%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : CSR146^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 07:47:21 AM UTC 2026
% Result : Theorem 0.21s 0.34s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR146^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n015.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 18:00:04 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.34 % (3890049)Will run a generic schedule for satisfiability detection.
% 0.21/0.34 % (3890061)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1546620599:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.21/0.34 % (3890061)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.34 % (3890058)% WARNING: option uhcvi not known.
% 0.21/0.34 % (3890058)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=723925256:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.21/0.34 % (3890058)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.34 % (3890058)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.34 % (3890062)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2488144987:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.21/0.34 % (3890060)dis+10_1_sil=32000:sp=arity:random_seed=3976222183:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.21/0.34 % (3890059)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=681422007:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.21/0.34 % (3890063)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4289797558:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.21/0.34 % (3890057)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=868966676_3000 on theBenchmark for (3000ds/0Mi)
% 0.21/0.34 % Exception at run slice level
% 0.21/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.34 % (3890061)Instruction limit reached!
% 0.21/0.34 % (3890061)------------------------------
% 0.21/0.34 % (3890061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3890061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3890061)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3890061)Termination reason: Instruction limit
% 0.21/0.34 % (3890061)Termination phase: Saturation
% 0.21/0.34 % (3890061)Time elapsed: 0.051 s
% 0.21/0.34 % (3890061)Peak memory usage: 12 MB
% 0.21/0.34 % (3890061)Instructions burned: 117 (million)
% 0.21/0.34 % (3890091)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=698452211:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.34 % Exception at run slice level
% 0.21/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.34 % (3890105)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=966958853:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.34 % (3890062) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3890049-3890062"...
% 0.21/0.34 % (3890062)...printing done.
% 0.21/0.34 % (3890062)Refutation found. Thanks to Tanya!
% 0.21/0.34 % SZS status Theorem for theBenchmark
% 0.21/0.34 % SZS output start Proof for theBenchmark
% 0.21/0.34 thf(type_def_5, type, num: $tType).
% 0.21/0.34 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.34 thf(func_def_0, type, holdsDuring_THFTYPE_IiooI: ($i > $o > $o)).
% 0.21/0.34 thf(func_def_3, type, lYearFn_THFTYPE_IiiI: ($i > $i)).
% 0.21/0.34 thf(func_def_5, type, wife_THFTYPE_IiioI: ($i > $i > $o)).
% 0.21/0.34 thf(func_def_6, type, husband_THFTYPE_IiioI: ($i > $i > $o)).
% 0.21/0.34 thf(func_def_7, type, inverse_THFTYPE_IIiioIIiioIoI: (($i > $i > $o) > ($i > $i > $o) > $o)).
% 0.21/0.34 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.21/0.34 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.34 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.34 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.34 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.34 thf(func_def_17, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.34 thf(func_def_19, type, db3: !>[X0: $tType]:(X0)).
% 0.21/0.34 thf(func_def_20, type, db4: !>[X0: $tType]:(X0)).
% 0.21/0.34 thf(func_def_22, type, sK3: (($i > $i > $i > $i > $i) > $i)).
% 0.21/0.34 thf(f1,axiom,(
% 0.21/0.34 (inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)),
% 0.21/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)).
% 0.21/0.34 thf(f2,axiom,(
% 0.21/0.34 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0) => ! [X2 : $i,X3 : $i] : ((X1 @ X2 @ X3) <=> (X0 @ X3 @ X2)))),
% 0.21/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)).
% 0.21/0.34 thf(f3,axiom,(
% 0.21/0.34 ! [X0 : $i] : (holdsDuring_THFTYPE_IiooI @ X0 @ $true)),
% 0.21/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 0.21/0.34 thf(f4,axiom,(
% 0.21/0.34 ? [X0 : $i] : (~ (husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X0))),
% 0.21/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4)).
% 0.21/0.34 thf(f5,axiom,(
% 0.21/0.34 (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i))),
% 0.21/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5)).
% 0.21/0.34 thf(f6,conjecture,(
% 0.21/0.34 ? [X0 : ($i > $i > $o)] : ((~ (X0 = (^[X1 : $i, X2 : $i] : ($true)))) & (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i)))),
% 0.21/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.21/0.34 thf(f7,negated_conjecture,(
% 0.21/0.34 ~ ? [X0 : ($i > $i > $o)] : ((~ (X0 = (^[X1 : $i, X2 : $i] : ($true)))) & (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i)))),
% 0.21/0.34 inference(negated_conjecture,[status(cth)],[f6])).
% 0.21/0.34 thf(f8,plain,(
% 0.21/0.34 (inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)),
% 0.21/0.34 inference(rectify,[],[f1])).
% 0.21/0.34 thf(f9,plain,(
% 0.21/0.34 (((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)) = $true)),
% 0.21/0.34 inference(fool_elimination,[],[f8])).
% 0.21/0.34 thf(f10,plain,(
% 0.21/0.34 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0) => ! [X2 : $i,X3 : $i] : ((X1 @ X2 @ X3) <=> (X0 @ X3 @ X2)))),
% 0.21/0.34 inference(rectify,[],[f2])).
% 0.21/0.34 thf(f11,plain,(
% 0.21/0.34 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) = $true) => ! [X2 : $i,X3 : $i] : (((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))))),
% 0.21/0.34 inference(fool_elimination,[],[f10])).
% 0.21/0.34 thf(f12,plain,(
% 0.21/0.34 ! [X0 : $i] : (holdsDuring_THFTYPE_IiooI @ X0 @ $true)),
% 0.21/0.34 inference(rectify,[],[f3])).
% 0.21/0.34 thf(f13,plain,(
% 0.21/0.34 ! [X0 : $i] : ($true = ((holdsDuring_THFTYPE_IiooI @ X0 @ $true)))),
% 0.21/0.34 inference(fool_elimination,[],[f12])).
% 0.21/0.34 thf(f14,plain,(
% 0.21/0.34 ? [X0 : $i] : (~ (husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X0))),
% 0.21/0.34 inference(rectify,[],[f4])).
% 0.21/0.34 thf(f15,plain,(
% 0.21/0.34 ? [X0 : $i] : (((~ (husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X0))) = $true)),
% 0.21/0.34 inference(fool_elimination,[],[f14])).
% 0.21/0.34 thf(f16,plain,(
% 0.21/0.34 (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i))),
% 0.21/0.34 inference(rectify,[],[f5])).
% 0.21/0.34 thf(f17,plain,(
% 0.21/0.34 (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i))) = $true)),
% 0.21/0.34 inference(fool_elimination,[],[f16])).
% 0.21/0.34 thf(f18,plain,(
% 0.21/0.34 ~ ? [X0 : ($i > $i > $o)] : ((~ (X0 = (^[X1 : $i, X2 : $i] : ($true)))) & (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i)))),
% 0.21/0.34 inference(rectify,[],[f7])).
% 0.21/0.34 thf(f19,plain,(
% 0.21/0.34 ~ ? [X0 : ($i > $i > $o)] : (($true = ((~ (X0 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))))) & (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i))) = $true))),
% 0.21/0.34 inference(fool_elimination,[],[f18])).
% 0.21/0.34 thf(f20,plain,(
% 0.21/0.34 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (! [X2 : $i,X3 : $i] : (((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))) | (((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) != $true))),
% 0.21/0.34 inference(ennf_transformation,[],[f11])).
% 0.21/0.34 thf(f21,plain,(
% 0.21/0.34 ! [X0 : ($i > $i > $o)] : (($true != ((~ (X0 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))))) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i))) != $true))),
% 0.21/0.34 inference(ennf_transformation,[],[f19])).
% 0.21/0.34 thf(f22,plain,(
% 0.21/0.34 ($true = ((~ (husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ sK0))))),
% 0.21/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15])).
% 0.21/0.34 thf(f23,plain,(
% 0.21/0.34 (((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)) = $true)),
% 0.21/0.34 inference(cnf_transformation,[],[f9])).
% 0.21/0.34 thf(f24,plain,(
% 0.21/0.34 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))) | (((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) != $true)) )),
% 0.21/0.34 inference(cnf_transformation,[],[f20])).
% 0.21/0.34 thf(f25,plain,(
% 0.21/0.34 ( ! [X0 : $i] : (($true = ((holdsDuring_THFTYPE_IiooI @ X0 @ $true)))) )),
% 0.21/0.34 inference(cnf_transformation,[],[f13])).
% 0.21/0.34 thf(f26,plain,(
% 0.21/0.34 ($true = ((~ (husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ sK0))))),
% 0.21/0.34 inference(cnf_transformation,[],[f22])).
% 0.21/0.34 thf(f27,plain,(
% 0.21/0.34 (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i))) = $true)),
% 0.21/0.34 inference(cnf_transformation,[],[f17])).
% 0.21/0.34 thf(f28,plain,(
% 0.21/0.34 ( ! [X0 : ($i > $i > $o)] : (($true != ((~ (X0 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))))) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i))) != $true)) )),
% 0.21/0.34 inference(cnf_transformation,[],[f21])).
% 0.21/0.34 thf(f30,definition,(
% 0.21/0.34 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.34 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.34 thf(f31,plain,(
% 0.21/0.34 ( ! [X0 : ($i > $i > $o)] : (($true = ((X0 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))))) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i))) != $true)) )),
% 0.21/0.34 inference(not_proxy_clausification,[],[f28])).
% 0.21/0.34 thf(f32,plain,(
% 0.21/0.34 ( ! [X0 : ($i > $i > $o)] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i))) != $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X0)) )),
% 0.21/0.34 inference(equality_proxy_clausification,[],[f31])).
% 0.21/0.34 thf(f33,plain,(
% 0.21/0.34 (((husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ sK0)) = $false)),
% 0.21/0.34 inference(not_proxy_clausification,[],[f26])).
% 0.21/0.34 thf(f34,plain,(
% 0.21/0.34 ( ! [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)) = $false)) )),
% 0.21/0.34 inference(iff_proxy_clausification,[],[f24])).
% 0.21/0.34 thf(f38,plain,(
% 0.21/0.34 ( ! [X0 : ($i > $i > $o)] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X0) | (((X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i)) = $false)) )),
% 0.21/0.34 inference(constrained_superposition,[],[f32,f30])).
% 0.21/0.34 thf(f46,plain,(
% 0.21/0.34 ( ! [X0 : ($i > $i > $o)] : ((((X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i)) = $false) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X0)) )),
% 0.21/0.34 inference(forward_subsumption_resolution,[],[f38,f25])).
% 0.21/0.34 thf(f54,plain,(
% 0.21/0.34 ($false = (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ lChris_THFTYPE_i @ lCorina_THFTYPE_i))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))))),
% 0.21/0.34 inference(primitive_instantiation,[],[f46])).
% 0.21/0.34 thf(f55,plain,(
% 0.21/0.34 ($false = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ lChris_THFTYPE_i @ lCorina_THFTYPE_i))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))))),
% 0.21/0.34 inference(primitive_instantiation,[],[f46])).
% 0.21/0.34 thf(f78,plain,(
% 0.21/0.34 ($false = ((~ (lChris_THFTYPE_i = lCorina_THFTYPE_i)))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))))),
% 0.21/0.34 inference(beta-eta_normalization,[],[f55])).
% 0.21/0.34 thf(f79,plain,(
% 0.21/0.34 ($true = ((lChris_THFTYPE_i = lCorina_THFTYPE_i))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))))),
% 0.21/0.34 inference(not_proxy_clausification,[],[f78])).
% 0.21/0.34 thf(f80,plain,(
% 0.21/0.34 (lChris_THFTYPE_i = lCorina_THFTYPE_i) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))))),
% 0.21/0.34 inference(equality_proxy_clausification,[],[f79])).
% 0.21/0.34 thf(f81,plain,(
% 0.21/0.34 ($false = ((lChris_THFTYPE_i = lCorina_THFTYPE_i))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = =)),
% 0.21/0.34 inference(beta-eta_normalization,[],[f54])).
% 0.21/0.34 thf(f82,plain,(
% 0.21/0.34 (lChris_THFTYPE_i != lCorina_THFTYPE_i) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = =)),
% 0.21/0.34 inference(equality_proxy_clausification,[],[f81])).
% 0.21/0.34 thf(f92,definition,(
% 0.21/0.34 spl1_3 <=> ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))))),
% 0.21/0.34 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.21/0.35 thf(f94,plain,(
% 0.21/0.35 ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1)))))) | ~spl1_3),
% 0.21/0.35 inference(avatar_component_clause,[],[f92])).
% 0.21/0.35 thf(f96,definition,(
% 0.21/0.35 spl1_4 <=> (lChris_THFTYPE_i = lCorina_THFTYPE_i)),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.21/0.35 thf(f98,plain,(
% 0.21/0.35 (lChris_THFTYPE_i = lCorina_THFTYPE_i) | ~spl1_4),
% 0.21/0.35 inference(avatar_component_clause,[],[f96])).
% 0.21/0.35 thf(f99,plain,(
% 0.21/0.35 spl1_3 | spl1_4),
% 0.21/0.35 inference(avatar_split_clause,[],[f80,f96,f92])).
% 0.21/0.35 thf(f101,definition,(
% 0.21/0.35 spl1_5 <=> ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = =)),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 0.21/0.35 thf(f103,plain,(
% 0.21/0.35 ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = =) | ~spl1_5),
% 0.21/0.35 inference(avatar_component_clause,[],[f101])).
% 0.21/0.35 thf(f104,plain,(
% 0.21/0.35 spl1_5 | ~spl1_4),
% 0.21/0.35 inference(avatar_split_clause,[],[f82,f96,f101])).
% 0.21/0.35 thf(f128,plain,(
% 0.21/0.35 ( ! [X0 : ($i > $i > $i)] : (($true != $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (wife_THFTYPE_IiioI @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) | (lCorina_THFTYPE_i != ((X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i)))) )),
% 0.21/0.35 inference(constrained_superposition,[],[f32,f27])).
% 0.21/0.35 thf(f132,plain,(
% 0.21/0.35 ( ! [X0 : ($i > $i > $i)] : (((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (wife_THFTYPE_IiioI @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) | (lCorina_THFTYPE_i != ((X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i)))) )),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f128])).
% 0.21/0.35 thf(f133,plain,(
% 0.21/0.35 ( ! [X0 : ($i > $i > $i)] : ((lCorina_THFTYPE_i != ((X0 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (wife_THFTYPE_IiioI @ (X0 @ Y0 @ Y1) @ Y0)))))) )),
% 0.21/0.35 inference(beta-eta_normalization,[],[f132])).
% 0.21/0.35 thf(f190,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)) = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ X1)))) ) | ~spl1_3),
% 0.21/0.35 inference(argument_congruence,[],[f94])).
% 0.21/0.35 thf(f191,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: (~ (X1 = Y0))))) ) | ~spl1_3),
% 0.21/0.35 inference(beta-eta_normalization,[],[f190])).
% 0.21/0.35 thf(f194,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X2)) = (((^[Y0 : $i]: (~ (X1 = Y0))) @ X2)))) ) | ~spl1_3),
% 0.21/0.35 inference(argument_congruence,[],[f191])).
% 0.21/0.35 thf(f196,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X2))) | ($true = (((^[Y0 : $i]: (~ (X1 = Y0))) @ X2)))) ) | ~spl1_3),
% 0.21/0.35 inference(iff_proxy_clausification,[],[f194])).
% 0.21/0.35 thf(f197,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (($true = $false) | ($true = ((~ (X1 = X2))))) ) | ~spl1_3),
% 0.21/0.35 inference(beta-eta_normalization,[],[f196])).
% 0.21/0.35 thf(f198,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (($true = $false) | ($false = ((X1 = X2)))) ) | ~spl1_3),
% 0.21/0.35 inference(not_proxy_clausification,[],[f197])).
% 0.21/0.35 thf(f199,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (($true = $false) | (X1 != X2)) ) | ~spl1_3),
% 0.21/0.35 inference(equality_proxy_clausification,[],[f198])).
% 0.21/0.35 thf(f200,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : ((X1 != X2)) ) | ~spl1_3),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f199])).
% 0.21/0.35 thf(f201,plain,(
% 0.21/0.35 $false | ~spl1_3),
% 0.21/0.35 inference(flex-flex_simplification,[],[f200])).
% 0.21/0.35 thf(f202,plain,(
% 0.21/0.35 ~spl1_3),
% 0.21/0.35 inference(avatar_contradiction_clause,[],[f201])).
% 0.21/0.35 thf(f223,plain,(
% 0.21/0.35 ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (wife_THFTYPE_IiioI @ ((^[Y2 : $i]: ((^[Y3 : $i]: (lCorina_THFTYPE_i)))) @ Y0 @ Y1) @ Y0)))))),
% 0.21/0.35 inference(equality_resolution,[],[f133])).
% 0.21/0.35 thf(f224,plain,(
% 0.21/0.35 ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ Y0)))))),
% 0.21/0.35 inference(beta-eta_normalization,[],[f223])).
% 0.21/0.35 thf(f228,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)) = ((= @ X1)))) ) | ~spl1_5),
% 0.21/0.35 inference(argument_congruence,[],[f103])).
% 0.21/0.35 thf(f229,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (((^[Y0 : $i]: ($true)) = ((= @ X1)))) ) | ~spl1_5),
% 0.21/0.35 inference(beta-eta_normalization,[],[f228])).
% 0.21/0.35 thf(f232,plain,(
% 0.21/0.35 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((husband_THFTYPE_IiioI @ X0 @ X1))) | ($false = ((wife_THFTYPE_IiioI @ X1 @ X0)))) )),
% 0.21/0.35 inference(constrained_superposition,[],[f34,f23])).
% 0.21/0.35 thf(f233,plain,(
% 0.21/0.35 ( ! [X0 : $i,X1 : $i] : (($true = ((husband_THFTYPE_IiioI @ X0 @ X1))) | ($false = ((wife_THFTYPE_IiioI @ X1 @ X0)))) )),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f232])).
% 0.21/0.35 thf(f235,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X2)) = ((X1 = X2)))) ) | ~spl1_5),
% 0.21/0.35 inference(argument_congruence,[],[f229])).
% 0.21/0.35 thf(f237,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X2))) | ($true = ((X1 = X2)))) ) | ~spl1_5),
% 0.21/0.35 inference(iff_proxy_clausification,[],[f235])).
% 0.21/0.35 thf(f238,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X2))) | (X1 = X2)) ) | ~spl1_5),
% 0.21/0.35 inference(equality_proxy_clausification,[],[f237])).
% 0.21/0.35 thf(f239,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (($true = $false) | (X1 = X2)) ) | ~spl1_5),
% 0.21/0.35 inference(beta-eta_normalization,[],[f238])).
% 0.21/0.35 thf(f240,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : ((X1 = X2)) ) | ~spl1_5),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f239])).
% 0.21/0.35 thf(f277,plain,(
% 0.21/0.35 ( ! [X0 : $i] : (($false = ((husband_THFTYPE_IiioI @ X0 @ sK0)))) ) | ~spl1_5),
% 0.21/0.35 inference(constrained_superposition,[],[f33,f240])).
% 0.21/0.35 thf(f337,plain,(
% 0.21/0.35 ( ! [X0 : $i,X1 : $i] : (($false = ((husband_THFTYPE_IiioI @ X1 @ X0)))) ) | ~spl1_5),
% 0.21/0.35 inference(constrained_superposition,[],[f277,f240])).
% 0.21/0.35 thf(f354,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)) = (((^[Y0 : $i]: ((^[Y1 : $i]: (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ Y0)))) @ X1)))) )),
% 0.21/0.35 inference(argument_congruence,[],[f224])).
% 0.21/0.35 thf(f355,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ X1)))) )),
% 0.21/0.35 inference(beta-eta_normalization,[],[f354])).
% 0.21/0.35 thf(f601,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X2)) = (((^[Y0 : $i]: (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ X1)) @ X2)))) )),
% 0.21/0.35 inference(argument_congruence,[],[f355])).
% 0.21/0.35 thf(f603,plain,(
% 0.21/0.35 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X2))) | ($true = (((^[Y0 : $i]: (wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ X1)) @ X2)))) )),
% 0.21/0.35 inference(iff_proxy_clausification,[],[f601])).
% 0.21/0.35 thf(f604,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (($true = $false) | ($true = ((wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ X1)))) )),
% 0.21/0.35 inference(beta-eta_normalization,[],[f603])).
% 0.21/0.35 thf(f605,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (($true = ((wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ X1)))) )),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f604])).
% 0.21/0.35 thf(f607,plain,(
% 0.21/0.35 ( ! [X1 : $i] : (($true = ((wife_THFTYPE_IiioI @ lChris_THFTYPE_i @ X1)))) ) | ~spl1_4),
% 0.21/0.35 inference(forward_demodulation,[],[f605,f98])).
% 0.21/0.35 thf(f618,plain,(
% 0.21/0.35 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((wife_THFTYPE_IiioI @ X1 @ X0)))) ) | ~spl1_5),
% 0.21/0.35 inference(constrained_superposition,[],[f337,f233])).
% 0.21/0.35 thf(f621,plain,(
% 0.21/0.35 ( ! [X0 : $i,X1 : $i] : (($false = ((wife_THFTYPE_IiioI @ X1 @ X0)))) ) | ~spl1_5),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f618])).
% 0.21/0.35 thf(f630,plain,(
% 0.21/0.35 ( ! [X0 : $i,X1 : $i] : (($true = ((wife_THFTYPE_IiioI @ X0 @ X1)))) ) | (~spl1_4 | ~spl1_5)),
% 0.21/0.35 inference(constrained_superposition,[],[f607,f240])).
% 0.21/0.35 thf(f663,plain,(
% 0.21/0.35 ($true = $false) | (~spl1_4 | ~spl1_5)),
% 0.21/0.35 inference(forward_demodulation,[],[f630,f621])).
% 0.21/0.35 thf(f664,plain,(
% 0.21/0.35 $false | (~spl1_4 | ~spl1_5)),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f663])).
% 0.21/0.35 thf(f665,plain,(
% 0.21/0.35 ~spl1_4 | ~spl1_5),
% 0.21/0.35 inference(avatar_contradiction_clause,[],[f664])).
% 0.21/0.35 cnf(s3, plain, spl1_3 | spl1_4, inference(sat_conversion,[],[f99])).
% 0.21/0.35 cnf(s4, plain, ~spl1_4 | spl1_5, inference(sat_conversion,[],[f104])).
% 0.21/0.35 cnf(s5, plain, ~spl1_3, inference(sat_conversion,[],[f202])).
% 0.21/0.35 cnf(s18, plain, ~spl1_4 | ~spl1_5, inference(sat_conversion,[],[f665])).
% 0.21/0.35 cnf(s23, plain, spl1_4, inference(rat,[],[s3,s5])).
% 0.21/0.35 cnf(s24, plain, ~spl1_5, inference(rat,[],[s18,s23])).
% 0.21/0.35 cnf(s25, plain, $false, inference(rat,[],[s4,s24,s23])).
% 0.21/0.35 thf(f668,plain,(
% 0.21/0.35 $false),
% 0.21/0.35 inference(avatar_sat_refutation,[],[s25])).
% 0.21/0.35 % SZS output end Proof for theBenchmark
% 0.21/0.35 % (3890062)------------------------------
% 0.21/0.35 % (3890062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (3890062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (3890062)CaDiCaL version: 2.1.3
% 0.21/0.35 % (3890062)Termination reason: Refutation
% 0.21/0.35 % (3890062)Time elapsed: 0.054 s
% 0.21/0.35 % (3890062)Peak memory usage: 13 MB
% 0.21/0.35 % (3890062)Instructions burned: 60 (million)
% 0.21/0.35 % (3890049)Success in time 0.092 s
% 0.21/0.35 % Vampire exiting
%------------------------------------------------------------------------------