%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO026^1 : 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 : n015.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 08:46:18 AM UTC 2026
% Result : Theorem 0.24s 0.30s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO026^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:25:53 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.30 % (3732324)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.30 % (3732335)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.30 % (3732335)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
% 0.24/0.30 % (3732335)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=4033718487:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.30 % (3732335)Refutation not found, incomplete strategy
% 0.24/0.30 % (3732335)------------------------------
% 0.24/0.30 % (3732335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3732335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3732335)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3732335)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (3732335)Time elapsed: 0.001 s
% 0.24/0.30 % (3732335)Peak memory usage: 12 MB
% 0.24/0.30 % (3732335)Instructions burned: 3 (million)
% 0.24/0.30 % (3732335)------------------------------
% 0.24/0.30 % (3732335)------------------------------
% 0.24/0.30 % (3732332)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=2245659930: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)
% 0.24/0.30 % (3732331)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3985304239:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.30 % (3732334)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4181166652:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.30 % (3732330)lrs+10_16_si=on:nwc=1.5:random_seed=2493466881:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.30 % (3732333)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3113239987:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.30 % (3732329)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=310534526:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.30 % (3732331)Refutation not found, incomplete strategy
% 0.24/0.30 % (3732331)------------------------------
% 0.24/0.30 % (3732331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3732331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3732331)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3732331)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (3732331)Time elapsed: 0.001 s
% 0.24/0.30 % (3732331)Peak memory usage: 12 MB
% 0.24/0.30 % (3732333)Refutation not found, incomplete strategy
% 0.24/0.30 % (3732333)------------------------------
% 0.24/0.30 % (3732333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3732333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3732333)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3732333)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (3732333)Time elapsed: 0.001 s
% 0.24/0.30 % (3732333)Peak memory usage: 12 MB
% 0.24/0.30 % (3732332)Refutation not found, incomplete strategy
% 0.24/0.30 % (3732332)------------------------------
% 0.24/0.30 % (3732332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3732332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3732329)Refutation not found, incomplete strategy
% 0.24/0.30 % (3732329)------------------------------
% 0.24/0.30 % (3732329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3732332)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3732329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3732332)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (3732332)Time elapsed: 0.001 s
% 0.24/0.30 % (3732332)Peak memory usage: 12 MB
% 0.24/0.30 % (3732332)Instructions burned: 1 (million)
% 0.24/0.30 % (3732329)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3732329)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (3732329)Time elapsed: 0.001 s
% 0.24/0.30 % (3732329)Peak memory usage: 12 MB
% 0.24/0.30 % (3732331)------------------------------
% 0.24/0.30 % (3732331)------------------------------
% 0.24/0.30 % (3732333)------------------------------
% 0.24/0.30 % (3732333)------------------------------
% 0.24/0.30 % (3732332)------------------------------
% 0.24/0.30 % (3732332)------------------------------
% 0.24/0.30 % (3732329)------------------------------
% 0.24/0.30 % (3732329)------------------------------
% 0.24/0.30 % (3732330)Refutation not found, incomplete strategy
% 0.24/0.30 % (3732330)------------------------------
% 0.24/0.30 % (3732330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3732330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3732330)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3732330)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (3732330)Time elapsed: 0.004 s
% 0.24/0.30 % (3732330)Peak memory usage: 12 MB
% 0.24/0.30 % (3732330)Instructions burned: 5 (million)
% 0.24/0.30 % (3732330)------------------------------
% 0.24/0.30 % (3732330)------------------------------
% 0.24/0.30 % (3732334) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3732324-3732334"...
% 0.24/0.30 % (3732337)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2585438541:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.30 % (3732337)Refutation not found, incomplete strategy
% 0.24/0.30 % (3732337)------------------------------
% 0.24/0.30 % (3732337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3732337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3732337)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3732337)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (3732337)Time elapsed: 0.001 s
% 0.24/0.30 % (3732337)Peak memory usage: 12 MB
% 0.24/0.30 % (3732337)Instructions burned: 2 (million)
% 0.24/0.30 % (3732334)...printing done.
% 0.24/0.30 % (3732337)------------------------------
% 0.24/0.30 % (3732337)------------------------------
% 0.24/0.30 % (3732334)Refutation found. Thanks to Tanya!
% 0.24/0.30 % SZS status Theorem for theBenchmark
% 0.24/0.30 % SZS output start Proof for theBenchmark
% 0.24/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.30 thf(func_def_0, type, p: (($o > $o) > $o)).
% 0.24/0.30 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.30 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.24/0.30 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.30 thf(func_def_7, type, sK0: ($o > $o)).
% 0.24/0.30 thf(func_def_8, type, sK1: $o).
% 0.24/0.30 thf(func_def_10, type, sK3: $o).
% 0.24/0.30 thf(func_def_11, type, sK4: $o).
% 0.24/0.30 thf(func_def_12, type, sK5: $o).
% 0.24/0.30 thf(f1,conjecture,(
% 0.24/0.30 ((p @ (^[X0 : $o] : (X0))) & (p @ (^[X0 : $o] : ($true))) & (p @ (^[X0 : $o] : (~X0))) & (p @ (^[X0 : $o] : ($false)))) => ! [X1 : ($o > $o)] : (p @ X1)),
% 0.24/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.24/0.30 thf(f2,negated_conjecture,(
% 0.24/0.30 ~(((p @ (^[X0 : $o] : (X0))) & (p @ (^[X0 : $o] : ($true))) & (p @ (^[X0 : $o] : (~X0))) & (p @ (^[X0 : $o] : ($false)))) => ! [X1 : ($o > $o)] : (p @ X1))),
% 0.24/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.30 thf(f3,plain,(
% 0.24/0.30 ~(((p @ (^[X0 : $o] : (X0))) & (p @ (^[X1 : $o] : ($true))) & (p @ (^[X2 : $o] : (~X2))) & (p @ (^[X3 : $o] : ($false)))) => ! [X4 : ($o > $o)] : (p @ X4))),
% 0.24/0.30 inference(rectify,[],[f2])).
% 0.24/0.30 thf(f4,plain,(
% 0.24/0.30 ~(((((p @ (^[Y0 : $o]: ($true)))) = $true) & (((p @ (^[Y0 : $o]: (Y0)))) = $true) & (((p @ (^[Y0 : $o]: ($false)))) = $true) & (((p @ (^[Y0 : $o]: (~ Y0)))) = $true)) => ! [X4 : ($o > $o)] : (((p @ X4)) = $true))),
% 0.24/0.30 inference(fool_elimination,[],[f3])).
% 0.24/0.30 thf(f5,plain,(
% 0.24/0.30 ~(((((p @ (^[Y0 : $o]: ($true)))) = $true) & (((p @ (^[Y0 : $o]: (Y0)))) = $true) & (((p @ (^[Y0 : $o]: ($false)))) = $true) & (((p @ (^[Y0 : $o]: (~ Y0)))) = $true)) => ! [X0 : ($o > $o)] : (((p @ X0)) = $true))),
% 0.24/0.30 inference(rectify,[],[f4])).
% 0.24/0.30 thf(f6,plain,(
% 0.24/0.30 ? [X0 : ($o > $o)] : (((p @ X0)) != $true) & ((((p @ (^[Y0 : $o]: ($true)))) = $true) & (((p @ (^[Y0 : $o]: (Y0)))) = $true) & (((p @ (^[Y0 : $o]: ($false)))) = $true) & (((p @ (^[Y0 : $o]: (~ Y0)))) = $true))),
% 0.24/0.30 inference(ennf_transformation,[],[f5])).
% 0.24/0.30 thf(f7,plain,(
% 0.24/0.30 (((p @ (^[Y0 : $o]: ($false)))) = $true) & (((p @ (^[Y0 : $o]: (~ Y0)))) = $true) & ? [X0 : ($o > $o)] : (((p @ X0)) != $true) & (((p @ (^[Y0 : $o]: (Y0)))) = $true) & (((p @ (^[Y0 : $o]: ($true)))) = $true)),
% 0.24/0.30 inference(flattening,[],[f6])).
% 0.24/0.30 thf(f8,plain,(
% 0.24/0.30 (((p @ (^[Y0 : $o]: ($false)))) = $true) & (((p @ (^[Y0 : $o]: (~ Y0)))) = $true) & (((p @ sK0)) != $true) & (((p @ (^[Y0 : $o]: (Y0)))) = $true) & (((p @ (^[Y0 : $o]: ($true)))) = $true)),
% 0.24/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7])).
% 0.24/0.30 thf(f9,plain,(
% 0.24/0.30 (((p @ (^[Y0 : $o]: ($true)))) = $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f8])).
% 0.24/0.30 thf(f10,plain,(
% 0.24/0.30 (((p @ (^[Y0 : $o]: (Y0)))) = $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f8])).
% 0.24/0.30 thf(f11,plain,(
% 0.24/0.30 (((p @ sK0)) != $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f8])).
% 0.24/0.30 thf(f12,plain,(
% 0.24/0.30 (((p @ (^[Y0 : $o]: (~ Y0)))) = $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f8])).
% 0.24/0.30 thf(f13,plain,(
% 0.24/0.30 (((p @ (^[Y0 : $o]: ($false)))) = $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f8])).
% 0.24/0.30 thf(f15,definition,(
% 0.24/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.24/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.24/0.30 thf(f16,plain,(
% 0.24/0.30 (((p @ ~)) = $true)),
% 0.24/0.30 inference(beta-eta_normalization,[],[f12])).
% 0.24/0.30 thf(f17,plain,(
% 0.24/0.30 ($true != $true) | (~ != sK0)),
% 0.24/0.30 inference(constrained_superposition,[],[f11,f16])).
% 0.24/0.30 thf(f18,plain,(
% 0.24/0.30 (~ != sK0)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f17])).
% 0.24/0.30 thf(f19,plain,(
% 0.24/0.30 (((sK0 @ sK1)) != ((~ sK1)))),
% 0.24/0.30 inference(negative_extensionality,[],[f18])).
% 0.24/0.30 thf(f20,plain,(
% 0.24/0.30 (((sK0 @ sK1)) = $true) | (((~ sK1)) = $true)),
% 0.24/0.30 inference(xor_proxy_clausification,[],[f19])).
% 0.24/0.30 thf(f21,plain,(
% 0.24/0.30 ($false = ((~ sK1))) | ($false = ((sK0 @ sK1)))),
% 0.24/0.30 inference(xor_proxy_clausification,[],[f19])).
% 0.24/0.30 thf(f22,plain,(
% 0.24/0.30 ($false = ((sK0 @ sK1))) | (sK1 = $true)),
% 0.24/0.30 inference(not_proxy_clausification,[],[f21])).
% 0.24/0.30 thf(f23,plain,(
% 0.24/0.30 (((sK0 @ sK1)) = $true) | (sK1 = $false)),
% 0.24/0.30 inference(not_proxy_clausification,[],[f20])).
% 0.24/0.30 thf(f25,definition,(
% 0.24/0.30 spl2_1 <=> (sK1 = $true)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.24/0.30 thf(f26,plain,(
% 0.24/0.30 (sK1 = $true) | ~spl2_1),
% 0.24/0.30 inference(avatar_component_clause,[],[f25])).
% 0.24/0.30 thf(f28,definition,(
% 0.24/0.30 spl2_2 <=> ($false = ((sK0 @ sK1)))),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.24/0.30 thf(f29,plain,(
% 0.24/0.30 ($false = ((sK0 @ sK1))) | ~spl2_2),
% 0.24/0.30 inference(avatar_component_clause,[],[f28])).
% 0.24/0.30 thf(f30,plain,(
% 0.24/0.30 spl2_1 | spl2_2),
% 0.24/0.30 inference(avatar_split_clause,[],[f22,f28,f25])).
% 0.24/0.30 thf(f32,definition,(
% 0.24/0.30 spl2_3 <=> (((sK0 @ sK1)) = $true)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.24/0.30 thf(f33,plain,(
% 0.24/0.30 (((sK0 @ sK1)) = $true) | ~spl2_3),
% 0.24/0.30 inference(avatar_component_clause,[],[f32])).
% 0.24/0.30 thf(f35,definition,(
% 0.24/0.30 spl2_4 <=> (sK1 = $false)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.24/0.30 thf(f36,plain,(
% 0.24/0.30 (sK1 = $false) | ~spl2_4),
% 0.24/0.30 inference(avatar_component_clause,[],[f35])).
% 0.24/0.30 thf(f37,plain,(
% 0.24/0.30 spl2_3 | spl2_4),
% 0.24/0.30 inference(avatar_split_clause,[],[f23,f35,f32])).
% 0.24/0.30 thf(f38,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_2 | ~spl2_3)),
% 0.24/0.30 inference(backward_demodulation,[],[f33,f29])).
% 0.24/0.30 thf(f39,plain,(
% 0.24/0.30 $false | (~spl2_2 | ~spl2_3)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f38])).
% 0.24/0.30 thf(f40,plain,(
% 0.24/0.30 ~spl2_2 | ~spl2_3),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f39])).
% 0.24/0.30 thf(f41,plain,(
% 0.24/0.30 ($true = ((sK0 @ $true))) | (~spl2_1 | ~spl2_3)),
% 0.24/0.30 inference(forward_demodulation,[],[f33,f26])).
% 0.24/0.30 thf(f42,plain,(
% 0.24/0.30 ($true != $true) | (sK0 != (^[Y0 : $o]: ($true)))),
% 0.24/0.30 inference(constrained_superposition,[],[f11,f9])).
% 0.24/0.30 thf(f43,plain,(
% 0.24/0.30 (sK0 != (^[Y0 : $o]: ($true)))),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f42])).
% 0.24/0.30 thf(f44,plain,(
% 0.24/0.30 ($true != $true) | (sK0 != (^[Y0 : $o]: ($false)))),
% 0.24/0.30 inference(constrained_superposition,[],[f11,f13])).
% 0.24/0.30 thf(f45,plain,(
% 0.24/0.30 (sK0 != (^[Y0 : $o]: ($false)))),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f44])).
% 0.24/0.30 thf(f46,plain,(
% 0.24/0.30 ($true != $true) | (sK0 != (^[Y0 : $o]: (Y0)))),
% 0.24/0.30 inference(constrained_superposition,[],[f11,f10])).
% 0.24/0.30 thf(f47,plain,(
% 0.24/0.30 (sK0 != (^[Y0 : $o]: (Y0)))),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f46])).
% 0.24/0.30 thf(f48,plain,(
% 0.24/0.30 ((((^[Y0 : $o]: ($true)) @ sK3)) != ((sK0 @ sK3)))),
% 0.24/0.30 inference(negative_extensionality,[],[f43])).
% 0.24/0.30 thf(f50,plain,(
% 0.24/0.30 ($false = ((sK0 @ sK3))) | ((((^[Y0 : $o]: ($true)) @ sK3)) = $false)),
% 0.24/0.30 inference(xor_proxy_clausification,[],[f48])).
% 0.24/0.30 thf(f51,plain,(
% 0.24/0.30 ($false = ((sK0 @ sK3))) | ($false = $true)),
% 0.24/0.30 inference(beta-eta_normalization,[],[f50])).
% 0.24/0.30 thf(f52,plain,(
% 0.24/0.30 ($false = ((sK0 @ sK3)))),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f51])).
% 0.24/0.30 thf(f54,plain,(
% 0.24/0.30 ((((^[Y0 : $o]: ($false)) @ sK4)) != ((sK0 @ sK4)))),
% 0.24/0.30 inference(negative_extensionality,[],[f45])).
% 0.24/0.30 thf(f55,plain,(
% 0.24/0.30 ((((^[Y0 : $o]: ($false)) @ sK4)) = $true) | (((sK0 @ sK4)) = $true)),
% 0.24/0.30 inference(xor_proxy_clausification,[],[f54])).
% 0.24/0.30 thf(f58,plain,(
% 0.24/0.30 ($false = $true) | (((sK0 @ sK4)) = $true)),
% 0.24/0.30 inference(beta-eta_normalization,[],[f55])).
% 0.24/0.30 thf(f59,plain,(
% 0.24/0.30 (((sK0 @ sK4)) = $true)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f58])).
% 0.24/0.30 thf(f60,plain,(
% 0.24/0.30 (((sK0 @ sK5)) != (((^[Y0 : $o]: (Y0)) @ sK5)))),
% 0.24/0.30 inference(negative_extensionality,[],[f47])).
% 0.24/0.30 thf(f61,plain,(
% 0.24/0.30 (((sK0 @ sK5)) = $true) | ($true = (((^[Y0 : $o]: (Y0)) @ sK5)))),
% 0.24/0.30 inference(xor_proxy_clausification,[],[f60])).
% 0.24/0.30 thf(f62,plain,(
% 0.24/0.30 ($false = ((sK0 @ sK5))) | ($false = (((^[Y0 : $o]: (Y0)) @ sK5)))),
% 0.24/0.30 inference(xor_proxy_clausification,[],[f60])).
% 0.24/0.30 thf(f63,plain,(
% 0.24/0.30 ($false = ((sK0 @ sK5))) | ($false = sK5)),
% 0.24/0.30 inference(beta-eta_normalization,[],[f62])).
% 0.24/0.30 thf(f64,plain,(
% 0.24/0.30 ($true = sK5) | (((sK0 @ sK5)) = $true)),
% 0.24/0.30 inference(beta-eta_normalization,[],[f61])).
% 0.24/0.30 thf(f66,definition,(
% 0.24/0.30 spl2_5 <=> ($false = sK5)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.24/0.30 thf(f67,plain,(
% 0.24/0.30 ($false = sK5) | ~spl2_5),
% 0.24/0.30 inference(avatar_component_clause,[],[f66])).
% 0.24/0.30 thf(f69,definition,(
% 0.24/0.30 spl2_6 <=> ($false = ((sK0 @ sK5)))),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition])).
% 0.24/0.30 thf(f70,plain,(
% 0.24/0.30 ($false = ((sK0 @ sK5))) | ~spl2_6),
% 0.24/0.30 inference(avatar_component_clause,[],[f69])).
% 0.24/0.30 thf(f71,plain,(
% 0.24/0.30 spl2_5 | spl2_6),
% 0.24/0.30 inference(avatar_split_clause,[],[f63,f69,f66])).
% 0.24/0.30 thf(f73,definition,(
% 0.24/0.30 spl2_7 <=> (((sK0 @ sK5)) = $true)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition])).
% 0.24/0.30 thf(f74,plain,(
% 0.24/0.30 (((sK0 @ sK5)) = $true) | ~spl2_7),
% 0.24/0.30 inference(avatar_component_clause,[],[f73])).
% 0.24/0.30 thf(f76,definition,(
% 0.24/0.30 spl2_8 <=> ($true = sK5)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition])).
% 0.24/0.30 thf(f77,plain,(
% 0.24/0.30 ($true = sK5) | ~spl2_8),
% 0.24/0.30 inference(avatar_component_clause,[],[f76])).
% 0.24/0.30 thf(f78,plain,(
% 0.24/0.30 spl2_7 | spl2_8),
% 0.24/0.30 inference(avatar_split_clause,[],[f64,f76,f73])).
% 0.24/0.30 thf(f79,plain,(
% 0.24/0.30 (((sK0 @ $false)) = $true) | (~spl2_5 | ~spl2_7)),
% 0.24/0.30 inference(forward_demodulation,[],[f74,f67])).
% 0.24/0.30 thf(f85,plain,(
% 0.24/0.30 ($false = sK3) | ($false = ((sK0 @ $true)))),
% 0.24/0.30 inference(constrained_superposition,[],[f52,f15])).
% 0.24/0.30 thf(f86,plain,(
% 0.24/0.30 ($true = ((sK0 @ $true))) | ($false = sK4)),
% 0.24/0.30 inference(constrained_superposition,[],[f59,f15])).
% 0.24/0.30 thf(f99,plain,(
% 0.24/0.30 ($false = $true) | ($false = sK3) | (~spl2_1 | ~spl2_3)),
% 0.24/0.30 inference(forward_demodulation,[],[f85,f41])).
% 0.24/0.30 thf(f100,plain,(
% 0.24/0.30 ($false = sK3) | (~spl2_1 | ~spl2_3)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f99])).
% 0.24/0.30 thf(f102,plain,(
% 0.24/0.30 (((sK0 @ $false)) = $false) | (~spl2_1 | ~spl2_3)),
% 0.24/0.30 inference(backward_demodulation,[],[f52,f100])).
% 0.24/0.30 thf(f103,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_7)),
% 0.24/0.30 inference(backward_demodulation,[],[f79,f102])).
% 0.24/0.30 thf(f104,plain,(
% 0.24/0.30 $false | (~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_7)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f103])).
% 0.24/0.30 thf(f105,plain,(
% 0.24/0.30 ~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_7),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f104])).
% 0.24/0.30 thf(f106,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_5 | ~spl2_8)),
% 0.24/0.30 inference(forward_demodulation,[],[f77,f67])).
% 0.24/0.30 thf(f107,plain,(
% 0.24/0.30 $false | (~spl2_5 | ~spl2_8)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f106])).
% 0.24/0.30 thf(f108,plain,(
% 0.24/0.30 ~spl2_5 | ~spl2_8),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f107])).
% 0.24/0.30 thf(f109,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_1 | ~spl2_4)),
% 0.24/0.30 inference(backward_demodulation,[],[f26,f36])).
% 0.24/0.30 thf(f110,plain,(
% 0.24/0.30 $false | (~spl2_1 | ~spl2_4)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f109])).
% 0.24/0.30 thf(f111,plain,(
% 0.24/0.30 ~spl2_1 | ~spl2_4),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f110])).
% 0.24/0.30 thf(f116,definition,(
% 0.24/0.30 spl2_10 <=> ($false = ((sK0 @ $true)))),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition])).
% 0.24/0.30 thf(f117,plain,(
% 0.24/0.30 ($false = ((sK0 @ $true))) | ~spl2_10),
% 0.24/0.30 inference(avatar_component_clause,[],[f116])).
% 0.24/0.30 thf(f120,definition,(
% 0.24/0.30 spl2_11 <=> ($true = ((sK0 @ $true)))),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition])).
% 0.24/0.30 thf(f121,plain,(
% 0.24/0.30 ($true = ((sK0 @ $true))) | ~spl2_11),
% 0.24/0.30 inference(avatar_component_clause,[],[f120])).
% 0.24/0.30 thf(f123,definition,(
% 0.24/0.30 spl2_12 <=> ($false = sK4)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition])).
% 0.24/0.30 thf(f124,plain,(
% 0.24/0.30 ($false = sK4) | ~spl2_12),
% 0.24/0.30 inference(avatar_component_clause,[],[f123])).
% 0.24/0.30 thf(f125,plain,(
% 0.24/0.30 spl2_11 | spl2_12),
% 0.24/0.30 inference(avatar_split_clause,[],[f86,f123,f120])).
% 0.24/0.30 thf(f130,plain,(
% 0.24/0.30 (((sK0 @ $false)) = $true) | ~spl2_12),
% 0.24/0.30 inference(backward_demodulation,[],[f59,f124])).
% 0.24/0.30 thf(f131,plain,(
% 0.24/0.30 ($true = ((sK0 @ $true))) | (~spl2_1 | ~spl2_3)),
% 0.24/0.30 inference(backward_demodulation,[],[f33,f26])).
% 0.24/0.30 thf(f132,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_6 | ~spl2_7)),
% 0.24/0.30 inference(forward_demodulation,[],[f74,f70])).
% 0.24/0.30 thf(f133,plain,(
% 0.24/0.30 $false | (~spl2_6 | ~spl2_7)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f132])).
% 0.24/0.30 thf(f134,plain,(
% 0.24/0.30 ~spl2_6 | ~spl2_7),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f133])).
% 0.24/0.30 thf(f138,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_1 | ~spl2_3 | ~spl2_10)),
% 0.24/0.30 inference(forward_demodulation,[],[f131,f117])).
% 0.24/0.30 thf(f139,plain,(
% 0.24/0.30 $false | (~spl2_1 | ~spl2_3 | ~spl2_10)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f138])).
% 0.24/0.30 thf(f140,plain,(
% 0.24/0.30 ~spl2_1 | ~spl2_3 | ~spl2_10),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f139])).
% 0.24/0.30 thf(f141,plain,(
% 0.24/0.30 (((sK0 @ $false)) = $false) | (~spl2_2 | ~spl2_4)),
% 0.24/0.30 inference(backward_demodulation,[],[f29,f36])).
% 0.24/0.30 thf(f142,plain,(
% 0.24/0.30 (((sK0 @ $false)) = $true) | (~spl2_5 | ~spl2_7)),
% 0.24/0.30 inference(forward_demodulation,[],[f74,f67])).
% 0.24/0.30 thf(f146,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_7)),
% 0.24/0.30 inference(forward_demodulation,[],[f142,f141])).
% 0.24/0.30 thf(f147,plain,(
% 0.24/0.30 $false | (~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_7)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f146])).
% 0.24/0.30 thf(f148,plain,(
% 0.24/0.30 ~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_7),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f147])).
% 0.24/0.30 thf(f149,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_2 | ~spl2_4 | ~spl2_12)),
% 0.24/0.30 inference(forward_demodulation,[],[f130,f141])).
% 0.24/0.30 thf(f150,plain,(
% 0.24/0.30 $false | (~spl2_2 | ~spl2_4 | ~spl2_12)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f149])).
% 0.24/0.30 thf(f151,plain,(
% 0.24/0.30 ~spl2_2 | ~spl2_4 | ~spl2_12),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f150])).
% 0.24/0.30 thf(f152,plain,(
% 0.24/0.30 ($false = ((sK0 @ $true))) | (~spl2_6 | ~spl2_8)),
% 0.24/0.30 inference(backward_demodulation,[],[f70,f77])).
% 0.24/0.30 thf(f153,plain,(
% 0.24/0.30 ($false = $true) | (~spl2_10 | ~spl2_11)),
% 0.24/0.30 inference(forward_demodulation,[],[f121,f117])).
% 0.24/0.30 thf(f154,plain,(
% 0.24/0.30 $false | (~spl2_10 | ~spl2_11)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f153])).
% 0.24/0.30 thf(f155,plain,(
% 0.24/0.30 ~spl2_10 | ~spl2_11),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f154])).
% 0.24/0.30 thf(f156,plain,(
% 0.24/0.30 spl2_10 | ~spl2_6 | ~spl2_8),
% 0.24/0.30 inference(avatar_split_clause,[],[f152,f76,f69,f116])).
% 0.24/0.30 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f30])).
% 0.24/0.30 cnf(s2, plain, spl2_3 | spl2_4, inference(sat_conversion,[],[f37])).
% 0.24/0.30 cnf(s3, plain, ~spl2_2 | ~spl2_3, inference(sat_conversion,[],[f40])).
% 0.24/0.30 cnf(s4, plain, spl2_5 | spl2_6, inference(sat_conversion,[],[f71])).
% 0.24/0.30 cnf(s5, plain, spl2_7 | spl2_8, inference(sat_conversion,[],[f78])).
% 0.24/0.30 cnf(s6, plain, ~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_7, inference(sat_conversion,[],[f105])).
% 0.24/0.30 cnf(s7, plain, ~spl2_5 | ~spl2_8, inference(sat_conversion,[],[f108])).
% 0.24/0.30 cnf(s8, plain, ~spl2_1 | ~spl2_4, inference(sat_conversion,[],[f111])).
% 0.24/0.30 cnf(s10, plain, spl2_11 | spl2_12, inference(sat_conversion,[],[f125])).
% 0.24/0.30 cnf(s13, plain, ~spl2_6 | ~spl2_7, inference(sat_conversion,[],[f134])).
% 0.24/0.30 cnf(s16, plain, ~spl2_1 | ~spl2_3 | ~spl2_10, inference(sat_conversion,[],[f140])).
% 0.24/0.30 cnf(s18, plain, ~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_7, inference(sat_conversion,[],[f148])).
% 0.24/0.30 cnf(s19, plain, ~spl2_2 | ~spl2_4 | ~spl2_12, inference(sat_conversion,[],[f151])).
% 0.24/0.30 cnf(s20, plain, ~spl2_10 | ~spl2_11, inference(sat_conversion,[],[f155])).
% 0.24/0.30 cnf(s21, plain, ~spl2_6 | ~spl2_8 | spl2_10, inference(sat_conversion,[],[f156])).
% 0.24/0.30 cnf(s22, plain, ~spl2_6 | spl2_10, inference(rat,[],[s5,s13,s21])).
% 0.24/0.30 cnf(s23, plain, ~spl2_4 | ~spl2_2, inference(rat,[],[s5,s18,s7,s4,s22,s20,s10,s19])).
% 0.24/0.30 cnf(s24, plain, ~spl2_2, inference(rat,[],[s23,s2,s3])).
% 0.24/0.30 cnf(s25, plain, spl2_1, inference(rat,[],[s1,s24])).
% 0.24/0.30 cnf(s26, plain, ~spl2_4, inference(rat,[],[s8,s25])).
% 0.24/0.30 cnf(s27, plain, spl2_3, inference(rat,[],[s2,s26])).
% 0.24/0.30 cnf(s28, plain, ~spl2_10, inference(rat,[],[s16,s25,s27])).
% 0.24/0.30 cnf(s32, plain, ~spl2_6, inference(rat,[],[s22,s28])).
% 0.24/0.30 cnf(s33, plain, spl2_5, inference(rat,[],[s4,s32])).
% 0.24/0.30 cnf(s34, plain, ~spl2_8, inference(rat,[],[s7,s33])).
% 0.24/0.30 cnf(s35, plain, ~spl2_7, inference(rat,[],[s6,s27,s25,s33])).
% 0.24/0.30 cnf(s36, plain, $false, inference(rat,[],[s5,s34,s35])).
% 0.24/0.30 thf(f158,plain,(
% 0.24/0.30 $false),
% 0.24/0.30 inference(avatar_sat_refutation,[],[s36])).
% 0.24/0.30 % SZS output end Proof for theBenchmark
% 0.24/0.30 % (3732334)------------------------------
% 0.24/0.30 % (3732334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3732334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3732334)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3732334)Termination reason: Refutation
% 0.24/0.30 % (3732334)Time elapsed: 0.006 s
% 0.24/0.30 % (3732334)Peak memory usage: 13 MB
% 0.24/0.30 % (3732334)Instructions burned: 8 (million)
% 0.24/0.30 % (3732324)Success in time 0.039 s
% 0.24/0.30 % Vampire exiting
%------------------------------------------------------------------------------