%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU891^5 : 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 08:31:53 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU891^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:44:08 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.28 % (1384113)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1384131)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (1384131)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
% 0.21/0.28 % (1384131)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=1375079635:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (1384131) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1384113-1384131"...
% 0.21/0.28 % (1384123)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3915942311:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (1384124)lrs+10_16_si=on:nwc=1.5:random_seed=1235209681:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (1384131)...printing done.
% 0.21/0.28 % (1384128)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2478771399:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (1384125)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=247624659:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (1384126)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=1711608710: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)
% 0.21/0.28 % (1384127)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2102928657:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (1384131)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, b: $tType).
% 0.21/0.28 thf(type_def_6, type, a: $tType).
% 0.21/0.28 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, cF: (b > a)).
% 0.21/0.28 thf(func_def_1, type, cS: (b > $o)).
% 0.21/0.28 thf(func_def_2, type, cR: (b > $o)).
% 0.21/0.28 thf(func_def_6, type, sP0: (a > $o)).
% 0.21/0.28 thf(func_def_7, type, sK1: (a > b)).
% 0.21/0.28 thf(func_def_8, type, sK2: a).
% 0.21/0.28 thf(func_def_9, type, sK3: b).
% 0.21/0.28 thf(func_def_10, type, sF4: (b > $o)).
% 0.21/0.28 thf(func_def_11, type, sF5: (b > a)).
% 0.21/0.28 thf(func_def_12, type, sF6: (b > $o)).
% 0.21/0.28 thf(func_def_13, type, sF7: a).
% 0.21/0.28 thf(func_def_14, type, sF8: $o).
% 0.21/0.28 thf(func_def_15, type, sF9: $o).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ! [X0 : a] : ((? [X1 : b] : ((cR @ X1) & (X0 = ((cF @ X1)))) | ? [X1 : b] : ((cS @ X1) & (X0 = ((cF @ X1))))) => ? [X1 : b] : ((X0 = ((cF @ X1))) & ((cS @ X1) | (cR @ X1))))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM34B_pme)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~ ! [X0 : a] : ((? [X1 : b] : ((cR @ X1) & (X0 = ((cF @ X1)))) | ? [X1 : b] : ((cS @ X1) & (X0 = ((cF @ X1))))) => ? [X1 : b] : ((X0 = ((cF @ X1))) & ((cS @ X1) | (cR @ X1))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~ ! [X0 : a] : ((? [X1 : b] : ((cR @ X1) & (X0 = ((cF @ X1)))) | ? [X2 : b] : ((cS @ X2) & (((cF @ X2)) = X0))) => ? [X3 : b] : ((((cF @ X3)) = X0) & ((cS @ X3) | (cR @ X3))))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~ ! [X0 : a] : ((? [X2 : b] : ((((cF @ X2)) = X0) & ($true = ((cS @ X2)))) | ? [X1 : b] : ((((cR @ X1)) = $true) & (((cF @ X1)) = X0))) => ? [X3 : b] : ((($true = ((cS @ X3))) | ($true = ((cR @ X3)))) & (((cF @ X3)) = X0)))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ? [X0 : a] : (! [X3 : b] : ((($true != ((cR @ X3))) & ($true != ((cS @ X3)))) | (((cF @ X3)) != X0)) & (? [X2 : b] : ((((cF @ X2)) = X0) & ($true = ((cS @ X2)))) | ? [X1 : b] : ((((cR @ X1)) = $true) & (((cF @ X1)) = X0))))),
% 0.21/0.28 inference(ennf_transformation,[],[f4])).
% 0.21/0.28 thf(f6,definition,(
% 0.21/0.28 ! [X0 : a] : (? [X1 : b] : ((((cR @ X1)) = $true) & (((cF @ X1)) = X0)) | ~ (((sP0 @ X0)) = $true))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ? [X0 : a] : (! [X3 : b] : ((($true != ((cR @ X3))) & ($true != ((cS @ X3)))) | (((cF @ X3)) != X0)) & (? [X2 : b] : ((((cF @ X2)) = X0) & ($true = ((cS @ X2)))) | (((sP0 @ X0)) = $true)))),
% 0.21/0.28 inference(definition_folding,[],[f5,f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ! [X0 : a] : (? [X1 : b] : ((((cR @ X1)) = $true) & (((cF @ X1)) = X0)) | (((sP0 @ X0)) != $true))),
% 0.21/0.28 inference(nnf_transformation,[],[f6])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ! [X0 : a] : ((($true = ((cR @ (sK1 @ X0)))) & (((cF @ (sK1 @ X0))) = X0)) | (((sP0 @ X0)) != $true))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK1 @ X0)],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ? [X0 : a] : (! [X1 : b] : (((((cR @ X1)) != $true) & (((cS @ X1)) != $true)) | (((cF @ X1)) != X0)) & (? [X2 : b] : ((((cF @ X2)) = X0) & ($true = ((cS @ X2)))) | (((sP0 @ X0)) = $true)))),
% 0.21/0.28 inference(rectify,[],[f7])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ! [X1 : b] : (((((cR @ X1)) != $true) & (((cS @ X1)) != $true)) | (((cF @ X1)) != sK2)) & (((sK2 = ((cF @ sK3))) & ($true = ((cS @ sK3)))) | ($true = ((sP0 @ sK2))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X2,sK3)],[f10])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ( ! [X0 : a] : ((((sP0 @ X0)) != $true) | (((cF @ (sK1 @ X0))) = X0)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 ( ! [X0 : a] : (($true = ((cR @ (sK1 @ X0)))) | (((sP0 @ X0)) != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ($true = ((cS @ sK3))) | ($true = ((sP0 @ sK2)))),
% 0.21/0.28 inference(cnf_transformation,[],[f11])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 (sK2 = ((cF @ sK3))) | ($true = ((sP0 @ sK2)))),
% 0.21/0.28 inference(cnf_transformation,[],[f11])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ( ! [X1 : b] : ((((cS @ X1)) != $true) | (((cF @ X1)) != sK2)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f11])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ( ! [X1 : b] : ((((cR @ X1)) != $true) | (((cF @ X1)) != sK2)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f11])).
% 0.21/0.28 thf(f19,definition,(
% 0.21/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.28 thf(f20,definition,(
% 0.21/0.28 ( ! [X1 : b] : ((((sF4 @ X1)) = ((cR @ X1)))) )),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ( ! [X1 : b] : ((((cR @ X1)) = ((sF4 @ X1)))) )),
% 0.21/0.28 inference(reorient_equations,[],[f20])).
% 0.21/0.28 thf(f22,definition,(
% 0.21/0.28 ( ! [X1 : b] : ((((sF5 @ X1)) = ((cF @ X1)))) )),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 ( ! [X1 : b] : ((((cF @ X1)) = ((sF5 @ X1)))) )),
% 0.21/0.28 inference(reorient_equations,[],[f22])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 ( ! [X1 : b] : ((((sF5 @ X1)) != sK2) | (((sF4 @ X1)) != $true)) )),
% 0.21/0.28 inference(definition_folding,[],[f17,f23,f21])).
% 0.21/0.28 thf(f25,definition,(
% 0.21/0.28 ( ! [X1 : b] : ((((sF6 @ X1)) = ((cS @ X1)))) )),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 ( ! [X1 : b] : ((((cS @ X1)) = ((sF6 @ X1)))) )),
% 0.21/0.28 inference(reorient_equations,[],[f25])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ( ! [X1 : b] : (($true != ((sF6 @ X1))) | (((sF5 @ X1)) != sK2)) )),
% 0.21/0.28 inference(definition_folding,[],[f16,f23,f26])).
% 0.21/0.28 thf(f28,definition,(
% 0.21/0.28 (sF7 = ((cF @ sK3)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 0.21/0.28 thf(f29,definition,(
% 0.21/0.28 (sF8 = ((sP0 @ sK2)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 (((sP0 @ sK2)) = sF8)),
% 0.21/0.28 inference(reorient_equations,[],[f29])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 (sK2 = sF7) | ($true = sF8)),
% 0.21/0.28 inference(definition_folding,[],[f15,f30,f28])).
% 0.21/0.28 thf(f32,definition,(
% 0.21/0.28 (sF9 = ((cS @ sK3)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
% 0.21/0.28 thf(f33,plain,(
% 0.21/0.28 (((cS @ sK3)) = sF9)),
% 0.21/0.28 inference(reorient_equations,[],[f32])).
% 0.21/0.28 thf(f34,plain,(
% 0.21/0.28 ($true = sF8) | ($true = sF9)),
% 0.21/0.28 inference(definition_folding,[],[f14,f30,f33])).
% 0.21/0.28 thf(f36,plain,(
% 0.21/0.28 ( ! [X1 : b] : ((((sF4 @ X1)) = $true) | (((cR @ X1)) = $false)) )),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f21])).
% 0.21/0.28 thf(f38,plain,(
% 0.21/0.28 ( ! [X1 : b] : (($true = ((sF6 @ X1))) | (((cS @ X1)) = $false)) )),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f26])).
% 0.21/0.28 thf(f39,plain,(
% 0.21/0.28 (sF9 = $false) | ($true = ((cS @ sK3)))),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f33])).
% 0.21/0.28 thf(f41,plain,(
% 0.21/0.28 (sF8 = $false) | ($true = ((sP0 @ sK2)))),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f30])).
% 0.21/0.28 thf(f44,definition,(
% 0.21/0.28 spl10_1 <=> ($true = sF9)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition])).
% 0.21/0.28 thf(f46,plain,(
% 0.21/0.28 ($true = sF9) | ~spl10_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f44])).
% 0.21/0.28 thf(f48,definition,(
% 0.21/0.28 spl10_2 <=> ($true = sF8)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition])).
% 0.21/0.28 thf(f50,plain,(
% 0.21/0.28 ($true = sF8) | ~spl10_2),
% 0.21/0.28 inference(avatar_component_clause,[],[f48])).
% 0.21/0.28 thf(f51,plain,(
% 0.21/0.28 spl10_1 | spl10_2),
% 0.21/0.28 inference(avatar_split_clause,[],[f34,f48,f44])).
% 0.21/0.28 thf(f53,definition,(
% 0.21/0.28 spl10_3 <=> (sK2 = sF7)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition])).
% 0.21/0.28 thf(f55,plain,(
% 0.21/0.28 (sK2 = sF7) | ~spl10_3),
% 0.21/0.28 inference(avatar_component_clause,[],[f53])).
% 0.21/0.28 thf(f56,plain,(
% 0.21/0.28 spl10_2 | spl10_3),
% 0.21/0.28 inference(avatar_split_clause,[],[f31,f53,f48])).
% 0.21/0.28 thf(f58,definition,(
% 0.21/0.28 spl10_4 <=> (((cS @ sK3)) = $false)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition])).
% 0.21/0.28 thf(f59,plain,(
% 0.21/0.28 (((cS @ sK3)) != $false) | spl10_4),
% 0.21/0.28 inference(avatar_component_clause,[],[f58])).
% 0.21/0.28 thf(f60,plain,(
% 0.21/0.28 (((cS @ sK3)) = $false) | ~spl10_4),
% 0.21/0.28 inference(avatar_component_clause,[],[f58])).
% 0.21/0.28 thf(f63,definition,(
% 0.21/0.28 spl10_5 <=> (sF9 = $false)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition])).
% 0.21/0.28 thf(f65,plain,(
% 0.21/0.28 (sF9 = $false) | ~spl10_5),
% 0.21/0.28 inference(avatar_component_clause,[],[f63])).
% 0.21/0.28 thf(f67,definition,(
% 0.21/0.28 spl10_6 <=> ($true = ((cS @ sK3)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition])).
% 0.21/0.28 thf(f69,plain,(
% 0.21/0.28 ($true = ((cS @ sK3))) | ~spl10_6),
% 0.21/0.28 inference(avatar_component_clause,[],[f67])).
% 0.21/0.28 thf(f70,plain,(
% 0.21/0.28 spl10_5 | spl10_6),
% 0.21/0.28 inference(avatar_split_clause,[],[f39,f67,f63])).
% 0.21/0.28 thf(f77,definition,(
% 0.21/0.28 spl10_8 <=> (sF8 = $false)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition])).
% 0.21/0.28 thf(f79,plain,(
% 0.21/0.28 (sF8 = $false) | ~spl10_8),
% 0.21/0.28 inference(avatar_component_clause,[],[f77])).
% 0.21/0.28 thf(f81,definition,(
% 0.21/0.28 spl10_9 <=> ($true = ((sP0 @ sK2)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition])).
% 0.21/0.28 thf(f83,plain,(
% 0.21/0.28 ($true = ((sP0 @ sK2))) | ~spl10_9),
% 0.21/0.28 inference(avatar_component_clause,[],[f81])).
% 0.21/0.28 thf(f84,plain,(
% 0.21/0.28 spl10_8 | spl10_9),
% 0.21/0.28 inference(avatar_split_clause,[],[f41,f81,f77])).
% 0.21/0.28 thf(f85,plain,(
% 0.21/0.28 ($true = $false) | (~spl10_2 | ~spl10_8)),
% 0.21/0.28 inference(forward_demodulation,[],[f79,f50])).
% 0.21/0.28 thf(f86,plain,(
% 0.21/0.28 $false | (~spl10_2 | ~spl10_8)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f85])).
% 0.21/0.28 thf(f87,plain,(
% 0.21/0.28 ~spl10_2 | ~spl10_8),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f86])).
% 0.21/0.28 thf(f91,plain,(
% 0.21/0.28 ( ! [X0 : b] : ((((sF5 @ X0)) != sK2) | (((sF6 @ X0)) = $false) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f27,f19])).
% 0.21/0.28 thf(f94,plain,(
% 0.21/0.28 ( ! [X0 : b] : ((((sF6 @ X0)) = $false) | (((sF5 @ X0)) != sK2)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f91])).
% 0.21/0.28 thf(f106,plain,(
% 0.21/0.28 (sF7 = ((sF5 @ sK3)))),
% 0.21/0.28 inference(constrained_superposition,[],[f23,f28])).
% 0.21/0.28 thf(f124,plain,(
% 0.21/0.28 ( ! [X0 : b] : ((((cS @ X0)) = $false) | (((sF5 @ X0)) != sK2) | ($true = $false)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f38,f94])).
% 0.21/0.28 thf(f130,plain,(
% 0.21/0.28 ( ! [X0 : b] : ((((cS @ X0)) = $false) | (((sF5 @ X0)) != sK2)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f124])).
% 0.21/0.28 thf(f133,plain,(
% 0.21/0.28 ( ! [X0 : a] : ((((sF5 @ (sK1 @ X0))) = X0) | (((sP0 @ X0)) != $true)) )),
% 0.21/0.28 inference(forward_demodulation,[],[f12,f23])).
% 0.21/0.28 thf(f136,plain,(
% 0.21/0.28 ( ! [X0 : a] : ((((sF4 @ (sK1 @ X0))) != $true) | (sK2 != X0) | (((sP0 @ X0)) != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f24,f133])).
% 0.21/0.28 thf(f137,plain,(
% 0.21/0.28 ( ! [X0 : a] : ((((cR @ (sK1 @ X0))) = $false) | ($true != $true) | (sK2 != X0) | (((sP0 @ X0)) != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f136,f36])).
% 0.21/0.28 thf(f140,plain,(
% 0.21/0.28 ( ! [X0 : a] : ((((cR @ (sK1 @ X0))) = $false) | (((sP0 @ X0)) != $true) | (sK2 != X0)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f137])).
% 0.21/0.28 thf(f142,plain,(
% 0.21/0.28 ( ! [X0 : a] : ((((sP0 @ X0)) != $true) | (((sP0 @ X0)) != $true) | (sK2 != X0) | ($true = $false)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f140,f13])).
% 0.21/0.28 thf(f145,plain,(
% 0.21/0.28 ( ! [X0 : a] : ((((sP0 @ X0)) != $true) | ($true = $false) | (sK2 != X0)) )),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f142])).
% 0.21/0.28 thf(f146,plain,(
% 0.21/0.28 ( ! [X0 : a] : ((((sP0 @ X0)) != $true) | (sK2 != X0)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f145])).
% 0.21/0.28 thf(f150,plain,(
% 0.21/0.28 (sK2 != sK2) | ($true != $true) | ~spl10_9),
% 0.21/0.28 inference(constrained_superposition,[],[f146,f83])).
% 0.21/0.28 thf(f153,plain,(
% 0.21/0.28 $false | ~spl10_9),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f150])).
% 0.21/0.28 thf(f154,plain,(
% 0.21/0.28 ~spl10_9),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f153])).
% 0.21/0.28 thf(f155,plain,(
% 0.21/0.28 ($true = $false) | (~spl10_1 | ~spl10_5)),
% 0.21/0.28 inference(forward_demodulation,[],[f46,f65])).
% 0.21/0.28 thf(f156,plain,(
% 0.21/0.28 $false | (~spl10_1 | ~spl10_5)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f155])).
% 0.21/0.28 thf(f157,plain,(
% 0.21/0.28 ~spl10_1 | ~spl10_5),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f156])).
% 0.21/0.28 thf(f158,plain,(
% 0.21/0.28 ($true = $false) | (~spl10_4 | ~spl10_6)),
% 0.21/0.28 inference(forward_demodulation,[],[f69,f60])).
% 0.21/0.28 thf(f159,plain,(
% 0.21/0.28 $false | (~spl10_4 | ~spl10_6)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f158])).
% 0.21/0.28 thf(f160,plain,(
% 0.21/0.28 ~spl10_4 | ~spl10_6),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f159])).
% 0.21/0.28 thf(f186,plain,(
% 0.21/0.28 (sK2 != ((sF5 @ sK3))) | ($false != $false) | spl10_4),
% 0.21/0.28 inference(constrained_superposition,[],[f59,f130])).
% 0.21/0.28 thf(f188,plain,(
% 0.21/0.28 (sK2 != ((sF5 @ sK3))) | spl10_4),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f186])).
% 0.21/0.28 thf(f189,plain,(
% 0.21/0.28 (sK2 != sF7) | spl10_4),
% 0.21/0.28 inference(forward_demodulation,[],[f188,f106])).
% 0.21/0.28 thf(f190,plain,(
% 0.21/0.28 $false | (~spl10_3 | spl10_4)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f189,f55])).
% 0.21/0.28 thf(f191,plain,(
% 0.21/0.28 ~spl10_3 | spl10_4),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f190])).
% 0.21/0.28 cnf(s1, plain, spl10_1 | spl10_2, inference(sat_conversion,[],[f51])).
% 0.21/0.28 cnf(s2, plain, spl10_2 | spl10_3, inference(sat_conversion,[],[f56])).
% 0.21/0.28 cnf(s4, plain, spl10_5 | spl10_6, inference(sat_conversion,[],[f70])).
% 0.21/0.28 cnf(s6, plain, spl10_8 | spl10_9, inference(sat_conversion,[],[f84])).
% 0.21/0.28 cnf(s7, plain, ~spl10_2 | ~spl10_8, inference(sat_conversion,[],[f87])).
% 0.21/0.28 cnf(s9, plain, ~spl10_9, inference(sat_conversion,[],[f154])).
% 0.21/0.28 cnf(s10, plain, ~spl10_1 | ~spl10_5, inference(sat_conversion,[],[f157])).
% 0.21/0.28 cnf(s11, plain, ~spl10_4 | ~spl10_6, inference(sat_conversion,[],[f160])).
% 0.21/0.28 cnf(s13, plain, ~spl10_3 | spl10_4, inference(sat_conversion,[],[f191])).
% 0.21/0.28 cnf(s14, plain, spl10_8, inference(rat,[],[s6,s9])).
% 0.21/0.28 cnf(s15, plain, ~spl10_2, inference(rat,[],[s7,s14])).
% 0.21/0.28 cnf(s17, plain, spl10_3, inference(rat,[],[s2,s15])).
% 0.21/0.28 cnf(s18, plain, spl10_4, inference(rat,[],[s13,s17])).
% 0.21/0.28 cnf(s20, plain, ~spl10_6, inference(rat,[],[s11,s18])).
% 0.21/0.28 cnf(s21, plain, spl10_5, inference(rat,[],[s4,s20])).
% 0.21/0.28 cnf(s22, plain, ~spl10_1, inference(rat,[],[s10,s21])).
% 0.21/0.28 cnf(s23, plain, $false, inference(rat,[],[s1,s15,s22])).
% 0.21/0.28 thf(f192,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s23])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (1384131)------------------------------
% 0.21/0.28 % (1384131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1384131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1384131)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1384131)Termination reason: Refutation
% 0.21/0.28 % (1384131)Time elapsed: 0.004 s
% 0.21/0.28 % (1384131)Peak memory usage: 13 MB
% 0.21/0.28 % (1384131)Instructions burned: 9 (million)
% 0.21/0.28 % (1384113)Success in time 0.023 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------