).
% 0.22/0.31 thf(f488,plain,(
% 0.22/0.31 (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | ((((^[Y0 : $i]: (~ (sK3 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | ($true != $true) | (~spl6_3 | ~spl6_17)),
% 0.22/0.31 inference(constrained_superposition,[],[f35,f427])).
% 0.22/0.31 thf(f489,plain,(
% 0.22/0.31 ((((^[Y0 : $i]: (~ (sK3 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))) = $true) | (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | (~spl6_3 | ~spl6_17)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f488])).
% 0.22/0.31 thf(f490,plain,(
% 0.22/0.31 (((~ (sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0))))))) = $true) | (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | (~spl6_3 | ~spl6_17)),
% 0.22/0.31 inference(beta-eta_normalization,[],[f489])).
% 0.22/0.31 thf(f491,plain,(
% 0.22/0.31 (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | ($false = ((sK3 @ (sK5 @ (^[Y0 : $i]: (~ (sK3 @ Y0))))))) | (~spl6_3 | ~spl6_17)),
% 0.22/0.31 inference(not_proxy_clausification,[],[f490])).
% 0.22/0.31 thf(f492,plain,(
% 0.22/0.31 ($false = $true) | (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | (~spl6_3 | ~spl6_17)),
% 0.22/0.31 inference(forward_demodulation,[],[f491,f427])).
% 0.22/0.31 thf(f493,plain,(
% 0.22/0.31 (((sP0 @ sK3 @ (^[Y0 : $i]: (~ (sK3 @ Y0))) @ sK4)) = $true) | (~spl6_3 | ~spl6_17)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f492])).
% 0.22/0.31 thf(f495,plain,(
% 0.22/0.31 ($true != $true) | (((sK3 @ sK4)) != $true) | (~spl6_3 | ~spl6_17)),
% 0.22/0.31 inference(constrained_superposition,[],[f14,f493])).
% 0.22/0.31 thf(f501,plain,(
% 0.22/0.31 (((sK3 @ sK4)) != $true) | (~spl6_3 | ~spl6_17)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f495])).
% 0.22/0.31 thf(f502,plain,(
% 0.22/0.31 $false | (~spl6_3 | ~spl6_11 | ~spl6_17)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f501,f166])).
% 0.22/0.31 thf(f503,plain,(
% 0.22/0.31 ~spl6_3 | ~spl6_11 | ~spl6_17),
% 0.22/0.31 inference(avatar_contradiction_clause,[],[f502])).
% 0.22/0.31 cnf(s7, plain, spl6_3 | spl6_8, inference(sat_conversion,[],[f57])).
% 0.22/0.31 cnf(s8, plain, spl6_7 | spl6_8, inference(sat_conversion,[],[f58])).
% 0.22/0.31 cnf(s12, plain, ~spl6_8, inference(sat_conversion,[],[f96])).
% 0.22/0.31 cnf(s15, plain, ~spl6_7 | ~spl6_11 | spl6_12, inference(sat_conversion,[],[f171])).
% 0.22/0.31 cnf(s19, plain, ~spl6_3 | ~spl6_7 | spl6_11, inference(sat_conversion,[],[f410])).
% 0.22/0.31 cnf(s26, plain, ~spl6_12 | spl6_17, inference(sat_conversion,[],[f487])).
% 0.22/0.31 cnf(s28, plain, ~spl6_3 | ~spl6_11 | ~spl6_17, inference(sat_conversion,[],[f503])).
% 0.22/0.31 cnf(s33, plain, spl6_7, inference(rat,[],[s8,s12])).
% 0.22/0.31 cnf(s35, plain, spl6_3, inference(rat,[],[s7,s12])).
% 0.22/0.31 cnf(s36, plain, spl6_11, inference(rat,[],[s19,s33,s35])).
% 0.22/0.31 cnf(s37, plain, ~spl6_17, inference(rat,[],[s28,s35,s36])).
% 0.22/0.31 cnf(s42, plain, spl6_12, inference(rat,[],[s15,s33,s36])).
% 0.22/0.31 cnf(s43, plain, $false, inference(rat,[],[s26,s37,s42])).
% 0.22/0.31 thf(f504,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(avatar_sat_refutation,[],[s43])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (1537682)------------------------------
% 0.22/0.31 % (1537682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1537682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1537682)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1537682)Termination reason: Refutation
% 0.22/0.31 % (1537682)Time elapsed: 0.023 s
% 0.22/0.31 % (1537682)Peak memory usage: 13 MB
% 0.22/0.31 % (1537682)Instructions burned: 42 (million)
% 0.22/0.31 % (1537677)Success in time 0.062 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------