%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO503^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:48:09 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO503^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n009.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 17:11:30 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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
% 0.21/0.27 % (91856)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (91863)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=800890379:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (91863)Refutation not found, incomplete strategy
% 0.21/0.27 % (91863)------------------------------
% 0.21/0.27 % (91863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (91863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (91863)CaDiCaL version: 2.1.3
% 0.21/0.27 % (91863)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.27 % (91863)Time elapsed: 0.0000 s
% 0.21/0.27 % (91863)Peak memory usage: 12 MB
% 0.21/0.27 % (91863)------------------------------
% 0.21/0.27 % (91863)------------------------------
% 0.21/0.27 % (91862)lrs+10_16_si=on:nwc=1.5:random_seed=2467707841:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (91864)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=2665814903: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)
% 0.21/0.27 % (91865)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2146985370:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (91866)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3725095314:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (91865)Refutation not found, incomplete strategy
% 0.21/0.27 % (91865)------------------------------
% 0.21/0.27 % (91865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (91865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (91865)CaDiCaL version: 2.1.3
% 0.21/0.27 % (91865)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.27 % (91865)Time elapsed: 0.002 s
% 0.21/0.27 % (91865)Peak memory usage: 12 MB
% 0.21/0.27 % (91865)Instructions burned: 2 (million)
% 0.21/0.27 % (91862)Refutation not found, incomplete strategy
% 0.21/0.27 % (91862)------------------------------
% 0.21/0.27 % (91862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (91862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (91862)CaDiCaL version: 2.1.3
% 0.21/0.27 % (91862)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.27 % (91862)Time elapsed: 0.002 s
% 0.21/0.27 % (91862)Peak memory usage: 12 MB
% 0.21/0.27 % (91862)Instructions burned: 3 (million)
% 0.21/0.27 % (91864)Refutation not found, incomplete strategy
% 0.21/0.27 % (91864)------------------------------
% 0.21/0.27 % (91864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (91864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (91864)CaDiCaL version: 2.1.3
% 0.21/0.27 % (91864)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.27 % (91864)Time elapsed: 0.003 s
% 0.21/0.27 % (91864)Peak memory usage: 12 MB
% 0.21/0.27 % (91864)Instructions burned: 3 (million)
% 0.21/0.27 % (91865)------------------------------
% 0.21/0.27 % (91865)------------------------------
% 0.21/0.27 % (91862)------------------------------
% 0.21/0.27 % (91862)------------------------------
% 0.21/0.27 % (91869)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=535057758:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.27 % (91864)------------------------------
% 0.21/0.27 % (91864)------------------------------
% 0.21/0.27 % (91869)Instruction limit reached!
% 0.21/0.27 % (91869)------------------------------
% 0.21/0.27 % (91869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (91869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (91869)CaDiCaL version: 2.1.3
% 0.21/0.27 % (91869)Termination reason: Instruction limit
% 0.21/0.27 % (91869)Termination phase: Saturation
% 0.21/0.27 % (91869)Time elapsed: 0.001 s
% 0.21/0.27 % (91869)Peak memory usage: 12 MB
% 0.21/0.27 % (91869)Instructions burned: 4 (million)
% 0.21/0.27 % (91866) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-91856-91866"...
% 0.21/0.27 % (91867)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (91867)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
% 0.21/0.27 % (91866)...printing done.
% 0.21/0.27 % (91866)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% 0.21/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.27 thf(func_def_0, type, a: $o).
% 0.21/0.27 thf(func_def_1, type, b: $o).
% 0.21/0.27 thf(func_def_2, type, c: $o).
% 0.21/0.27 thf(func_def_3, type, f: ($o > $o)).
% 0.21/0.27 thf(func_def_4, type, g: ($o > $o)).
% 0.21/0.27 thf(func_def_5, type, p: (($o > $o) > $o)).
% 0.21/0.27 thf(func_def_10, type, sK1: $o).
% 0.21/0.27 thf(f1,conjecture,(
% 0.21/0.27 (a = b) | ~(p @ f) | (p @ g) | ~(g @ a) | ~(f @ b) | ~(g @ b) | ~(f @ a)),
% 0.21/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',claim)).
% 0.21/0.27 thf(f2,negated_conjecture,(
% 0.21/0.27 ~((a = b) | ~(p @ f) | (p @ g) | ~(g @ a) | ~(f @ b) | ~(g @ b) | ~(f @ a))),
% 0.21/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.27 thf(f3,plain,(
% 0.21/0.27 ~((a = b) | ~(p @ f) | (p @ g) | ~(g @ a) | ~(f @ b) | ~(g @ b) | ~(f @ a))),
% 0.21/0.27 inference(rectify,[],[f2])).
% 0.21/0.27 thf(f4,plain,(
% 0.21/0.27 ~(((b = $true) <=> (a = $true)) | ~ (((p @ f)) = $true) | (((p @ g)) = $true) | ~ (((g @ a)) = $true) | ~ (((f @ b)) = $true) | ~ (((g @ b)) = $true) | ~ (((f @ a)) = $true))),
% 0.21/0.27 inference(fool_elimination,[],[f3])).
% 0.21/0.27 thf(f5,plain,(
% 0.21/0.27 ~((((p @ f)) != $true) | (((p @ g)) = $true) | (((g @ b)) != $true) | (((g @ a)) != $true) | (((f @ b)) != $true) | (((f @ a)) != $true) | ((b = $true) <=> (a = $true)))),
% 0.21/0.27 inference(flattening,[],[f4])).
% 0.21/0.27 thf(f6,plain,(
% 0.21/0.27 (((f @ b)) = $true) & (((p @ f)) = $true) & (((f @ a)) = $true) & ((a = $true) <~> (b = $true)) & (((g @ a)) = $true) & (((g @ b)) = $true) & (((p @ g)) != $true)),
% 0.21/0.27 inference(ennf_transformation,[],[f5])).
% 0.21/0.27 thf(f7,plain,(
% 0.21/0.27 (((f @ b)) = $true) & (((p @ f)) = $true) & (((f @ a)) = $true) & (((b != $true) | (a != $true)) & ((b = $true) | (a = $true))) & (((g @ a)) = $true) & (((g @ b)) = $true) & (((p @ g)) != $true)),
% 0.21/0.27 inference(nnf_transformation,[],[f6])).
% 0.21/0.27 thf(f8,plain,(
% 0.21/0.27 (((f @ b)) = $true) & (((p @ f)) = $true) & (((f @ a)) = $true) & ((b != $true) | (a != $true)) & ((b = $true) | (a = $true)) & (((g @ a)) = $true) & (((g @ b)) = $true) & (((p @ g)) != $true)),
% 0.21/0.27 inference(flattening,[],[f7])).
% 0.21/0.27 thf(f9,plain,(
% 0.21/0.27 (((p @ g)) != $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f10,plain,(
% 0.21/0.27 (((g @ b)) = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f11,plain,(
% 0.21/0.27 (((g @ a)) = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f12,plain,(
% 0.21/0.27 (a = $true) | (b = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f13,plain,(
% 0.21/0.27 (b != $true) | (a != $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f14,plain,(
% 0.21/0.27 (((f @ a)) = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f15,plain,(
% 0.21/0.27 (((p @ f)) = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f16,plain,(
% 0.21/0.27 (((f @ b)) = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f18,definition,(
% 0.21/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.27 thf(f20,definition,(
% 0.21/0.27 spl0_1 <=> (b = $true)),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.21/0.27 thf(f21,plain,(
% 0.21/0.27 (b != $true) | spl0_1),
% 0.21/0.27 inference(avatar_component_clause,[],[f20])).
% 0.21/0.27 thf(f23,definition,(
% 0.21/0.27 spl0_2 <=> (a = $true)),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.21/0.27 thf(f24,plain,(
% 0.21/0.27 (a != $true) | spl0_2),
% 0.21/0.27 inference(avatar_component_clause,[],[f23])).
% 0.21/0.27 thf(f25,plain,(
% 0.21/0.27 ~spl0_1 | ~spl0_2),
% 0.21/0.27 inference(avatar_split_clause,[],[f13,f23,f20])).
% 0.21/0.27 thf(f26,plain,(
% 0.21/0.27 (b = $true) | ~spl0_1),
% 0.21/0.27 inference(avatar_component_clause,[],[f20])).
% 0.21/0.27 thf(f27,plain,(
% 0.21/0.27 (a = $true) | ~spl0_2),
% 0.21/0.27 inference(avatar_component_clause,[],[f23])).
% 0.21/0.27 thf(f28,plain,(
% 0.21/0.27 spl0_1 | spl0_2),
% 0.21/0.27 inference(avatar_split_clause,[],[f12,f23,f20])).
% 0.21/0.27 thf(f30,plain,(
% 0.21/0.27 (((f @ $true)) = $true) | ~spl0_2),
% 0.21/0.27 inference(backward_demodulation,[],[f14,f27])).
% 0.21/0.27 thf(f31,plain,(
% 0.21/0.27 ($true != $true) | (f != g)),
% 0.21/0.27 inference(constrained_superposition,[],[f9,f15])).
% 0.21/0.27 thf(f32,plain,(
% 0.21/0.27 (f != g)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f31])).
% 0.21/0.27 thf(f33,plain,(
% 0.21/0.27 (((g @ sK1)) != ((f @ sK1)))),
% 0.21/0.27 inference(negative_extensionality,[],[f32])).
% 0.21/0.27 thf(f35,plain,(
% 0.21/0.27 (((g @ sK1)) = $false) | (((f @ sK1)) = $false)),
% 0.21/0.27 inference(xor_proxy_clausification,[],[f33])).
% 0.21/0.27 thf(f37,definition,(
% 0.21/0.27 spl0_3 <=> (((f @ sK1)) = $false)),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.21/0.27 thf(f38,plain,(
% 0.21/0.27 (((f @ sK1)) = $false) | ~spl0_3),
% 0.21/0.27 inference(avatar_component_clause,[],[f37])).
% 0.21/0.27 thf(f40,definition,(
% 0.21/0.27 spl0_4 <=> (((g @ sK1)) = $false)),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.21/0.27 thf(f41,plain,(
% 0.21/0.27 (((g @ sK1)) = $false) | ~spl0_4),
% 0.21/0.27 inference(avatar_component_clause,[],[f40])).
% 0.21/0.27 thf(f42,plain,(
% 0.21/0.27 spl0_3 | spl0_4),
% 0.21/0.27 inference(avatar_split_clause,[],[f35,f40,f37])).
% 0.21/0.27 thf(f59,plain,(
% 0.21/0.27 (b = $false) | ($true != $true) | spl0_1),
% 0.21/0.27 inference(constrained_superposition,[],[f21,f18])).
% 0.21/0.27 thf(f63,plain,(
% 0.21/0.27 (sK1 = $false) | ($false = ((f @ $true))) | ~spl0_3),
% 0.21/0.27 inference(constrained_superposition,[],[f38,f18])).
% 0.21/0.27 thf(f77,plain,(
% 0.21/0.27 (b = $false) | spl0_1),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f59])).
% 0.21/0.27 thf(f78,plain,(
% 0.21/0.27 (sK1 = $false) | ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.21/0.27 inference(forward_demodulation,[],[f63,f30])).
% 0.21/0.27 thf(f79,plain,(
% 0.21/0.27 (sK1 = $false) | (~spl0_2 | ~spl0_3)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f78])).
% 0.21/0.27 thf(f82,plain,(
% 0.21/0.27 (((f @ $false)) = $true) | spl0_1),
% 0.21/0.27 inference(backward_demodulation,[],[f16,f77])).
% 0.21/0.27 thf(f85,plain,(
% 0.21/0.27 (((f @ $false)) = $false) | (~spl0_2 | ~spl0_3)),
% 0.21/0.27 inference(backward_demodulation,[],[f38,f79])).
% 0.21/0.27 thf(f86,plain,(
% 0.21/0.27 ($false = $true) | (spl0_1 | ~spl0_2 | ~spl0_3)),
% 0.21/0.27 inference(backward_demodulation,[],[f82,f85])).
% 0.21/0.27 thf(f87,plain,(
% 0.21/0.27 $false | (spl0_1 | ~spl0_2 | ~spl0_3)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f86])).
% 0.21/0.27 thf(f88,plain,(
% 0.21/0.27 spl0_1 | ~spl0_2 | ~spl0_3),
% 0.21/0.27 inference(avatar_contradiction_clause,[],[f87])).
% 0.21/0.27 thf(f90,definition,(
% 0.21/0.27 spl0_7 <=> ($false = ((f @ $true)))),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.21/0.27 thf(f91,plain,(
% 0.21/0.27 ($false = ((f @ $true))) | ~spl0_7),
% 0.21/0.27 inference(avatar_component_clause,[],[f90])).
% 0.21/0.27 thf(f93,definition,(
% 0.21/0.27 spl0_8 <=> (sK1 = $false)),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])).
% 0.21/0.27 thf(f94,plain,(
% 0.21/0.27 (sK1 = $false) | ~spl0_8),
% 0.21/0.27 inference(avatar_component_clause,[],[f93])).
% 0.21/0.27 thf(f95,plain,(
% 0.21/0.27 spl0_7 | spl0_8 | ~spl0_3),
% 0.21/0.27 inference(avatar_split_clause,[],[f63,f37,f93,f90])).
% 0.21/0.27 thf(f96,plain,(
% 0.21/0.27 (((f @ $true)) = $true) | ~spl0_1),
% 0.21/0.27 inference(backward_demodulation,[],[f16,f26])).
% 0.21/0.27 thf(f97,plain,(
% 0.21/0.27 (((g @ $true)) = $true) | ~spl0_1),
% 0.21/0.27 inference(backward_demodulation,[],[f10,f26])).
% 0.21/0.27 thf(f103,definition,(
% 0.21/0.27 spl0_9 <=> (((g @ $true)) = $true)),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 0.21/0.27 thf(f104,plain,(
% 0.21/0.27 (((g @ $true)) = $true) | ~spl0_9),
% 0.21/0.27 inference(avatar_component_clause,[],[f103])).
% 0.21/0.27 thf(f106,plain,(
% 0.21/0.27 spl0_9 | ~spl0_1),
% 0.21/0.27 inference(avatar_split_clause,[],[f97,f20,f103])).
% 0.21/0.27 thf(f107,plain,(
% 0.21/0.27 (((f @ $false)) = $false) | (~spl0_3 | ~spl0_8)),
% 0.21/0.27 inference(backward_demodulation,[],[f38,f94])).
% 0.21/0.27 thf(f109,plain,(
% 0.21/0.27 ($true != $true) | (a = $false) | spl0_2),
% 0.21/0.27 inference(constrained_superposition,[],[f24,f18])).
% 0.21/0.27 thf(f110,plain,(
% 0.21/0.27 (a = $false) | spl0_2),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f109])).
% 0.21/0.27 thf(f111,plain,(
% 0.21/0.27 (((g @ $false)) = $true) | spl0_2),
% 0.21/0.27 inference(backward_demodulation,[],[f11,f110])).
% 0.21/0.27 thf(f112,plain,(
% 0.21/0.27 (((f @ $false)) = $true) | spl0_2),
% 0.21/0.27 inference(backward_demodulation,[],[f14,f110])).
% 0.21/0.27 thf(f114,plain,(
% 0.21/0.27 ($false = $true) | (spl0_2 | ~spl0_3 | ~spl0_8)),
% 0.21/0.27 inference(forward_demodulation,[],[f112,f107])).
% 0.21/0.27 thf(f115,plain,(
% 0.21/0.27 $false | (spl0_2 | ~spl0_3 | ~spl0_8)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f114])).
% 0.21/0.27 thf(f116,plain,(
% 0.21/0.27 spl0_2 | ~spl0_3 | ~spl0_8),
% 0.21/0.27 inference(avatar_contradiction_clause,[],[f115])).
% 0.21/0.27 thf(f117,plain,(
% 0.21/0.27 ($false = $true) | (~spl0_1 | ~spl0_7)),
% 0.21/0.27 inference(backward_demodulation,[],[f96,f91])).
% 0.21/0.27 thf(f118,plain,(
% 0.21/0.27 $false | (~spl0_1 | ~spl0_7)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f117])).
% 0.21/0.27 thf(f119,plain,(
% 0.21/0.27 ~spl0_1 | ~spl0_7),
% 0.21/0.27 inference(avatar_contradiction_clause,[],[f118])).
% 0.21/0.27 thf(f129,plain,(
% 0.21/0.27 (((g @ $true)) = $false) | (sK1 = $false) | ~spl0_4),
% 0.21/0.27 inference(constrained_superposition,[],[f41,f18])).
% 0.21/0.27 thf(f132,plain,(
% 0.21/0.27 (sK1 = $false) | ($false = $true) | (~spl0_4 | ~spl0_9)),
% 0.21/0.27 inference(forward_demodulation,[],[f129,f104])).
% 0.21/0.27 thf(f133,plain,(
% 0.21/0.27 (sK1 = $false) | (~spl0_4 | ~spl0_9)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f132])).
% 0.21/0.27 thf(f134,plain,(
% 0.21/0.27 spl0_8 | ~spl0_4 | ~spl0_9),
% 0.21/0.27 inference(avatar_split_clause,[],[f133,f103,f40,f93])).
% 0.21/0.27 thf(f136,plain,(
% 0.21/0.27 (((g @ $false)) = $false) | (~spl0_4 | ~spl0_8)),
% 0.21/0.27 inference(backward_demodulation,[],[f41,f94])).
% 0.21/0.27 thf(f137,plain,(
% 0.21/0.27 ($false = $true) | (spl0_2 | ~spl0_4 | ~spl0_8)),
% 0.21/0.27 inference(backward_demodulation,[],[f111,f136])).
% 0.21/0.27 thf(f138,plain,(
% 0.21/0.27 $false | (spl0_2 | ~spl0_4 | ~spl0_8)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f137])).
% 0.21/0.27 thf(f139,plain,(
% 0.21/0.27 spl0_2 | ~spl0_4 | ~spl0_8),
% 0.21/0.27 inference(avatar_contradiction_clause,[],[f138])).
% 0.21/0.27 thf(f141,definition,(
% 0.21/0.27 spl0_10 <=> (b = $false)),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.21/0.27 thf(f142,plain,(
% 0.21/0.27 (b = $false) | ~spl0_10),
% 0.21/0.27 inference(avatar_component_clause,[],[f141])).
% 0.21/0.27 thf(f149,plain,(
% 0.21/0.27 (((g @ $true)) = $true) | ~spl0_2),
% 0.21/0.27 inference(backward_demodulation,[],[f11,f27])).
% 0.21/0.27 thf(f154,plain,(
% 0.21/0.27 spl0_10 | spl0_1),
% 0.21/0.27 inference(avatar_split_clause,[],[f77,f20,f141])).
% 0.21/0.27 thf(f155,plain,(
% 0.21/0.27 spl0_9 | ~spl0_2),
% 0.21/0.27 inference(avatar_split_clause,[],[f149,f23,f103])).
% 0.21/0.27 thf(f159,plain,(
% 0.21/0.27 (((g @ $false)) = $true) | ~spl0_10),
% 0.21/0.27 inference(backward_demodulation,[],[f10,f142])).
% 0.21/0.27 thf(f163,plain,(
% 0.21/0.27 ($false = $true) | (~spl0_4 | ~spl0_8 | ~spl0_10)),
% 0.21/0.27 inference(forward_demodulation,[],[f159,f136])).
% 0.21/0.27 thf(f164,plain,(
% 0.21/0.27 $false | (~spl0_4 | ~spl0_8 | ~spl0_10)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f163])).
% 0.21/0.27 thf(f165,plain,(
% 0.21/0.27 ~spl0_4 | ~spl0_8 | ~spl0_10),
% 0.21/0.27 inference(avatar_contradiction_clause,[],[f164])).
% 0.21/0.27 cnf(s1, plain, ~spl0_1 | ~spl0_2, inference(sat_conversion,[],[f25])).
% 0.21/0.27 cnf(s2, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f28])).
% 0.21/0.27 cnf(s3, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f42])).
% 0.21/0.27 cnf(s6, plain, spl0_1 | ~spl0_2 | ~spl0_3, inference(sat_conversion,[],[f88])).
% 0.21/0.27 cnf(s7, plain, ~spl0_3 | spl0_7 | spl0_8, inference(sat_conversion,[],[f95])).
% 0.21/0.27 cnf(s9, plain, ~spl0_1 | spl0_9, inference(sat_conversion,[],[f106])).
% 0.21/0.27 cnf(s11, plain, spl0_2 | ~spl0_3 | ~spl0_8, inference(sat_conversion,[],[f116])).
% 0.21/0.27 cnf(s12, plain, ~spl0_1 | ~spl0_7, inference(sat_conversion,[],[f119])).
% 0.21/0.27 cnf(s14, plain, ~spl0_4 | spl0_8 | ~spl0_9, inference(sat_conversion,[],[f134])).
% 0.21/0.27 cnf(s15, plain, spl0_2 | ~spl0_4 | ~spl0_8, inference(sat_conversion,[],[f139])).
% 0.21/0.27 cnf(s19, plain, spl0_1 | spl0_10, inference(sat_conversion,[],[f154])).
% 0.21/0.27 cnf(s20, plain, ~spl0_2 | spl0_9, inference(sat_conversion,[],[f155])).
% 0.21/0.27 cnf(s24, plain, ~spl0_4 | ~spl0_8 | ~spl0_10, inference(sat_conversion,[],[f165])).
% 0.21/0.27 cnf(s25, plain, spl0_1, inference(rat,[],[s14,s24,s3,s6,s20,s2,s19])).
% 0.21/0.27 cnf(s26, plain, ~spl0_7, inference(rat,[],[s12,s25])).
% 0.21/0.27 cnf(s27, plain, spl0_9, inference(rat,[],[s9,s25])).
% 0.21/0.27 cnf(s28, plain, ~spl0_2, inference(rat,[],[s1,s25])).
% 0.21/0.27 cnf(s29, plain, ~spl0_4, inference(rat,[],[s14,s15,s27,s28])).
% 0.21/0.27 cnf(s30, plain, spl0_3, inference(rat,[],[s3,s29])).
% 0.21/0.27 cnf(s32, plain, spl0_8, inference(rat,[],[s7,s26,s30])).
% 0.21/0.27 cnf(s33, plain, $false, inference(rat,[],[s11,s28,s30,s32])).
% 0.21/0.27 thf(f166,plain,(
% 0.21/0.27 $false),
% 0.21/0.27 inference(avatar_sat_refutation,[],[s33])).
% 0.21/0.27 % SZS output end Proof for theBenchmark
% 0.21/0.27 % (91866)------------------------------
% 0.21/0.27 % (91866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (91866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (91866)CaDiCaL version: 2.1.3
% 0.21/0.27 % (91866)Termination reason: Refutation
% 0.21/0.27 % (91866)Time elapsed: 0.006 s
% 0.21/0.27 % (91866)Peak memory usage: 13 MB
% 0.21/0.27 % (91866)Instructions burned: 9 (million)
% 0.21/0.27 % (91856)Success in time 0.053 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------