%------------------------------------------------------------------------------
% File : Vampire-SAT---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 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 08:50:23 AM UTC 2026
% Result : Theorem 0.19s 0.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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 SAT
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:17:18 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.31 % (3834225)Will run a generic schedule for satisfiability detection.
% 0.19/0.31 % (3834231)% WARNING: option uhcvi not known.
% 0.19/0.31 % (3834233)dis+10_1_sil=32000:sp=arity:random_seed=3638494501:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.31 % (3834230)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=571813246_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.31 % (3834231)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1108895284:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.31 % (3834232)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3452452745:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.31 % (3834231)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.31 % (3834231)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.31 % Exception at run slice level
% 0.19/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.31 % (3834234)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=509935672:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.31 % (3834236)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2606080028:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.31 % (3834234)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.31 % (3834233)Refutation not found, incomplete strategy
% 0.19/0.31 % (3834233)------------------------------
% 0.19/0.31 % (3834233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834233)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834233)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.31 % (3834233)Time elapsed: 0.008 s
% 0.19/0.31 % (3834233)Peak memory usage: 12 MB
% 0.19/0.31 % (3834233)Instructions burned: 12 (million)
% 0.19/0.31 % (3834231)Refutation not found, incomplete strategy
% 0.19/0.31 % (3834231)------------------------------
% 0.19/0.31 % (3834231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834231)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834231)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.31 % (3834231)Time elapsed: 0.008 s
% 0.19/0.31 % (3834231)Peak memory usage: 12 MB
% 0.19/0.31 % (3834231)Instructions burned: 12 (million)
% 0.19/0.31 % (3834233)------------------------------
% 0.19/0.31 % (3834233)------------------------------
% 0.19/0.31 % (3834231)------------------------------
% 0.19/0.31 % (3834231)------------------------------
% 0.19/0.31 % (3834234)Refutation not found, incomplete strategy
% 0.19/0.31 % (3834234)------------------------------
% 0.19/0.31 % (3834234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834234)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834234)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.31 % (3834234)Time elapsed: 0.006 s
% 0.19/0.31 % (3834234)Peak memory usage: 12 MB
% 0.19/0.31 % (3834234)Instructions burned: 22 (million)
% 0.19/0.31 % (3834234)------------------------------
% 0.19/0.31 % (3834234)------------------------------
% 0.19/0.31 % (3834235)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=705459046:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.31 % (3834236)Refutation not found, incomplete strategy
% 0.19/0.31 % (3834236)------------------------------
% 0.19/0.31 % (3834236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834236)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834236)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.31 % (3834236)Time elapsed: 0.016 s
% 0.19/0.31 % (3834241)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1140726799:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.31 % (3834236)Peak memory usage: 12 MB
% 0.19/0.31 % (3834236)Instructions burned: 12 (million)
% 0.19/0.31 % Exception at run slice level
% 0.19/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.31 % (3834236)------------------------------
% 0.19/0.31 % (3834236)------------------------------
% 0.19/0.31 % (3834235)Refutation not found, incomplete strategy
% 0.19/0.31 % (3834235)------------------------------
% 0.19/0.31 % (3834235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834235)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834235)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.31 % (3834235)Time elapsed: 0.011 s
% 0.19/0.31 % (3834235)Peak memory usage: 12 MB
% 0.19/0.31 % (3834235)Instructions burned: 11 (million)
% 0.19/0.31 % (3834232)Refutation not found, incomplete strategy
% 0.19/0.31 % (3834232)------------------------------
% 0.19/0.31 % (3834232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834232)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834232)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.31 % (3834232)Time elapsed: 0.024 s
% 0.19/0.31 % (3834232)Peak memory usage: 12 MB
% 0.19/0.31 % (3834232)Instructions burned: 21 (million)
% 0.19/0.31 % (3834232)------------------------------
% 0.19/0.31 % (3834232)------------------------------
% 0.19/0.31 % (3834235)------------------------------
% 0.19/0.31 % (3834235)------------------------------
% 0.19/0.31 % (3834244)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2891090621:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.31 % (3834245)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3328962093:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.19/0.31 % (3834245)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.31 % (3834245)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.31 % (3834246)ott-21_1_sil=16000:fs=off:random_seed=490282753:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/0.31 % (3834244)Refutation not found, incomplete strategy
% 0.19/0.31 % (3834244)------------------------------
% 0.19/0.31 % (3834244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834244)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834244)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.31 % (3834244)Time elapsed: 0.007 s
% 0.19/0.31 % (3834244)Peak memory usage: 12 MB
% 0.19/0.31 % (3834244)Instructions burned: 10 (million)
% 0.19/0.31 % (3834244)------------------------------
% 0.19/0.31 % (3834244)------------------------------
% 0.19/0.31 % (3834245)Refutation not found, incomplete strategy
% 0.19/0.31 % (3834245)------------------------------
% 0.19/0.31 % (3834245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834245)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834245)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.31 % (3834245)Time elapsed: 0.007 s
% 0.19/0.31 % (3834245)Peak memory usage: 12 MB
% 0.19/0.31 % (3834245)Instructions burned: 12 (million)
% 0.19/0.31 % (3834245)------------------------------
% 0.19/0.31 % (3834245)------------------------------
% 0.19/0.31 % (3834250)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1751781206:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.19/0.31 % (3834249)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3741612032:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.19/0.31 % Exception at run slice level
% 0.19/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.31 % (3834251)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3643513903:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 0.19/0.31 % (3834252)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=318587050:i=889:ins=1_2999 on theBenchmark for (2999ds/889Mi)
% 0.19/0.31 % Exception at run slice level
% 0.19/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.31 % (3834251) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3834225-3834251"...
% 0.19/0.31 % (3834251)...printing done.
% 0.19/0.31 % (3834251)Refutation found. Thanks to Tanya!
% 0.19/0.31 % SZS status Theorem for theBenchmark
% 0.19/0.31 % SZS output start Proof for theBenchmark
% 0.19/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.31 thf(func_def_0, type, eps: (($i > $o) > $i)).
% 0.19/0.31 thf(func_def_2, type, if: ($o > $i > $i > $i)).
% 0.19/0.31 thf(func_def_5, type, vOR: ($o > $o > $o)).
% 0.19/0.31 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.19/0.31 thf(func_def_7, type, db3: !>[X0: $tType]:(X0)).
% 0.19/0.31 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.31 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.31 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.31 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.19/0.31 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.31 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.31 thf(func_def_14, type, sK0: $o).
% 0.19/0.31 thf(f1,axiom,(
% 0.19/0.31 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax)).
% 0.19/0.31 thf(f2,axiom,(
% 0.19/0.31 (if = (^[X0 : $o, X1 : $i, X2 : $i] : ((eps @ (^[X3 : $i] : (((X3 = X2) & ~X0) | ((X3 = X1) & X0)))))))),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifd)).
% 0.19/0.31 thf(f3,conjecture,(
% 0.19/0.31 ! [X0 : $o,X1 : $i] : (((if @ X0 @ X1 @ X1)) = X1)),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.19/0.31 thf(f4,negated_conjecture,(
% 0.19/0.31 ~ ! [X0 : $o,X1 : $i] : (((if @ X0 @ X1 @ X1)) = X1)),
% 0.19/0.31 inference(negated_conjecture,[status(cth)],[f3])).
% 0.19/0.31 thf(f5,plain,(
% 0.19/0.31 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.19/0.31 inference(rectify,[],[f1])).
% 0.19/0.31 thf(f6,plain,(
% 0.19/0.31 ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) = $true) => (((X0 @ (eps @ X0))) = $true))),
% 0.19/0.31 inference(fool_elimination,[],[f5])).
% 0.19/0.31 thf(f7,plain,(
% 0.19/0.31 (if = (^[X0 : $o, X1 : $i, X2 : $i] : ((eps @ (^[X3 : $i] : (((X3 = X2) & ~X0) | ((X3 = X1) & X0)))))))),
% 0.19/0.31 inference(rectify,[],[f2])).
% 0.19/0.31 thf(f8,plain,(
% 0.19/0.31 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))),
% 0.19/0.31 inference(fool_elimination,[],[f7])).
% 0.19/0.31 thf(f9,plain,(
% 0.19/0.31 ! [X0 : ($i > $o)] : ((((X0 @ (eps @ X0))) = $true) | ! [X1 : $i] : (((X0 @ X1)) != $true))),
% 0.19/0.31 inference(ennf_transformation,[],[f6])).
% 0.19/0.31 thf(f10,plain,(
% 0.19/0.31 ? [X0 : $o,X1 : $i] : (((if @ X0 @ X1 @ X1)) != X1)),
% 0.19/0.31 inference(ennf_transformation,[],[f4])).
% 0.19/0.31 thf(f11,plain,(
% 0.19/0.31 (sK1 != ((if @ sK0 @ sK1 @ sK1)))),
% 0.19/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10])).
% 0.19/0.31 thf(f12,plain,(
% 0.19/0.31 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | (((X0 @ (eps @ X0))) = $true)) )),
% 0.19/0.31 inference(cnf_transformation,[],[f9])).
% 0.19/0.31 thf(f13,plain,(
% 0.19/0.31 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))),
% 0.19/0.31 inference(cnf_transformation,[],[f8])).
% 0.19/0.31 thf(f14,plain,(
% 0.19/0.31 (sK1 != ((if @ sK0 @ sK1 @ sK1)))),
% 0.19/0.31 inference(cnf_transformation,[],[f11])).
% 0.19/0.31 thf(f16,definition,(
% 0.19/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.31 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.31 thf(f17,plain,(
% 0.19/0.31 (sK1 != (((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))) @ sK0 @ sK1 @ sK1)))),
% 0.19/0.31 inference(definition_unfolding,[],[f14,f13])).
% 0.19/0.31 thf(f18,definition,(
% 0.19/0.31 (sF2 = (((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))) @ sK0 @ sK1 @ sK1)))),
% 0.19/0.31 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.19/0.31 thf(f19,plain,(
% 0.19/0.31 ((((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))) @ sK0 @ sK1 @ sK1)) = sF2)),
% 0.19/0.31 inference(reorient_equations,[],[f18])).
% 0.19/0.31 thf(f20,plain,(
% 0.19/0.31 (sK1 != sF2)),
% 0.19/0.31 inference(definition_folding,[],[f17,f19])).
% 0.19/0.31 thf(f21,plain,(
% 0.19/0.31 (sF2 = ((eps @ (^[Y0 : $i]: ((sK0 & (sK1 = Y0)) | ((~ sK0) & (sK1 = Y0)))))))),
% 0.19/0.31 inference(beta-eta_normalization,[],[f19])).
% 0.19/0.31 thf(f34,plain,(
% 0.19/0.31 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | (((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.19/0.31 inference(constrained_superposition,[],[f12,f16])).
% 0.19/0.31 thf(f37,plain,(
% 0.19/0.31 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.19/0.31 inference(trivial_inequality_removal,[],[f34])).
% 0.19/0.31 thf(f52,plain,(
% 0.19/0.31 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: ((sK0 & (sK1 = Y0)) | ((~ sK0) & (sK1 = Y0)))) @ sF2))) | ($false = (((^[Y0 : $i]: ((sK0 & (sK1 = Y0)) | ((~ sK0) & (sK1 = Y0)))) @ X0)))) )),
% 0.19/0.31 inference(constrained_superposition,[],[f37,f21])).
% 0.19/0.31 thf(f95,plain,(
% 0.19/0.31 ( ! [X0 : $i] : (($true = (((sK0 & (sK1 = sF2)) | ((~ sK0) & (sK1 = sF2))))) | ($false = (((sK0 & (sK1 = X0)) | ((~ sK0) & (sK1 = X0)))))) )),
% 0.19/0.31 inference(beta-eta_normalization,[],[f52])).
% 0.19/0.31 thf(f96,plain,(
% 0.19/0.31 ( ! [X0 : $i] : (($true = (((~ sK0) & (sK1 = sF2)))) | ($false = (((sK0 & (sK1 = X0)) | ((~ sK0) & (sK1 = X0))))) | ($true = ((sK0 & (sK1 = sF2))))) )),
% 0.19/0.31 inference(or_proxy_clausification,[],[f95])).
% 0.19/0.31 thf(f97,plain,(
% 0.19/0.31 ( ! [X0 : $i] : (($true = ((sK1 = sF2))) | ($false = (((sK0 & (sK1 = X0)) | ((~ sK0) & (sK1 = X0))))) | ($true = ((sK0 & (sK1 = sF2))))) )),
% 0.19/0.31 inference(and_proxy_clausification,[],[f96])).
% 0.19/0.31 thf(f117,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | ($false = (((sK0 & (sK1 = X0)) | ((~ sK0) & (sK1 = X0))))) | ($true = ((sK0 & (sK1 = sF2))))) )),
% 0.19/0.31 inference(equality_proxy_clausification,[],[f97])).
% 0.19/0.31 thf(f118,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | ($false = (((~ sK0) & (sK1 = X0)))) | ($true = ((sK0 & (sK1 = sF2))))) )),
% 0.19/0.31 inference(or_proxy_clausification,[],[f117])).
% 0.19/0.31 thf(f119,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | ($false = ((sK0 & (sK1 = X0)))) | ($true = ((sK0 & (sK1 = sF2))))) )),
% 0.19/0.31 inference(or_proxy_clausification,[],[f117])).
% 0.19/0.31 thf(f120,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | ($false = ((sK1 = X0))) | ($true = ((sK0 & (sK1 = sF2)))) | (sK0 = $false)) )),
% 0.19/0.31 inference(and_proxy_clausification,[],[f119])).
% 0.19/0.31 thf(f121,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | ($true = ((sK0 & (sK1 = sF2)))) | (sK0 = $false)) )),
% 0.19/0.31 inference(equality_proxy_clausification,[],[f120])).
% 0.19/0.31 thf(f122,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | ($true = ((sK1 = sF2))) | (sK0 = $false)) )),
% 0.19/0.31 inference(and_proxy_clausification,[],[f121])).
% 0.19/0.31 thf(f124,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | (sK1 = sF2) | (sK0 = $false)) )),
% 0.19/0.31 inference(equality_proxy_clausification,[],[f122])).
% 0.19/0.31 thf(f125,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | (sK0 = $false)) )),
% 0.19/0.31 inference(duplicate_literal_removal,[],[f124])).
% 0.19/0.31 thf(f126,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | ($false = ((sK1 = X0))) | ($true = ((sK0 & (sK1 = sF2)))) | ($false = ((~ sK0)))) )),
% 0.19/0.31 inference(and_proxy_clausification,[],[f118])).
% 0.19/0.31 thf(f127,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | ($true = ((sK0 & (sK1 = sF2)))) | ($false = ((~ sK0)))) )),
% 0.19/0.31 inference(equality_proxy_clausification,[],[f126])).
% 0.19/0.31 thf(f128,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | ($true = ((sK1 = sF2))) | ($false = ((~ sK0)))) )),
% 0.19/0.31 inference(and_proxy_clausification,[],[f127])).
% 0.19/0.31 thf(f132,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | (sK1 = sF2) | ($false = ((~ sK0)))) )),
% 0.19/0.31 inference(equality_proxy_clausification,[],[f128])).
% 0.19/0.31 thf(f133,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | (sK1 = sF2) | ($true = sK0)) )),
% 0.19/0.31 inference(not_proxy_clausification,[],[f132])).
% 0.19/0.31 thf(f134,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 = sF2) | (sK1 != X0) | ($true = sK0)) )),
% 0.19/0.31 inference(duplicate_literal_removal,[],[f133])).
% 0.19/0.31 thf(f150,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 != X0) | (sK0 = $false)) )),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f125,f20])).
% 0.19/0.31 thf(f152,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 != X0) | ($true = sK0)) )),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f134,f20])).
% 0.19/0.31 thf(f154,definition,(
% 0.19/0.31 spl3_1 <=> ! [X0 : $i] : (sK1 != X0)),
% 0.19/0.31 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.19/0.31 thf(f155,plain,(
% 0.19/0.31 ( ! [X0 : $i] : ((sK1 != X0)) ) | ~spl3_1),
% 0.19/0.31 inference(avatar_component_clause,[],[f154])).
% 0.19/0.31 thf(f157,definition,(
% 0.19/0.31 spl3_2 <=> (sK0 = $false)),
% 0.19/0.31 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.19/0.31 thf(f159,plain,(
% 0.19/0.31 (sK0 = $false) | ~spl3_2),
% 0.19/0.31 inference(avatar_component_clause,[],[f157])).
% 0.19/0.31 thf(f161,plain,(
% 0.19/0.31 spl3_2 | spl3_1),
% 0.19/0.31 inference(avatar_split_clause,[],[f150,f154,f157])).
% 0.19/0.31 thf(f163,definition,(
% 0.19/0.31 spl3_3 <=> ($true = sK0)),
% 0.19/0.31 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.19/0.31 thf(f165,plain,(
% 0.19/0.31 ($true = sK0) | ~spl3_3),
% 0.19/0.31 inference(avatar_component_clause,[],[f163])).
% 0.19/0.31 thf(f167,plain,(
% 0.19/0.31 spl3_3 | spl3_1),
% 0.19/0.31 inference(avatar_split_clause,[],[f152,f154,f163])).
% 0.19/0.31 thf(f168,plain,(
% 0.19/0.31 ($true = $false) | (~spl3_2 | ~spl3_3)),
% 0.19/0.31 inference(forward_demodulation,[],[f165,f159])).
% 0.19/0.31 thf(f169,plain,(
% 0.19/0.31 $false | (~spl3_2 | ~spl3_3)),
% 0.19/0.31 inference(trivial_inequality_removal,[],[f168])).
% 0.19/0.31 thf(f170,plain,(
% 0.19/0.31 ~spl3_2 | ~spl3_3),
% 0.19/0.31 inference(avatar_contradiction_clause,[],[f169])).
% 0.19/0.31 thf(f258,plain,(
% 0.19/0.31 $false | ~spl3_1),
% 0.19/0.31 inference(equality_resolution,[],[f155])).
% 0.19/0.31 thf(f259,plain,(
% 0.19/0.31 ~spl3_1),
% 0.19/0.31 inference(avatar_contradiction_clause,[],[f258])).
% 0.19/0.31 cnf(s2, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f161])).
% 0.19/0.31 cnf(s4, plain, spl3_1 | spl3_3, inference(sat_conversion,[],[f167])).
% 0.19/0.31 cnf(s5, plain, ~spl3_2 | ~spl3_3, inference(sat_conversion,[],[f170])).
% 0.19/0.31 cnf(s6, plain, ~spl3_1, inference(sat_conversion,[],[f259])).
% 0.19/0.31 cnf(s7, plain, spl3_3, inference(rat,[],[s4,s6])).
% 0.19/0.31 cnf(s8, plain, ~spl3_2, inference(rat,[],[s5,s7])).
% 0.19/0.31 cnf(s9, plain, $false, inference(rat,[],[s2,s8,s6])).
% 0.19/0.31 thf(f260,plain,(
% 0.19/0.31 $false),
% 0.19/0.31 inference(avatar_sat_refutation,[],[s9])).
% 0.19/0.31 % SZS output end Proof for theBenchmark
% 0.19/0.31 % (3834251)------------------------------
% 0.19/0.31 % (3834251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3834251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3834251)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3834251)Termination reason: Refutation
% 0.19/0.31 % (3834251)Time elapsed: 0.007 s
% 0.19/0.31 % (3834251)Peak memory usage: 12 MB
% 0.19/0.31 % (3834251)Instructions burned: 11 (million)
% 0.19/0.31 % (3834225)Success in time 0.087 s
% 0.19/0.31 % Vampire exiting
%------------------------------------------------------------------------------