%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO540^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:48:23 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO540^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n007.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 17:11:56 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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
% 0.21/0.26 % (3667318)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.26 % (3667326)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=460100144: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)
% 0.21/0.26 % (3667326) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3667318-3667326"...
% 0.21/0.26 % (3667326)...printing done.
% 0.21/0.26 % (3667323)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=903147402:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.26 % (3667324)lrs+10_16_si=on:nwc=1.5:random_seed=1199654425:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.26 % (3667326)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% 0.21/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.26 thf(func_def_0, type, eps: (($i > $o) > $i)).
% 0.21/0.26 thf(func_def_2, type, if: ($o > $i > $i > $i)).
% 0.21/0.26 thf(func_def_3, type, vOR: ($o > $o > $o)).
% 0.21/0.26 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.21/0.26 thf(func_def_5, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.26 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.26 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.26 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.21/0.26 thf(func_def_9, type, db3: !>[X0: $tType]:(X0)).
% 0.21/0.26 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.26 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.26 thf(func_def_15, type, sK1: $o).
% 0.21/0.26 thf(f1,axiom,(
% 0.21/0.26 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.21/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax)).
% 0.21/0.26 thf(f2,axiom,(
% 0.21/0.26 ((^[X0 : $o, X1 : $i, X2 : $i] : ((eps @ (^[X3 : $i] : (((X3 = X1) & X0) | (~X0 & (X3 = X2))))))) = if)),
% 0.21/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifd)).
% 0.21/0.26 thf(f3,conjecture,(
% 0.21/0.26 ! [X1 : $i,X0 : $o] : (((if @ X0 @ X1 @ X1)) = X1)),
% 0.21/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.21/0.26 thf(f4,negated_conjecture,(
% 0.21/0.26 ~ ! [X1 : $i,X0 : $o] : (((if @ X0 @ X1 @ X1)) = X1)),
% 0.21/0.26 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.26 thf(f5,plain,(
% 0.21/0.26 ((^[X0 : $o, X1 : $i, X2 : $i] : ((eps @ (^[X3 : $i] : (((X3 = X1) & X0) | (~X0 & (X3 = X2))))))) = if)),
% 0.21/0.26 inference(rectify,[],[f2])).
% 0.21/0.26 thf(f6,plain,(
% 0.21/0.26 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | (Y0 & (Y1 = Y3)))))))))))),
% 0.21/0.26 inference(fool_elimination,[],[f5])).
% 0.21/0.26 thf(f7,plain,(
% 0.21/0.26 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.21/0.26 inference(rectify,[],[f1])).
% 0.21/0.26 thf(f8,plain,(
% 0.21/0.26 ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) = $true) => (((X0 @ (eps @ X0))) = $true))),
% 0.21/0.26 inference(fool_elimination,[],[f7])).
% 0.21/0.26 thf(f9,plain,(
% 0.21/0.26 ! [X0 : ($i > $o)] : ((((X0 @ (eps @ X0))) = $true) | ! [X1 : $i] : (((X0 @ X1)) != $true))),
% 0.21/0.26 inference(ennf_transformation,[],[f8])).
% 0.21/0.26 thf(f10,plain,(
% 0.21/0.26 ? [X1 : $i,X0 : $o] : (((if @ X0 @ X1 @ X1)) != X1)),
% 0.21/0.26 inference(ennf_transformation,[],[f4])).
% 0.21/0.26 thf(f11,plain,(
% 0.21/0.26 ? [X0 : $i,X1 : $o] : (((if @ X1 @ X0 @ X0)) != X0)),
% 0.21/0.26 inference(rectify,[],[f10])).
% 0.21/0.26 thf(f12,plain,(
% 0.21/0.26 (sK0 != ((if @ sK1 @ sK0 @ sK0)))),
% 0.21/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11])).
% 0.21/0.26 thf(f13,plain,(
% 0.21/0.26 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | (Y0 & (Y1 = Y3)))))))))))),
% 0.21/0.26 inference(cnf_transformation,[],[f6])).
% 0.21/0.26 thf(f14,plain,(
% 0.21/0.26 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) != $true)) )),
% 0.21/0.26 inference(cnf_transformation,[],[f9])).
% 0.21/0.26 thf(f15,plain,(
% 0.21/0.26 (sK0 != ((if @ sK1 @ sK0 @ sK0)))),
% 0.21/0.26 inference(cnf_transformation,[],[f12])).
% 0.21/0.26 thf(f18,definition,(
% 0.21/0.26 spl2_1 <=> (sK0 = ((if @ sK1 @ sK0 @ sK0)))),
% 0.21/0.26 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.21/0.26 thf(f20,plain,(
% 0.21/0.26 (sK0 != ((if @ sK1 @ sK0 @ sK0))) | spl2_1),
% 0.21/0.26 inference(avatar_component_clause,[],[f18])).
% 0.21/0.26 thf(f21,plain,(
% 0.21/0.26 ~spl2_1),
% 0.21/0.26 inference(avatar_split_clause,[],[f15,f18])).
% 0.21/0.26 thf(f23,definition,(
% 0.21/0.26 spl2_2 <=> (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | (Y0 & (Y1 = Y3)))))))))))),
% 0.21/0.26 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.21/0.26 thf(f25,plain,(
% 0.21/0.26 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | (Y0 & (Y1 = Y3))))))))))) | ~spl2_2),
% 0.21/0.26 inference(avatar_component_clause,[],[f23])).
% 0.21/0.26 thf(f26,plain,(
% 0.21/0.26 spl2_2),
% 0.21/0.26 inference(avatar_split_clause,[],[f13,f23])).
% 0.21/0.26 thf(f36,plain,(
% 0.21/0.26 ( ! [X1 : $o] : (((((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | (Y0 & (Y1 = Y3)))))))))) @ X1)) = ((if @ X1)))) ) | ~spl2_2),
% 0.21/0.26 inference(argument_congruence,[],[f25])).
% 0.21/0.26 thf(f37,plain,(
% 0.21/0.26 ( ! [X1 : $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: (eps @ (^[Y2 : $i]: (((Y1 = Y2) & (~ X1)) | (X1 & (Y0 = Y2)))))))) = ((if @ X1)))) ) | ~spl2_2),
% 0.21/0.26 inference(beta-eta_normalization,[],[f36])).
% 0.21/0.26 thf(f55,plain,(
% 0.21/0.26 ( ! [X2 : $i,X1 : $o] : ((((if @ X1 @ X2)) = (((^[Y0 : $i]: ((^[Y1 : $i]: (eps @ (^[Y2 : $i]: (((Y1 = Y2) & (~ X1)) | (X1 & (Y0 = Y2)))))))) @ X2)))) ) | ~spl2_2),
% 0.21/0.26 inference(argument_congruence,[],[f37])).
% 0.21/0.26 thf(f56,plain,(
% 0.21/0.26 ( ! [X2 : $i,X1 : $o] : ((((if @ X1 @ X2)) = (^[Y0 : $i]: (eps @ (^[Y1 : $i]: (((Y0 = Y1) & (~ X1)) | (X1 & (X2 = Y1)))))))) ) | ~spl2_2),
% 0.21/0.26 inference(beta-eta_normalization,[],[f55])).
% 0.21/0.26 thf(f81,definition,(
% 0.21/0.26 spl2_3 <=> (sK0 = ((if @ $true @ sK0 @ sK0)))),
% 0.21/0.26 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.21/0.26 thf(f83,plain,(
% 0.21/0.26 (sK0 != ((if @ $true @ sK0 @ sK0))) | spl2_3),
% 0.21/0.26 inference(avatar_component_clause,[],[f81])).
% 0.21/0.26 thf(f90,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X1 : $o] : (((((^[Y0 : $i]: (eps @ (^[Y1 : $i]: (((Y0 = Y1) & (~ X1)) | (X1 & (X2 = Y1)))))) @ X3)) = ((if @ X1 @ X2 @ X3)))) ) | ~spl2_2),
% 0.21/0.26 inference(argument_congruence,[],[f56])).
% 0.21/0.26 thf(f91,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X1 : $o] : ((((if @ X1 @ X2 @ X3)) = ((eps @ (^[Y0 : $i]: (((X3 = Y0) & (~ X1)) | (X1 & (X2 = Y0)))))))) ) | ~spl2_2),
% 0.21/0.26 inference(beta-eta_normalization,[],[f90])).
% 0.21/0.26 thf(f93,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((((^[Y0 : $i]: (((X2 = Y0) & (~ X0)) | (X0 & (X1 = Y0)))) @ X3)) != $true) | ($true = (((^[Y0 : $i]: (((X2 = Y0) & (~ X0)) | (X0 & (X1 = Y0)))) @ (if @ X0 @ X1 @ X2))))) ) | ~spl2_2),
% 0.21/0.26 inference(superposition,[],[f14,f91])).
% 0.21/0.26 thf(f94,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((((X2 = X3) & (~ X0)) | (X0 & (X1 = X3)))) != $true) | (((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0)) | (X0 & (X1 = (if @ X0 @ X1 @ X2))))) = $true)) ) | ~spl2_2),
% 0.21/0.26 inference(beta-eta_normalization,[],[f93])).
% 0.21/0.26 thf(f95,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($false = ((X0 & (X1 = X3)))) | (((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0)) | (X0 & (X1 = (if @ X0 @ X1 @ X2))))) = $true)) ) | ~spl2_2),
% 0.21/0.26 inference(or_proxy_clausification,[],[f94])).
% 0.21/0.26 thf(f96,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0)) | (X0 & (X1 = (if @ X0 @ X1 @ X2))))) = $true) | ((((X2 = X3) & (~ X0))) = $false)) ) | ~spl2_2),
% 0.21/0.26 inference(or_proxy_clausification,[],[f94])).
% 0.21/0.26 thf(f97,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X0 & (X1 = (if @ X0 @ X1 @ X2)))) = $true) | ((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0))) = $true) | ((((X2 = X3) & (~ X0))) = $false)) ) | ~spl2_2),
% 0.21/0.26 inference(or_proxy_clausification,[],[f96])).
% 0.21/0.26 thf(f99,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((((X2 = X3) & (~ X0))) = $false) | ((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0))) = $true) | ($true = X0)) ) | ~spl2_2),
% 0.21/0.26 inference(and_proxy_clausification,[],[f97])).
% 0.21/0.26 thf(f100,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0))) = $true) | ($true = X0) | (((X2 = X3)) = $false) | (((~ X0)) = $false)) ) | ~spl2_2),
% 0.21/0.26 inference(and_proxy_clausification,[],[f99])).
% 0.21/0.26 thf(f102,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X2 = (if @ X0 @ X1 @ X2))) = $true) | (((X2 = X3)) = $false) | (((~ X0)) = $false) | ($true = X0)) ) | ~spl2_2),
% 0.21/0.26 inference(and_proxy_clausification,[],[f100])).
% 0.21/0.26 thf(f103,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((~ X0)) = $false) | ($true = X0) | (((if @ X0 @ X1 @ X2)) = X2) | (((X2 = X3)) = $false)) ) | ~spl2_2),
% 0.21/0.26 inference(equality_proxy_clausification,[],[f102])).
% 0.21/0.26 thf(f104,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = X0) | (((if @ X0 @ X1 @ X2)) = X2) | (((X2 = X3)) = $false) | ($true = X0)) ) | ~spl2_2),
% 0.21/0.26 inference(not_proxy_clausification,[],[f103])).
% 0.21/0.26 thf(f105,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((if @ X0 @ X1 @ X2)) = X2) | ($true = X0) | (X2 != X3) | ($true = X0)) ) | ~spl2_2),
% 0.21/0.26 inference(equality_proxy_clausification,[],[f104])).
% 0.21/0.26 thf(f106,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((if @ X0 @ X1 @ X2)) = X2) | ($true = X0) | (X2 != X3)) ) | ~spl2_2),
% 0.21/0.26 inference(duplicate_literal_removal,[],[f105])).
% 0.21/0.26 thf(f120,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X1 = X3)) = $false) | ($false = X0) | (((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0)) | (X0 & (X1 = (if @ X0 @ X1 @ X2))))) = $true)) ) | ~spl2_2),
% 0.21/0.26 inference(and_proxy_clausification,[],[f95])).
% 0.21/0.26 thf(f121,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0)) | (X0 & (X1 = (if @ X0 @ X1 @ X2))))) = $true) | ($false = X0) | (X1 != X3)) ) | ~spl2_2),
% 0.21/0.26 inference(equality_proxy_clausification,[],[f120])).
% 0.21/0.26 thf(f122,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X0 & (X1 = (if @ X0 @ X1 @ X2)))) = $true) | ((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0))) = $true) | ($false = X0) | (X1 != X3)) ) | ~spl2_2),
% 0.21/0.26 inference(or_proxy_clausification,[],[f121])).
% 0.21/0.26 thf(f123,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((((X2 = (if @ X0 @ X1 @ X2)) & (~ X0))) = $true) | ($false = X0) | (((X1 = (if @ X0 @ X1 @ X2))) = $true) | (X1 != X3)) ) | ~spl2_2),
% 0.21/0.26 inference(and_proxy_clausification,[],[f122])).
% 0.21/0.26 thf(f130,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X1 = (if @ X0 @ X1 @ X2))) = $true) | (((~ X0)) = $true) | ($false = X0) | (X1 != X3)) ) | ~spl2_2),
% 0.21/0.26 inference(and_proxy_clausification,[],[f123])).
% 0.21/0.26 thf(f134,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((X1 != X3) | ($false = X0) | (((if @ X0 @ X1 @ X2)) = X1) | (((~ X0)) = $true)) ) | ~spl2_2),
% 0.21/0.26 inference(equality_proxy_clausification,[],[f130])).
% 0.21/0.26 thf(f135,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($false = X0) | (X1 != X3) | (((if @ X0 @ X1 @ X2)) = X1) | ($false = X0)) ) | ~spl2_2),
% 0.21/0.26 inference(not_proxy_clausification,[],[f134])).
% 0.21/0.26 thf(f136,plain,(
% 0.21/0.26 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((if @ X0 @ X1 @ X2)) = X1) | ($false = X0) | (X1 != X3)) ) | ~spl2_2),
% 0.21/0.26 inference(duplicate_literal_removal,[],[f135])).
% 0.21/0.26 thf(f186,plain,(
% 0.21/0.26 ( ! [X0 : $i] : ((sK0 != sK0) | (sK0 != X0) | (sK1 = $true)) ) | (spl2_1 | ~spl2_2)),
% 0.21/0.26 inference(superposition,[],[f20,f106])).
% 0.21/0.26 thf(f187,plain,(
% 0.21/0.26 ( ! [X0 : $i] : ((sK1 = $true) | (sK0 != X0)) ) | (spl2_1 | ~spl2_2)),
% 0.21/0.26 inference(trivial_inequality_removal,[],[f186])).
% 0.21/0.26 thf(f189,definition,(
% 0.21/0.26 spl2_5 <=> ! [X0 : $i] : (sK0 != X0)),
% 0.21/0.26 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.21/0.26 thf(f190,plain,(
% 0.21/0.26 ( ! [X0 : $i] : ((sK0 != X0)) ) | ~spl2_5),
% 0.21/0.26 inference(avatar_component_clause,[],[f189])).
% 0.21/0.26 thf(f192,definition,(
% 0.21/0.26 spl2_6 <=> (sK1 = $true)),
% 0.21/0.26 introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition])).
% 0.21/0.26 thf(f195,plain,(
% 0.21/0.26 spl2_5 | spl2_6 | spl2_1 | ~spl2_2),
% 0.21/0.26 inference(avatar_split_clause,[],[f187,f23,f18,f192,f189])).
% 0.21/0.26 thf(f201,plain,(
% 0.21/0.26 ( ! [X0 : $i] : (($true = $false) | (sK0 != sK0) | (sK0 != X0)) ) | (~spl2_2 | spl2_3)),
% 0.21/0.26 inference(superposition,[],[f83,f136])).
% 0.21/0.26 thf(f202,plain,(
% 0.21/0.26 ( ! [X0 : $i] : ((sK0 != X0)) ) | (~spl2_2 | spl2_3)),
% 0.21/0.26 inference(trivial_inequality_removal,[],[f201])).
% 0.21/0.26 thf(f203,plain,(
% 0.21/0.26 spl2_5 | ~spl2_2 | spl2_3),
% 0.21/0.26 inference(avatar_split_clause,[],[f202,f81,f23,f189])).
% 0.21/0.26 thf(f205,plain,(
% 0.21/0.26 $false | ~spl2_5),
% 0.21/0.26 inference(equality_resolution,[],[f190])).
% 0.21/0.26 thf(f208,plain,(
% 0.21/0.26 ~spl2_5),
% 0.21/0.26 inference(avatar_contradiction_clause,[],[f205])).
% 0.21/0.26 thf(f209,definition,(
% 0.21/0.26 (sK1 != $true) | (sK0 != ((if @ $true @ sK0 @ sK0))) | (sK0 = ((if @ sK1 @ sK0 @ sK0)))),
% 0.21/0.26 introduced(theory,[theory_tautology_sat_conflict])).
% 0.21/0.26 cnf(s1, plain, ~spl2_1, inference(sat_conversion,[],[f21])).
% 0.21/0.26 cnf(s2, plain, spl2_2, inference(sat_conversion,[],[f26])).
% 0.21/0.26 cnf(s5, plain, spl2_1 | ~spl2_2 | spl2_5 | spl2_6, inference(sat_conversion,[],[f195])).
% 0.21/0.26 cnf(s7, plain, ~spl2_2 | spl2_3 | spl2_5, inference(sat_conversion,[],[f203])).
% 0.21/0.26 cnf(s9, plain, ~spl2_5, inference(sat_conversion,[],[f208])).
% 0.21/0.26 cnf(s10, plain, spl2_1 | ~spl2_3 | ~spl2_6, inference(sat_conversion,[],[f209])).
% 0.21/0.26 cnf(s11, plain, ~spl2_2 | spl2_3, inference(rat,[],[s7,s9])).
% 0.21/0.26 cnf(s13, plain, spl2_1 | ~spl2_2 | spl2_6, inference(rat,[],[s5,s9])).
% 0.21/0.26 cnf(s14, plain, spl2_3, inference(rat,[],[s11,s2])).
% 0.21/0.26 cnf(s15, plain, ~spl2_6, inference(rat,[],[s10,s14,s1])).
% 0.21/0.26 cnf(s17, plain, $false, inference(rat,[],[s13,s2,s15,s1])).
% 0.21/0.26 thf(f210,plain,(
% 0.21/0.26 $false),
% 0.21/0.26 inference(avatar_sat_refutation,[],[s17])).
% 0.21/0.26 % SZS output end Proof for theBenchmark
% 0.21/0.26 % (3667326)------------------------------
% 0.21/0.26 % (3667326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (3667326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (3667326)CaDiCaL version: 2.1.3
% 0.21/0.26 % (3667326)Termination reason: Refutation
% 0.21/0.26 % (3667326)Time elapsed: 0.004 s
% 0.21/0.26 % (3667326)Peak memory usage: 13 MB
% 0.21/0.26 % (3667326)Instructions burned: 9 (million)
% 0.21/0.26 % (3667318)Success in time 0.03 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------