%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CSR144^1 : 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 : 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 07:47:09 AM UTC 2026
% Result : Theorem 0.24s 0.35s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR144^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n015.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 18:00:19 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.31 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
% 0.24/0.35 % (3891947)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.35 % (3891958)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.35 % (3891958)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
% 0.24/0.35 % (3891958)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=1306818334:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.35 % (3891955)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=3187312164: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)
% 0.24/0.35 % (3891958) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3891947-3891958"...
% 0.24/0.35 % (3891952)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=492539732:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.35 % (3891954)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3467881353:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.35 % (3891953)lrs+10_16_si=on:nwc=1.5:random_seed=550494877:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.35 % (3891958)...printing done.
% 0.24/0.35 % (3891958)Refutation found. Thanks to Tanya!
% 0.24/0.35 % SZS status Theorem for theBenchmark
% 0.24/0.35 % SZS output start Proof for theBenchmark
% 0.24/0.35 thf(type_def_5, type, num: $tType).
% 0.24/0.35 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.35 thf(func_def_0, type, believes_THFTYPE_IiooI: ($i > $o > $o)).
% 0.24/0.35 thf(func_def_1, type, considers_THFTYPE_IiooI: ($i > $o > $o)).
% 0.24/0.35 thf(func_def_2, type, holdsDuring_THFTYPE_IiooI: ($i > $o > $o)).
% 0.24/0.35 thf(func_def_3, type, husband_THFTYPE_IiioI: ($i > $i > $o)).
% 0.24/0.35 thf(func_def_5, type, wife_THFTYPE_IiioI: ($i > $i > $o)).
% 0.24/0.35 thf(func_def_6, type, inverse_THFTYPE_IIiioIIiioIoI: (($i > $i > $o) > ($i > $i > $o) > $o)).
% 0.24/0.35 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.24/0.35 thf(func_def_11, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.24/0.35 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.35 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.35 thf(func_def_14, type, sK0: ($o > $i > $i)).
% 0.24/0.35 thf(func_def_15, type, sF1: ($i > $o)).
% 0.24/0.35 thf(func_def_16, type, sF2: ($i > $o)).
% 0.24/0.35 thf(func_def_17, type, sF3: ($i > $o)).
% 0.24/0.35 thf(f1,axiom,(
% 0.24/0.35 (inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)),
% 0.24/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax)).
% 0.24/0.35 thf(f2,axiom,(
% 0.24/0.35 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0) => ! [X2 : $i,X3 : $i] : ((X1 @ X2 @ X3) <=> (X0 @ X3 @ X2)))),
% 0.24/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_001)).
% 0.24/0.35 thf(f3,axiom,(
% 0.24/0.35 ! [X0 : $o,X1 : $i] : ((believes_THFTYPE_IiooI @ X1 @ X0) => ? [X2 : $i] : (holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0)))),
% 0.24/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_002)).
% 0.24/0.35 thf(f4,axiom,(
% 0.24/0.35 ! [X0 : $i] : (~ ? [X1 : $i] : (holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))),
% 0.24/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_003)).
% 0.24/0.35 thf(f5,conjecture,(
% 0.24/0.35 ? [X0 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))),
% 0.24/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.24/0.35 thf(f6,negated_conjecture,(
% 0.24/0.35 ~ ? [X0 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))),
% 0.24/0.35 inference(negated_conjecture,[status(cth)],[f5])).
% 0.24/0.35 thf(f7,plain,(
% 0.24/0.35 (inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)),
% 0.24/0.35 inference(rectify,[],[f1])).
% 0.24/0.35 thf(f8,plain,(
% 0.24/0.35 (((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)) = $true)),
% 0.24/0.35 inference(fool_elimination,[],[f7])).
% 0.24/0.35 thf(f9,plain,(
% 0.24/0.35 ! [X0 : $i] : (~ ? [X1 : $i] : (holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))),
% 0.24/0.35 inference(rectify,[],[f4])).
% 0.24/0.35 thf(f10,plain,(
% 0.24/0.35 ! [X0 : $i] : (((~ (?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))))) = $true)),
% 0.24/0.35 inference(fool_elimination,[],[f9])).
% 0.24/0.35 thf(f11,plain,(
% 0.24/0.35 ! [X0 : $o,X1 : $i] : ((believes_THFTYPE_IiooI @ X1 @ X0) => ? [X2 : $i] : (holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0)))),
% 0.24/0.35 inference(rectify,[],[f3])).
% 0.24/0.35 thf(f12,plain,(
% 0.24/0.35 ! [X1 : $i,X0 : $o] : ((((believes_THFTYPE_IiooI @ X1 @ X0)) = $true) => ? [X2 : $i] : (((holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0))) = $true))),
% 0.24/0.35 inference(fool_elimination,[],[f11])).
% 0.24/0.35 thf(f13,plain,(
% 0.24/0.35 ~ ? [X0 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))),
% 0.24/0.35 inference(rectify,[],[f6])).
% 0.24/0.35 thf(f14,plain,(
% 0.24/0.35 ~ ? [X0 : $i] : (((~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))) = $true)),
% 0.24/0.35 inference(fool_elimination,[],[f13])).
% 0.24/0.35 thf(f15,plain,(
% 0.24/0.35 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0) => ! [X2 : $i,X3 : $i] : ((X1 @ X2 @ X3) <=> (X0 @ X3 @ X2)))),
% 0.24/0.35 inference(rectify,[],[f2])).
% 0.24/0.35 thf(f16,plain,(
% 0.24/0.35 ! [X1 : ($i > $i > $o),X0 : ($i > $i > $o)] : ((((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) = $true) => ! [X2 : $i,X3 : $i] : (((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))))),
% 0.24/0.35 inference(fool_elimination,[],[f15])).
% 0.24/0.35 thf(f17,plain,(
% 0.24/0.35 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (! [X2 : $i,X3 : $i] : (((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))) | (((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) != $true))),
% 0.24/0.35 inference(ennf_transformation,[],[f16])).
% 0.24/0.35 thf(f18,plain,(
% 0.24/0.35 ! [X0 : $i] : (((~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))) != $true)),
% 0.24/0.35 inference(ennf_transformation,[],[f14])).
% 0.24/0.35 thf(f19,plain,(
% 0.24/0.35 ! [X1 : $i,X0 : $o] : ((((believes_THFTYPE_IiooI @ X1 @ X0)) != $true) | ? [X2 : $i] : (((holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0))) = $true))),
% 0.24/0.35 inference(ennf_transformation,[],[f12])).
% 0.24/0.35 thf(f20,plain,(
% 0.24/0.35 ! [X0 : $i,X1 : $o] : ((((believes_THFTYPE_IiooI @ X0 @ X1)) != $true) | ? [X2 : $i] : (((holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X0 @ X1))) = $true))),
% 0.24/0.35 inference(rectify,[],[f19])).
% 0.24/0.35 thf(f21,plain,(
% 0.24/0.35 ! [X0 : $i,X1 : $o] : ((((believes_THFTYPE_IiooI @ X0 @ X1)) != $true) | (((holdsDuring_THFTYPE_IiooI @ (sK0 @ X1 @ X0) @ (considers_THFTYPE_IiooI @ X0 @ X1))) = $true))),
% 0.24/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f20])).
% 0.24/0.35 thf(f22,plain,(
% 0.24/0.35 ( ! [X0 : $i,X1 : $o] : ((((holdsDuring_THFTYPE_IiooI @ (sK0 @ X1 @ X0) @ (considers_THFTYPE_IiooI @ X0 @ X1))) = $true) | (((believes_THFTYPE_IiooI @ X0 @ X1)) != $true)) )),
% 0.24/0.35 inference(cnf_transformation,[],[f21])).
% 0.24/0.35 thf(f23,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))) != $true)) )),
% 0.24/0.35 inference(cnf_transformation,[],[f18])).
% 0.24/0.35 thf(f24,plain,(
% 0.24/0.35 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))) | (((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) != $true)) )),
% 0.24/0.35 inference(cnf_transformation,[],[f17])).
% 0.24/0.35 thf(f25,plain,(
% 0.24/0.35 (((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)) = $true)),
% 0.24/0.35 inference(cnf_transformation,[],[f8])).
% 0.24/0.35 thf(f26,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((~ (?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))))) = $true)) )),
% 0.24/0.35 inference(cnf_transformation,[],[f10])).
% 0.24/0.35 thf(f28,definition,(
% 0.24/0.35 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.24/0.35 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.24/0.35 thf(f29,definition,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF1 @ X0)) = ((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))) )),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 0.24/0.35 thf(f30,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = ((sF1 @ X0)))) )),
% 0.24/0.35 inference(reorient_equations,[],[f29])).
% 0.24/0.35 thf(f31,definition,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF2 @ X0)) = ((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (sF1 @ X0))))) )),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.24/0.35 thf(f32,definition,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF3 @ X0)) = ((~ (sF2 @ X0))))) )),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.24/0.35 thf(f33,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF3 @ X0)) != $true)) )),
% 0.24/0.35 inference(definition_folding,[],[f23,f32,f31,f30])).
% 0.24/0.35 thf(f34,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF3 @ X0)) = $true) | ($false = ((~ (sF2 @ X0))))) )),
% 0.24/0.35 inference(iff_proxy_clausification,[],[f32])).
% 0.24/0.35 thf(f37,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF3 @ X0)) = $true) | (((sF2 @ X0)) = $true)) )),
% 0.24/0.35 inference(not_proxy_clausification,[],[f34])).
% 0.24/0.35 thf(f39,plain,(
% 0.24/0.35 ( ! [X0 : $i] : (($false = ((sF2 @ X0))) | (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (sF1 @ X0))) = $true)) )),
% 0.24/0.35 inference(iff_proxy_clausification,[],[f31])).
% 0.24/0.35 thf(f40,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $true) | ($false = ((sF1 @ X0)))) )),
% 0.24/0.35 inference(iff_proxy_clausification,[],[f30])).
% 0.24/0.35 thf(f41,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $false) | (((sF1 @ X0)) = $true)) )),
% 0.24/0.35 inference(iff_proxy_clausification,[],[f30])).
% 0.24/0.35 thf(f42,plain,(
% 0.24/0.35 ( ! [X0 : $i] : (($false = ((?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))))))) )),
% 0.24/0.35 inference(not_proxy_clausification,[],[f26])).
% 0.24/0.35 thf(f43,plain,(
% 0.24/0.35 ( ! [X0 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))) @ X1)))) )),
% 0.24/0.35 inference(pi_proxy_clausification,[],[f42])).
% 0.24/0.35 thf(f44,plain,(
% 0.24/0.35 ( ! [X0 : $i,X1 : $i] : ((((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))) = $false)) )),
% 0.24/0.35 inference(beta-eta_normalization,[],[f43])).
% 0.24/0.35 thf(f45,plain,(
% 0.24/0.35 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) != $true) | (((X1 @ X2 @ X3)) = $true) | (((X0 @ X3 @ X2)) = $false)) )),
% 0.24/0.35 inference(iff_proxy_clausification,[],[f24])).
% 0.24/0.35 thf(f46,plain,(
% 0.24/0.35 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) != $true) | (((X1 @ X2 @ X3)) = $false) | (((X0 @ X3 @ X2)) = $true)) )),
% 0.24/0.35 inference(iff_proxy_clausification,[],[f24])).
% 0.24/0.35 thf(f59,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF2 @ X0)) = $true)) )),
% 0.24/0.35 inference(forward_subsumption_resolution,[],[f37,f33])).
% 0.24/0.35 thf(f66,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (sF1 @ X0))) = $true) | ($false = $true)) )),
% 0.24/0.35 inference(forward_demodulation,[],[f39,f59])).
% 0.24/0.35 thf(f67,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (sF1 @ X0))) = $true)) )),
% 0.24/0.35 inference(trivial_inequality_removal,[],[f66])).
% 0.24/0.35 thf(f68,plain,(
% 0.24/0.35 ( ! [X0 : $i] : (($false = ((sF1 @ X0))) | (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) = $true)) )),
% 0.24/0.35 inference(constrained_superposition,[],[f67,f28])).
% 0.24/0.35 thf(f70,definition,(
% 0.24/0.35 spl4_1 <=> (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) = $true)),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.24/0.35 thf(f74,definition,(
% 0.24/0.35 spl4_2 <=> ! [X0 : $i] : ($false = ((sF1 @ X0)))),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.24/0.35 thf(f75,plain,(
% 0.24/0.35 ( ! [X0 : $i] : (($false = ((sF1 @ X0)))) ) | ~spl4_2),
% 0.24/0.35 inference(avatar_component_clause,[],[f74])).
% 0.24/0.35 thf(f76,plain,(
% 0.24/0.35 spl4_1 | spl4_2),
% 0.24/0.35 inference(avatar_split_clause,[],[f68,f74,f70])).
% 0.24/0.35 thf(f85,definition,(
% 0.24/0.35 spl4_3 <=> ! [X1 : $i] : ($false = ((wife_THFTYPE_IiioI @ X1 @ lMax_THFTYPE_i)))),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.24/0.35 thf(f86,plain,(
% 0.24/0.35 ( ! [X1 : $i] : (($false = ((wife_THFTYPE_IiioI @ X1 @ lMax_THFTYPE_i)))) ) | ~spl4_3),
% 0.24/0.35 inference(avatar_component_clause,[],[f85])).
% 0.24/0.35 thf(f107,plain,(
% 0.24/0.35 ( ! [X0 : $i] : (($false = $true) | (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))) != $true)) )),
% 0.24/0.35 inference(constrained_superposition,[],[f22,f44])).
% 0.24/0.35 thf(f111,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))) != $true)) )),
% 0.24/0.35 inference(trivial_inequality_removal,[],[f107])).
% 0.24/0.35 thf(f149,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) != $true) | (((wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)) = $false)) )),
% 0.24/0.35 inference(constrained_superposition,[],[f111,f28])).
% 0.24/0.35 thf(f184,plain,(
% 0.24/0.35 ~spl4_1 | spl4_3),
% 0.24/0.35 inference(avatar_split_clause,[],[f149,f85,f70])).
% 0.24/0.35 thf(f214,plain,(
% 0.24/0.35 ( ! [X0 : $i,X1 : $i] : ((((husband_THFTYPE_IiioI @ X0 @ X1)) = $true) | ($true != $true) | ($false = ((wife_THFTYPE_IiioI @ X1 @ X0)))) )),
% 0.24/0.35 inference(constrained_superposition,[],[f45,f25])).
% 0.24/0.35 thf(f216,plain,(
% 0.24/0.35 ( ! [X0 : $i,X1 : $i] : (($false = ((wife_THFTYPE_IiioI @ X1 @ X0))) | (((husband_THFTYPE_IiioI @ X0 @ X1)) = $true)) )),
% 0.24/0.35 inference(trivial_inequality_removal,[],[f214])).
% 0.24/0.35 thf(f220,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) != $true) | (((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $true)) )),
% 0.24/0.35 inference(constrained_superposition,[],[f111,f216])).
% 0.24/0.35 thf(f223,plain,(
% 0.24/0.35 ( ! [X0 : $i,X1 : $i] : (($false = ((husband_THFTYPE_IiioI @ X0 @ X1))) | (((wife_THFTYPE_IiioI @ X1 @ X0)) = $true) | ($true != $true)) )),
% 0.24/0.35 inference(constrained_superposition,[],[f46,f25])).
% 0.24/0.35 thf(f226,plain,(
% 0.24/0.35 ( ! [X0 : $i,X1 : $i] : (($false = ((husband_THFTYPE_IiioI @ X0 @ X1))) | (((wife_THFTYPE_IiioI @ X1 @ X0)) = $true)) )),
% 0.24/0.35 inference(trivial_inequality_removal,[],[f223])).
% 0.24/0.35 thf(f227,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)) = $true) | ($false = ((sF1 @ X0))) | ($false = $true)) )),
% 0.24/0.35 inference(constrained_superposition,[],[f226,f40])).
% 0.24/0.35 thf(f230,plain,(
% 0.24/0.35 ( ! [X0 : $i] : (($false = ((sF1 @ X0))) | (((wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)) = $true)) )),
% 0.24/0.35 inference(trivial_inequality_removal,[],[f227])).
% 0.24/0.35 thf(f233,plain,(
% 0.24/0.35 ( ! [X0 : $i] : (($false = $true) | ($false = ((sF1 @ X0)))) ) | ~spl4_3),
% 0.24/0.35 inference(forward_demodulation,[],[f230,f86])).
% 0.24/0.35 thf(f234,plain,(
% 0.24/0.35 ( ! [X0 : $i] : (($false = ((sF1 @ X0)))) ) | ~spl4_3),
% 0.24/0.35 inference(trivial_inequality_removal,[],[f233])).
% 0.24/0.35 thf(f237,plain,(
% 0.24/0.35 spl4_2 | ~spl4_3),
% 0.24/0.35 inference(avatar_split_clause,[],[f234,f85,f74])).
% 0.24/0.35 thf(f239,definition,(
% 0.24/0.35 spl4_10 <=> ! [X0 : $i] : (((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $true)),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition])).
% 0.24/0.35 thf(f240,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $true)) ) | ~spl4_10),
% 0.24/0.35 inference(avatar_component_clause,[],[f239])).
% 0.24/0.35 thf(f242,definition,(
% 0.24/0.35 spl4_11 <=> (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) = $true)),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition])).
% 0.24/0.35 thf(f245,plain,(
% 0.24/0.35 spl4_10 | ~spl4_11),
% 0.24/0.35 inference(avatar_split_clause,[],[f220,f242,f239])).
% 0.24/0.35 thf(f256,plain,(
% 0.24/0.35 (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) = $true) | ~spl4_2),
% 0.24/0.35 inference(constrained_superposition,[],[f67,f75])).
% 0.24/0.35 thf(f258,plain,(
% 0.24/0.35 spl4_11 | ~spl4_2),
% 0.24/0.35 inference(avatar_split_clause,[],[f256,f74,f242])).
% 0.24/0.35 thf(f289,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF1 @ X0)) = $true) | ($false = $true)) ) | ~spl4_10),
% 0.24/0.35 inference(constrained_superposition,[],[f41,f240])).
% 0.24/0.35 thf(f292,plain,(
% 0.24/0.35 ( ! [X0 : $i] : ((((sF1 @ X0)) = $true)) ) | ~spl4_10),
% 0.24/0.35 inference(trivial_inequality_removal,[],[f289])).
% 0.24/0.35 thf(f298,plain,(
% 0.24/0.35 ($false = $true) | (~spl4_2 | ~spl4_10)),
% 0.24/0.35 inference(forward_demodulation,[],[f292,f75])).
% 0.24/0.35 thf(f299,plain,(
% 0.24/0.35 $false | (~spl4_2 | ~spl4_10)),
% 0.24/0.35 inference(trivial_inequality_removal,[],[f298])).
% 0.24/0.35 thf(f300,plain,(
% 0.24/0.35 ~spl4_2 | ~spl4_10),
% 0.24/0.35 inference(avatar_contradiction_clause,[],[f299])).
% 0.24/0.35 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f76])).
% 0.24/0.35 cnf(s12, plain, ~spl4_1 | spl4_3, inference(sat_conversion,[],[f184])).
% 0.24/0.35 cnf(s16, plain, spl4_2 | ~spl4_3, inference(sat_conversion,[],[f237])).
% 0.24/0.35 cnf(s18, plain, spl4_10 | ~spl4_11, inference(sat_conversion,[],[f245])).
% 0.24/0.35 cnf(s21, plain, ~spl4_2 | spl4_11, inference(sat_conversion,[],[f258])).
% 0.24/0.35 cnf(s24, plain, ~spl4_2 | ~spl4_10, inference(sat_conversion,[],[f300])).
% 0.24/0.35 cnf(s25, plain, ~spl4_2, inference(rat,[],[s18,s21,s24])).
% 0.24/0.35 cnf(s26, plain, ~spl4_3, inference(rat,[],[s16,s25])).
% 0.24/0.35 cnf(s27, plain, spl4_1, inference(rat,[],[s1,s25])).
% 0.24/0.35 cnf(s30, plain, $false, inference(rat,[],[s12,s26,s27])).
% 0.24/0.35 thf(f301,plain,(
% 0.24/0.35 $false),
% 0.24/0.35 inference(avatar_sat_refutation,[],[s30])).
% 0.24/0.35 % SZS output end Proof for theBenchmark
% 0.24/0.35 % (3891958)------------------------------
% 0.24/0.35 % (3891958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.35 % (3891958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.35 % (3891958)CaDiCaL version: 2.1.3
% 0.24/0.35 % (3891958)Termination reason: Refutation
% 0.24/0.35 % (3891958)Time elapsed: 0.010 s
% 0.24/0.35 % (3891958)Peak memory usage: 13 MB
% 0.24/0.35 % (3891958)Instructions burned: 18 (million)
% 0.24/0.35 % (3891947)Success in time 0.036 s
% 0.24/0.35 % Vampire exiting
%------------------------------------------------------------------------------