%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO017^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:46:17 AM UTC 2026
% Result : Theorem 0.11s 0.29s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO017^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n017.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 16:16:52 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.23 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
% 0.11/0.29 % (534391)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.29 % (534401)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=394975422:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.11/0.29 % (534401)Refutation not found, incomplete strategy
% 0.11/0.29 % (534401)------------------------------
% 0.11/0.29 % (534401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (534401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (534401)CaDiCaL version: 2.1.3
% 0.11/0.29 % (534401)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.29 % (534401)Time elapsed: 0.002 s
% 0.11/0.29 % (534401)Peak memory usage: 12 MB
% 0.11/0.29 % (534401)Instructions burned: 3 (million)
% 0.11/0.29 % (534401)------------------------------
% 0.11/0.29 % (534401)------------------------------
% 0.11/0.29 % (534402)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.11/0.29 % (534402)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
% 0.11/0.29 % (534396)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3215236162:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.11/0.29 % (534397)lrs+10_16_si=on:nwc=1.5:random_seed=3619050499:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.11/0.29 % (534398)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3048087990:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.11/0.29 % (534399)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=4203949323: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)
% 0.11/0.29 % (534400)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2356992402:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.11/0.29 % (534396)Refutation not found, incomplete strategy
% 0.11/0.29 % (534396)------------------------------
% 0.11/0.29 % (534396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (534398)Refutation not found, incomplete strategy
% 0.11/0.29 % (534398)------------------------------
% 0.11/0.29 % (534398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (534396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (534398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (534396)CaDiCaL version: 2.1.3
% 0.11/0.29 % (534398)CaDiCaL version: 2.1.3
% 0.11/0.29 % (534402)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=2369266887:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.11/0.29 % (534396)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.29 % (534396)Time elapsed: 0.001 s
% 0.11/0.29 % (534398)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.29 % (534398)Time elapsed: 0.001 s
% 0.11/0.29 % (534396)Peak memory usage: 12 MB
% 0.11/0.29 % (534398)Peak memory usage: 12 MB
% 0.11/0.29 % (534397)Refutation not found, incomplete strategy
% 0.11/0.29 % (534397)------------------------------
% 0.11/0.29 % (534397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (534397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (534397)CaDiCaL version: 2.1.3
% 0.11/0.29 % (534397)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.29 % (534397)Time elapsed: 0.001 s
% 0.11/0.29 % (534397)Peak memory usage: 12 MB
% 0.11/0.29 % (534397)Instructions burned: 1 (million)
% 0.11/0.29 % (534400)Refutation not found, incomplete strategy
% 0.11/0.29 % (534400)------------------------------
% 0.11/0.29 % (534400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (534400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (534400)CaDiCaL version: 2.1.3
% 0.11/0.29 % (534400)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.29 % (534400)Time elapsed: 0.001 s
% 0.11/0.29 % (534400)Peak memory usage: 12 MB
% 0.11/0.29 % (534400)Instructions burned: 1 (million)
% 0.11/0.29 % (534396)------------------------------
% 0.11/0.29 % (534396)------------------------------
% 0.11/0.29 % (534398)------------------------------
% 0.11/0.29 % (534398)------------------------------
% 0.11/0.29 % (534397)------------------------------
% 0.11/0.29 % (534397)------------------------------
% 0.11/0.29 % (534400)------------------------------
% 0.11/0.29 % (534400)------------------------------
% 0.11/0.29 % (534399)Refutation not found, incomplete strategy
% 0.11/0.29 % (534399)------------------------------
% 0.11/0.29 % (534399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (534399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (534399)CaDiCaL version: 2.1.3
% 0.11/0.29 % (534399)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.29 % (534399)Time elapsed: 0.003 s
% 0.11/0.29 % (534399)Peak memory usage: 12 MB
% 0.11/0.29 % (534399)Instructions burned: 3 (million)
% 0.11/0.29 % (534399)------------------------------
% 0.11/0.29 % (534399)------------------------------
% 0.11/0.29 % (534404)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3361628568:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.11/0.29 % (534402) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-534391-534402"...
% 0.11/0.29 % (534404)Instruction limit reached!
% 0.11/0.29 % (534404)------------------------------
% 0.11/0.29 % (534404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (534404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (534404)CaDiCaL version: 2.1.3
% 0.11/0.29 % (534404)Termination reason: Instruction limit
% 0.11/0.29 % (534404)Termination phase: Saturation
% 0.11/0.29 % (534404)Time elapsed: 0.002 s
% 0.11/0.29 % (534404)Peak memory usage: 12 MB
% 0.11/0.29 % (534404)Instructions burned: 5 (million)
% 0.11/0.29 % (534402)...printing done.
% 0.11/0.29 % (534402)Refutation found. Thanks to Tanya!
% 0.11/0.29 % SZS status Theorem for theBenchmark
% 0.11/0.29 % SZS output start Proof for theBenchmark
% 0.11/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.11/0.29 thf(func_def_0, type, h: ($o > $o)).
% 0.11/0.29 thf(func_def_4, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.11/0.29 thf(func_def_5, type, sF0: $o).
% 0.11/0.29 thf(func_def_6, type, sF1: $o).
% 0.11/0.29 thf(func_def_7, type, sF2: $o).
% 0.11/0.29 thf(func_def_8, type, sF3: $o).
% 0.11/0.29 thf(f1,conjecture,(
% 0.11/0.29 (((h @ $false)) = ((h @ (((h @ $true)) = ((h @ $false))))))),
% 0.11/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.11/0.29 thf(f2,negated_conjecture,(
% 0.11/0.29 ~ (((h @ $false)) = ((h @ (((h @ $true)) = ((h @ $false))))))),
% 0.11/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.11/0.29 thf(f3,plain,(
% 0.11/0.29 ~ (((h @ $false)) = ((h @ (((h @ $true)) = ((h @ $false))))))),
% 0.11/0.29 inference(rectify,[],[f2])).
% 0.11/0.29 thf(f4,plain,(
% 0.11/0.29 ~ (((h @ ((h @ $true) = (h @ $false)))) = ((h @ $false)))),
% 0.11/0.29 inference(fool_elimination,[],[f3])).
% 0.11/0.29 thf(f5,plain,(
% 0.11/0.29 (((h @ ((h @ $true) = (h @ $false)))) != ((h @ $false)))),
% 0.11/0.29 inference(flattening,[],[f4])).
% 0.11/0.29 thf(f6,plain,(
% 0.11/0.29 (((h @ ((h @ $true) = (h @ $false)))) != ((h @ $false)))),
% 0.11/0.29 inference(cnf_transformation,[],[f5])).
% 0.11/0.29 thf(f8,definition,(
% 0.11/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.11/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.11/0.29 thf(f9,definition,(
% 0.11/0.29 (sF0 = ((h @ $true)))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 0.11/0.29 thf(f10,plain,(
% 0.11/0.29 (((h @ $true)) = sF0)),
% 0.11/0.29 inference(reorient_equations,[],[f9])).
% 0.11/0.29 thf(f11,definition,(
% 0.11/0.29 (sF1 = ((h @ $false)))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 0.11/0.29 thf(f12,definition,(
% 0.11/0.29 (sF2 = ((sF0 = sF1)))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.11/0.29 thf(f13,plain,(
% 0.11/0.29 (((sF0 = sF1)) = sF2)),
% 0.11/0.29 inference(reorient_equations,[],[f12])).
% 0.11/0.29 thf(f14,definition,(
% 0.11/0.29 (sF3 = ((h @ sF2)))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.11/0.29 thf(f15,plain,(
% 0.11/0.29 (((h @ sF2)) = sF3)),
% 0.11/0.29 inference(reorient_equations,[],[f14])).
% 0.11/0.29 thf(f16,plain,(
% 0.11/0.29 (sF1 != sF3)),
% 0.11/0.29 inference(definition_folding,[],[f6,f11,f15,f13,f11,f10])).
% 0.11/0.29 thf(f17,plain,(
% 0.11/0.29 (((sF0 = sF1)) = $true) | ($false = sF2)),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f13])).
% 0.11/0.29 thf(f18,plain,(
% 0.11/0.29 ($true = sF2) | (((sF0 = sF1)) = $false)),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f13])).
% 0.11/0.29 thf(f19,plain,(
% 0.11/0.29 (sF1 != sF0) | ($true = sF2)),
% 0.11/0.29 inference(equality_proxy_clausification,[],[f18])).
% 0.11/0.29 thf(f20,plain,(
% 0.11/0.29 ($true = sF0) | ($true = sF2) | (sF1 = $true)),
% 0.11/0.29 inference(xor_proxy_clausification,[],[f19])).
% 0.11/0.29 thf(f21,plain,(
% 0.11/0.29 ($true = sF2) | ($false = sF0) | (sF1 = $false)),
% 0.11/0.29 inference(xor_proxy_clausification,[],[f19])).
% 0.11/0.29 thf(f22,plain,(
% 0.11/0.29 ($false = sF2) | (sF1 = sF0)),
% 0.11/0.29 inference(equality_proxy_clausification,[],[f17])).
% 0.11/0.29 thf(f23,plain,(
% 0.11/0.29 (sF1 = $true) | ($false = sF2) | ($false = sF0)),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f22])).
% 0.11/0.29 thf(f24,plain,(
% 0.11/0.29 ($false = sF2) | (sF1 = $false) | ($true = sF0)),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f22])).
% 0.11/0.29 thf(f25,plain,(
% 0.11/0.29 ($true = ((h @ sF2))) | ($false = sF3)),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f15])).
% 0.11/0.29 thf(f26,plain,(
% 0.11/0.29 ($true = sF3) | ($false = ((h @ sF2)))),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f15])).
% 0.11/0.29 thf(f27,plain,(
% 0.11/0.29 (sF1 = $true) | ($true = sF3)),
% 0.11/0.29 inference(xor_proxy_clausification,[],[f16])).
% 0.11/0.29 thf(f28,plain,(
% 0.11/0.29 ($false = sF3) | (sF1 = $false)),
% 0.11/0.29 inference(xor_proxy_clausification,[],[f16])).
% 0.11/0.29 thf(f29,plain,(
% 0.11/0.29 ($false = sF0) | (((h @ $true)) = $true)),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f10])).
% 0.11/0.29 thf(f30,plain,(
% 0.11/0.29 ($true = sF0) | (((h @ $true)) = $false)),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f10])).
% 0.11/0.29 thf(f31,plain,(
% 0.11/0.29 ($false = ((h @ $false))) | (sF1 = $true)),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f11])).
% 0.11/0.29 thf(f32,plain,(
% 0.11/0.29 (sF1 = $false) | ($true = ((h @ $false)))),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f11])).
% 0.11/0.29 thf(f34,definition,(
% 0.11/0.29 spl4_1 <=> ($false = sF0)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.11/0.29 thf(f36,plain,(
% 0.11/0.29 ($false = sF0) | ~spl4_1),
% 0.11/0.29 inference(avatar_component_clause,[],[f34])).
% 0.11/0.29 thf(f38,definition,(
% 0.11/0.29 spl4_2 <=> ($true = sF2)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.11/0.29 thf(f39,plain,(
% 0.11/0.29 ($true != sF2) | spl4_2),
% 0.11/0.29 inference(avatar_component_clause,[],[f38])).
% 0.11/0.29 thf(f40,plain,(
% 0.11/0.29 ($true = sF2) | ~spl4_2),
% 0.11/0.29 inference(avatar_component_clause,[],[f38])).
% 0.11/0.29 thf(f42,definition,(
% 0.11/0.29 spl4_3 <=> (sF1 = $false)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.11/0.29 thf(f44,plain,(
% 0.11/0.29 (sF1 = $false) | ~spl4_3),
% 0.11/0.29 inference(avatar_component_clause,[],[f42])).
% 0.11/0.29 thf(f45,plain,(
% 0.11/0.29 spl4_1 | spl4_2 | spl4_3),
% 0.11/0.29 inference(avatar_split_clause,[],[f21,f42,f38,f34])).
% 0.11/0.29 thf(f47,definition,(
% 0.11/0.29 spl4_4 <=> ($true = sF0)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.11/0.29 thf(f49,plain,(
% 0.11/0.29 ($true = sF0) | ~spl4_4),
% 0.11/0.29 inference(avatar_component_clause,[],[f47])).
% 0.11/0.29 thf(f51,definition,(
% 0.11/0.29 spl4_5 <=> (sF1 = $true)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.11/0.29 thf(f53,plain,(
% 0.11/0.29 (sF1 = $true) | ~spl4_5),
% 0.11/0.29 inference(avatar_component_clause,[],[f51])).
% 0.11/0.29 thf(f54,plain,(
% 0.11/0.29 spl4_4 | spl4_2 | spl4_5),
% 0.11/0.29 inference(avatar_split_clause,[],[f20,f51,f38,f47])).
% 0.11/0.29 thf(f56,definition,(
% 0.11/0.29 spl4_6 <=> ($false = sF2)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
% 0.11/0.29 thf(f58,plain,(
% 0.11/0.29 ($false = sF2) | ~spl4_6),
% 0.11/0.29 inference(avatar_component_clause,[],[f56])).
% 0.11/0.29 thf(f59,plain,(
% 0.11/0.29 spl4_3 | spl4_4 | spl4_6),
% 0.11/0.29 inference(avatar_split_clause,[],[f24,f56,f47,f42])).
% 0.11/0.29 thf(f60,plain,(
% 0.11/0.29 spl4_5 | spl4_1 | spl4_6),
% 0.11/0.29 inference(avatar_split_clause,[],[f23,f56,f34,f51])).
% 0.11/0.29 thf(f62,definition,(
% 0.11/0.29 spl4_7 <=> ($true = sF3)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition])).
% 0.11/0.29 thf(f64,plain,(
% 0.11/0.29 ($true = sF3) | ~spl4_7),
% 0.11/0.29 inference(avatar_component_clause,[],[f62])).
% 0.11/0.29 thf(f66,definition,(
% 0.11/0.29 spl4_8 <=> ($false = ((h @ sF2)))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition])).
% 0.11/0.29 thf(f68,plain,(
% 0.11/0.29 ($false = ((h @ sF2))) | ~spl4_8),
% 0.11/0.29 inference(avatar_component_clause,[],[f66])).
% 0.11/0.29 thf(f69,plain,(
% 0.11/0.29 spl4_7 | spl4_8),
% 0.11/0.29 inference(avatar_split_clause,[],[f26,f66,f62])).
% 0.11/0.29 thf(f71,definition,(
% 0.11/0.29 spl4_9 <=> ($false = sF3)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition])).
% 0.11/0.29 thf(f73,plain,(
% 0.11/0.29 ($false = sF3) | ~spl4_9),
% 0.11/0.29 inference(avatar_component_clause,[],[f71])).
% 0.11/0.29 thf(f75,definition,(
% 0.11/0.29 spl4_10 <=> ($true = ((h @ sF2)))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition])).
% 0.11/0.29 thf(f77,plain,(
% 0.11/0.29 ($true = ((h @ sF2))) | ~spl4_10),
% 0.11/0.29 inference(avatar_component_clause,[],[f75])).
% 0.11/0.29 thf(f78,plain,(
% 0.11/0.29 spl4_9 | spl4_10),
% 0.11/0.29 inference(avatar_split_clause,[],[f25,f75,f71])).
% 0.11/0.29 thf(f79,plain,(
% 0.11/0.29 spl4_3 | spl4_9),
% 0.11/0.29 inference(avatar_split_clause,[],[f28,f71,f42])).
% 0.11/0.29 thf(f80,plain,(
% 0.11/0.29 spl4_7 | spl4_5),
% 0.11/0.29 inference(avatar_split_clause,[],[f27,f51,f62])).
% 0.11/0.29 thf(f82,definition,(
% 0.11/0.29 spl4_11 <=> (((h @ $true)) = $false)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition])).
% 0.11/0.29 thf(f84,plain,(
% 0.11/0.29 (((h @ $true)) = $false) | ~spl4_11),
% 0.11/0.29 inference(avatar_component_clause,[],[f82])).
% 0.11/0.29 thf(f85,plain,(
% 0.11/0.29 spl4_4 | spl4_11),
% 0.11/0.29 inference(avatar_split_clause,[],[f30,f82,f47])).
% 0.11/0.29 thf(f87,definition,(
% 0.11/0.29 spl4_12 <=> (((h @ $true)) = $true)),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition])).
% 0.11/0.29 thf(f89,plain,(
% 0.11/0.29 (((h @ $true)) = $true) | ~spl4_12),
% 0.11/0.29 inference(avatar_component_clause,[],[f87])).
% 0.11/0.29 thf(f90,plain,(
% 0.11/0.29 spl4_1 | spl4_12),
% 0.11/0.29 inference(avatar_split_clause,[],[f29,f87,f34])).
% 0.11/0.29 thf(f92,definition,(
% 0.11/0.29 spl4_13 <=> ($true = ((h @ $false)))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition])).
% 0.11/0.29 thf(f94,plain,(
% 0.11/0.29 ($true = ((h @ $false))) | ~spl4_13),
% 0.11/0.29 inference(avatar_component_clause,[],[f92])).
% 0.11/0.29 thf(f95,plain,(
% 0.11/0.29 spl4_13 | spl4_3),
% 0.11/0.29 inference(avatar_split_clause,[],[f32,f42,f92])).
% 0.11/0.29 thf(f97,definition,(
% 0.11/0.29 spl4_14 <=> ($false = ((h @ $false)))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition])).
% 0.11/0.29 thf(f99,plain,(
% 0.11/0.29 ($false = ((h @ $false))) | ~spl4_14),
% 0.11/0.29 inference(avatar_component_clause,[],[f97])).
% 0.11/0.29 thf(f100,plain,(
% 0.11/0.29 spl4_5 | spl4_14),
% 0.11/0.29 inference(avatar_split_clause,[],[f31,f97,f51])).
% 0.11/0.29 thf(f108,plain,(
% 0.11/0.29 ($true = $false) | (~spl4_7 | ~spl4_9)),
% 0.11/0.29 inference(forward_demodulation,[],[f73,f64])).
% 0.11/0.29 thf(f109,plain,(
% 0.11/0.29 $false | (~spl4_7 | ~spl4_9)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f108])).
% 0.11/0.29 thf(f110,plain,(
% 0.11/0.29 ~spl4_7 | ~spl4_9),
% 0.11/0.29 inference(avatar_contradiction_clause,[],[f109])).
% 0.11/0.29 thf(f119,plain,(
% 0.11/0.29 ($true = $false) | (~spl4_3 | ~spl4_5)),
% 0.11/0.29 inference(forward_demodulation,[],[f53,f44])).
% 0.11/0.29 thf(f120,plain,(
% 0.11/0.29 $false | (~spl4_3 | ~spl4_5)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f119])).
% 0.11/0.29 thf(f121,plain,(
% 0.11/0.29 ~spl4_3 | ~spl4_5),
% 0.11/0.29 inference(avatar_contradiction_clause,[],[f120])).
% 0.11/0.29 thf(f122,plain,(
% 0.11/0.29 ($true = $false) | (~spl4_1 | ~spl4_4)),
% 0.11/0.29 inference(forward_demodulation,[],[f36,f49])).
% 0.11/0.29 thf(f123,plain,(
% 0.11/0.29 $false | (~spl4_1 | ~spl4_4)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f122])).
% 0.11/0.29 thf(f124,plain,(
% 0.11/0.29 ~spl4_1 | ~spl4_4),
% 0.11/0.29 inference(avatar_contradiction_clause,[],[f123])).
% 0.11/0.29 thf(f130,plain,(
% 0.11/0.29 (((h @ $true)) = $false) | (~spl4_2 | ~spl4_8)),
% 0.11/0.29 inference(forward_demodulation,[],[f68,f40])).
% 0.11/0.29 thf(f131,plain,(
% 0.11/0.29 spl4_11 | ~spl4_2 | ~spl4_8),
% 0.11/0.29 inference(avatar_split_clause,[],[f130,f66,f38,f82])).
% 0.11/0.29 thf(f132,plain,(
% 0.11/0.29 (((h @ $true)) = $true) | (~spl4_2 | ~spl4_10)),
% 0.11/0.29 inference(forward_demodulation,[],[f77,f40])).
% 0.11/0.29 thf(f133,plain,(
% 0.11/0.29 spl4_12 | ~spl4_2 | ~spl4_10),
% 0.11/0.29 inference(avatar_split_clause,[],[f132,f75,f38,f87])).
% 0.11/0.29 thf(f137,plain,(
% 0.11/0.29 ($true = $false) | (~spl4_11 | ~spl4_12)),
% 0.11/0.29 inference(forward_demodulation,[],[f89,f84])).
% 0.11/0.29 thf(f138,plain,(
% 0.11/0.29 $false | (~spl4_11 | ~spl4_12)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f137])).
% 0.11/0.29 thf(f139,plain,(
% 0.11/0.29 ~spl4_11 | ~spl4_12),
% 0.11/0.29 inference(avatar_contradiction_clause,[],[f138])).
% 0.11/0.29 thf(f140,plain,(
% 0.11/0.29 ($true = $false) | (~spl4_2 | ~spl4_6)),
% 0.11/0.29 inference(forward_demodulation,[],[f58,f40])).
% 0.11/0.29 thf(f141,plain,(
% 0.11/0.29 $false | (~spl4_2 | ~spl4_6)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f140])).
% 0.11/0.29 thf(f142,plain,(
% 0.11/0.29 ~spl4_2 | ~spl4_6),
% 0.11/0.29 inference(avatar_contradiction_clause,[],[f141])).
% 0.11/0.29 thf(f149,plain,(
% 0.11/0.29 ($true != $true) | ($false = sF2) | spl4_2),
% 0.11/0.29 inference(constrained_superposition,[],[f39,f8])).
% 0.11/0.29 thf(f150,plain,(
% 0.11/0.29 ($false = sF2) | spl4_2),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f149])).
% 0.11/0.29 thf(f151,plain,(
% 0.11/0.29 spl4_6 | spl4_2),
% 0.11/0.29 inference(avatar_split_clause,[],[f150,f38,f56])).
% 0.11/0.29 thf(f158,plain,(
% 0.11/0.29 ($false = ((h @ $false))) | (~spl4_6 | ~spl4_8)),
% 0.11/0.29 inference(forward_demodulation,[],[f68,f58])).
% 0.11/0.29 thf(f159,plain,(
% 0.11/0.29 spl4_14 | ~spl4_6 | ~spl4_8),
% 0.11/0.29 inference(avatar_split_clause,[],[f158,f66,f56,f97])).
% 0.11/0.29 thf(f160,plain,(
% 0.11/0.29 ($true = ((h @ $false))) | (~spl4_6 | ~spl4_10)),
% 0.11/0.29 inference(forward_demodulation,[],[f77,f58])).
% 0.11/0.29 thf(f161,plain,(
% 0.11/0.29 spl4_13 | ~spl4_6 | ~spl4_10),
% 0.11/0.29 inference(avatar_split_clause,[],[f160,f75,f56,f92])).
% 0.11/0.29 thf(f169,plain,(
% 0.11/0.29 ($true = $false) | (~spl4_13 | ~spl4_14)),
% 0.11/0.29 inference(forward_demodulation,[],[f99,f94])).
% 0.11/0.29 thf(f170,plain,(
% 0.11/0.29 $false | (~spl4_13 | ~spl4_14)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f169])).
% 0.11/0.29 thf(f171,plain,(
% 0.11/0.29 ~spl4_13 | ~spl4_14),
% 0.11/0.29 inference(avatar_contradiction_clause,[],[f170])).
% 0.11/0.29 cnf(s1, plain, spl4_1 | spl4_2 | spl4_3, inference(sat_conversion,[],[f45])).
% 0.11/0.29 cnf(s2, plain, spl4_2 | spl4_4 | spl4_5, inference(sat_conversion,[],[f54])).
% 0.11/0.29 cnf(s3, plain, spl4_3 | spl4_4 | spl4_6, inference(sat_conversion,[],[f59])).
% 0.11/0.29 cnf(s4, plain, spl4_1 | spl4_5 | spl4_6, inference(sat_conversion,[],[f60])).
% 0.11/0.29 cnf(s5, plain, spl4_7 | spl4_8, inference(sat_conversion,[],[f69])).
% 0.11/0.29 cnf(s6, plain, spl4_9 | spl4_10, inference(sat_conversion,[],[f78])).
% 0.11/0.29 cnf(s7, plain, spl4_3 | spl4_9, inference(sat_conversion,[],[f79])).
% 0.11/0.29 cnf(s8, plain, spl4_5 | spl4_7, inference(sat_conversion,[],[f80])).
% 0.11/0.29 cnf(s9, plain, spl4_4 | spl4_11, inference(sat_conversion,[],[f85])).
% 0.11/0.29 cnf(s10, plain, spl4_1 | spl4_12, inference(sat_conversion,[],[f90])).
% 0.11/0.29 cnf(s11, plain, spl4_3 | spl4_13, inference(sat_conversion,[],[f95])).
% 0.11/0.29 cnf(s12, plain, spl4_5 | spl4_14, inference(sat_conversion,[],[f100])).
% 0.11/0.29 cnf(s13, plain, ~spl4_7 | ~spl4_9, inference(sat_conversion,[],[f110])).
% 0.11/0.29 cnf(s15, plain, ~spl4_3 | ~spl4_5, inference(sat_conversion,[],[f121])).
% 0.11/0.29 cnf(s16, plain, ~spl4_1 | ~spl4_4, inference(sat_conversion,[],[f124])).
% 0.11/0.29 cnf(s17, plain, ~spl4_2 | ~spl4_8 | spl4_11, inference(sat_conversion,[],[f131])).
% 0.11/0.29 cnf(s18, plain, ~spl4_2 | ~spl4_10 | spl4_12, inference(sat_conversion,[],[f133])).
% 0.11/0.29 cnf(s19, plain, ~spl4_11 | ~spl4_12, inference(sat_conversion,[],[f139])).
% 0.11/0.29 cnf(s20, plain, ~spl4_2 | ~spl4_6, inference(sat_conversion,[],[f142])).
% 0.11/0.29 cnf(s23, plain, spl4_2 | spl4_6, inference(sat_conversion,[],[f151])).
% 0.11/0.29 cnf(s25, plain, ~spl4_6 | ~spl4_8 | spl4_14, inference(sat_conversion,[],[f159])).
% 0.11/0.29 cnf(s26, plain, ~spl4_6 | ~spl4_10 | spl4_13, inference(sat_conversion,[],[f161])).
% 0.11/0.29 cnf(s27, plain, ~spl4_13 | ~spl4_14, inference(sat_conversion,[],[f171])).
% 0.11/0.29 cnf(s28, plain, spl4_2 | spl4_1, inference(rat,[],[s6,s26,s13,s27,s8,s12,s15,s1,s23])).
% 0.11/0.29 cnf(s29, plain, spl4_1, inference(rat,[],[s7,s13,s15,s5,s4,s17,s20,s28,s19,s10])).
% 0.11/0.29 cnf(s30, plain, ~spl4_4, inference(rat,[],[s16,s29])).
% 0.11/0.29 cnf(s31, plain, spl4_11, inference(rat,[],[s9,s30])).
% 0.11/0.29 cnf(s32, plain, ~spl4_12, inference(rat,[],[s19,s31])).
% 0.11/0.29 cnf(s33, plain, spl4_2, inference(rat,[],[s5,s25,s13,s27,s7,s11,s15,s2,s23,s30])).
% 0.11/0.29 cnf(s34, plain, ~spl4_6, inference(rat,[],[s20,s33])).
% 0.11/0.29 cnf(s35, plain, ~spl4_10, inference(rat,[],[s18,s32,s33])).
% 0.11/0.29 cnf(s37, plain, spl4_3, inference(rat,[],[s3,s30,s34])).
% 0.11/0.29 cnf(s38, plain, spl4_9, inference(rat,[],[s6,s35])).
% 0.11/0.29 cnf(s39, plain, ~spl4_5, inference(rat,[],[s15,s37])).
% 0.11/0.29 cnf(s40, plain, ~spl4_7, inference(rat,[],[s13,s38])).
% 0.11/0.29 cnf(s42, plain, $false, inference(rat,[],[s8,s40,s39])).
% 0.11/0.29 thf(f172,plain,(
% 0.11/0.29 $false),
% 0.11/0.29 inference(avatar_sat_refutation,[],[s42])).
% 0.11/0.29 % SZS output end Proof for theBenchmark
% 0.11/0.29 % (534402)------------------------------
% 0.11/0.29 % (534402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (534402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (534402)CaDiCaL version: 2.1.3
% 0.11/0.29 % (534402)Termination reason: Refutation
% 0.11/0.29 % (534402)Time elapsed: 0.010 s
% 0.11/0.29 % (534402)Peak memory usage: 13 MB
% 0.11/0.29 % (534402)Instructions burned: 5 (million)
% 0.11/0.29 % (534391)Success in time 0.054 s
% 0.11/0.29 % Vampire exiting
%------------------------------------------------------------------------------