%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO506^1 : 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 : 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 08:50:21 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO506^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:09:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.30 % (3662226)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (3662235)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3530423369:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (3662235)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (3662235)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662235)------------------------------
% 0.20/0.30 % (3662235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662235)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662235)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662235)Time elapsed: 0.001 s
% 0.20/0.30 % (3662235)Peak memory usage: 12 MB
% 0.20/0.30 % (3662235)Instructions burned: 1 (million)
% 0.20/0.30 % (3662235)------------------------------
% 0.20/0.30 % (3662235)------------------------------
% 0.20/0.30 % (3662232)% WARNING: option uhcvi not known.
% 0.20/0.30 % (3662231)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=282440464_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (3662232)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3811639281:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (3662234)dis+10_1_sil=32000:sp=arity:random_seed=2015609344:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (3662233)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3359375474:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (3662232)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 % (3662232)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (3662236)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2761397303:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (3662234)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662234)------------------------------
% 0.20/0.30 % (3662234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662234)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662234)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662234)Time elapsed: 0.002 s
% 0.20/0.30 % (3662234)Peak memory usage: 12 MB
% 0.20/0.30 % (3662234)Instructions burned: 1 (million)
% 0.20/0.30 % (3662232)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662232)------------------------------
% 0.20/0.30 % (3662232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662232)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662232)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662232)Time elapsed: 0.002 s
% 0.20/0.30 % (3662232)Peak memory usage: 12 MB
% 0.20/0.30 % (3662232)Instructions burned: 1 (million)
% 0.20/0.30 % (3662236)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662236)------------------------------
% 0.20/0.30 % (3662236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662236)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662236)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662236)Time elapsed: 0.001 s
% 0.20/0.30 % (3662236)Peak memory usage: 12 MB
% 0.20/0.30 % (3662236)Instructions burned: 1 (million)
% 0.20/0.30 % (3662234)------------------------------
% 0.20/0.30 % (3662234)------------------------------
% 0.20/0.30 % (3662236)------------------------------
% 0.20/0.30 % (3662236)------------------------------
% 0.20/0.30 % (3662232)------------------------------
% 0.20/0.30 % (3662232)------------------------------
% 0.20/0.30 % (3662233)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662233)------------------------------
% 0.20/0.30 % (3662233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662233)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662233)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662233)Time elapsed: 0.003 s
% 0.20/0.30 % (3662233)Peak memory usage: 12 MB
% 0.20/0.30 % (3662233)Instructions burned: 3 (million)
% 0.20/0.30 % (3662233)------------------------------
% 0.20/0.30 % (3662233)------------------------------
% 0.20/0.30 % (3662237)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2755693396:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % (3662237)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662237)------------------------------
% 0.20/0.30 % (3662237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662237)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662237)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662237)Time elapsed: 0.002 s
% 0.20/0.30 % (3662237)Peak memory usage: 12 MB
% 0.20/0.30 % (3662237)Instructions burned: 2 (million)
% 0.20/0.30 % (3662237)------------------------------
% 0.20/0.30 % (3662237)------------------------------
% 0.20/0.30 % (3662246)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=2484997874:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.30 % (3662246)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (3662246)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.30 % (3662246)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662246)------------------------------
% 0.20/0.30 % (3662246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662246)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662246)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662246)Time elapsed: 0.001 s
% 0.20/0.30 % (3662246)Peak memory usage: 12 MB
% 0.20/0.30 % (3662246)Instructions burned: 1 (million)
% 0.20/0.30 % (3662239)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2797851329:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.30 % (3662246)------------------------------
% 0.20/0.30 % (3662246)------------------------------
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (3662245)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3343345490:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (3662248)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1084747222:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.20/0.30 % (3662247)ott-21_1_sil=16000:fs=off:random_seed=1224279141:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/0.30 % (3662245)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662245)------------------------------
% 0.20/0.30 % (3662245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662245)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662245)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662245)Time elapsed: 0.002 s
% 0.20/0.30 % (3662245)Peak memory usage: 12 MB
% 0.20/0.30 % (3662245)Instructions burned: 1 (million)
% 0.20/0.30 % (3662245)------------------------------
% 0.20/0.30 % (3662245)------------------------------
% 0.20/0.30 % (3662249)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3277576880:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (3662254)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2061522345:i=889:ins=1_2999 on theBenchmark for (2999ds/889Mi)
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (3662248)Refutation not found, incomplete strategy
% 0.20/0.30 % (3662248)------------------------------
% 0.20/0.30 % (3662248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662248)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662248)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (3662248)Time elapsed: 0.004 s
% 0.20/0.30 % (3662248)Peak memory usage: 12 MB
% 0.20/0.30 % (3662248)Instructions burned: 4 (million)
% 0.20/0.30 % (3662248)------------------------------
% 0.20/0.30 % (3662248)------------------------------
% 0.20/0.30 % (3662251)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2590808098:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 0.20/0.30 % (3662251) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3662226-3662251"...
% 0.20/0.30 % (3662255)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=4087163090:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2999 on theBenchmark for (2999ds/692Mi)
% 0.20/0.30 % (3662255)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (3662251)...printing done.
% 0.20/0.30 % (3662263)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=832628219:i=9515:nm=5_2999 on theBenchmark for (2999ds/9515Mi)
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (3662251)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(func_def_0, type, c: ($o > $i > $i > $i)).
% 0.20/0.30 thf(func_def_2, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.30 thf(func_def_7, type, sF2: ($i > $i > $i)).
% 0.20/0.30 thf(func_def_8, type, sF3: ($i > $i > $i)).
% 0.20/0.30 thf(func_def_9, type, sF4: $o).
% 0.20/0.30 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.20/0.30 thf(f1,conjecture,(
% 0.20/0.30 ~ ! [X0 : $i,X1 : $i] : (((c @ $false @ X0 @ X1)) = X1) | ~ ! [X0 : $i,X1 : $i] : (((c @ $true @ X0 @ X1)) = X0) | ! [X0 : $i,X1 : $i] : (((c @ (X0 = X1) @ X0 @ X1)) = X1)),
% 0.20/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',claim)).
% 0.20/0.30 thf(f2,negated_conjecture,(
% 0.20/0.30 ~(~ ! [X0 : $i,X1 : $i] : (((c @ $false @ X0 @ X1)) = X1) | ~ ! [X0 : $i,X1 : $i] : (((c @ $true @ X0 @ X1)) = X0) | ! [X0 : $i,X1 : $i] : (((c @ (X0 = X1) @ X0 @ X1)) = X1))),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.30 thf(f3,plain,(
% 0.20/0.30 ~(~ ! [X0 : $i,X1 : $i] : (((c @ $false @ X0 @ X1)) = X1) | ~ ! [X2 : $i,X3 : $i] : (((c @ $true @ X2 @ X3)) = X2) | ! [X4 : $i,X5 : $i] : (((c @ (X4 = X5) @ X4 @ X5)) = X5))),
% 0.20/0.30 inference(rectify,[],[f2])).
% 0.20/0.30 thf(f4,plain,(
% 0.20/0.30 ~(~ ! [X0 : $i,X1 : $i] : (((c @ $false @ X0 @ X1)) = X1) | ~ ! [X2 : $i,X3 : $i] : (((c @ $true @ X2 @ X3)) = X2) | ! [X4 : $i,X5 : $i] : (((c @ (X4 = X5) @ X4 @ X5)) = X5))),
% 0.20/0.30 inference(fool_elimination,[],[f3])).
% 0.20/0.30 thf(f5,plain,(
% 0.20/0.30 ! [X0 : $i,X1 : $i] : (((c @ $false @ X0 @ X1)) = X1) & ! [X2 : $i,X3 : $i] : (((c @ $true @ X2 @ X3)) = X2) & ? [X4 : $i,X5 : $i] : (((c @ (X4 = X5) @ X4 @ X5)) != X5)),
% 0.20/0.30 inference(ennf_transformation,[],[f4])).
% 0.20/0.30 thf(f6,plain,(
% 0.20/0.30 ! [X0 : $i,X1 : $i] : (((c @ $false @ X0 @ X1)) = X1) & ! [X2 : $i,X3 : $i] : (((c @ $true @ X2 @ X3)) = X2) & (sK1 != ((c @ (sK0 = sK1) @ sK0 @ sK1)))),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0),skolemize(X5,sK1)],[f5])).
% 0.20/0.30 thf(f7,plain,(
% 0.20/0.30 (sK1 != ((c @ (sK0 = sK1) @ sK0 @ sK1)))),
% 0.20/0.30 inference(cnf_transformation,[],[f6])).
% 0.20/0.30 thf(f8,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i] : ((((c @ $true @ X2 @ X3)) = X2)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f6])).
% 0.20/0.30 thf(f9,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((c @ $false @ X0 @ X1)) = X1)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f6])).
% 0.20/0.30 thf(f11,definition,(
% 0.20/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.30 thf(f12,definition,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((sF2 @ X1 @ X0)) = ((c @ $false @ X0 @ X1)))) )),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.20/0.30 thf(f13,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((c @ $false @ X0 @ X1)) = ((sF2 @ X1 @ X0)))) )),
% 0.20/0.30 inference(reorient_equations,[],[f12])).
% 0.20/0.30 thf(f14,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((sF2 @ X1 @ X0)) = X1)) )),
% 0.20/0.30 inference(definition_folding,[],[f9,f13])).
% 0.20/0.30 thf(f15,definition,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i] : ((((sF3 @ X3 @ X2)) = ((c @ $true @ X2 @ X3)))) )),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.20/0.30 thf(f16,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i] : ((((c @ $true @ X2 @ X3)) = ((sF3 @ X3 @ X2)))) )),
% 0.20/0.30 inference(reorient_equations,[],[f15])).
% 0.20/0.30 thf(f17,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i] : ((((sF3 @ X3 @ X2)) = X2)) )),
% 0.20/0.30 inference(definition_folding,[],[f8,f16])).
% 0.20/0.30 thf(f18,definition,(
% 0.20/0.30 (sF4 = ((sK0 = sK1)))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.20/0.30 thf(f19,plain,(
% 0.20/0.30 (((sK0 = sK1)) = sF4)),
% 0.20/0.30 inference(reorient_equations,[],[f18])).
% 0.20/0.30 thf(f20,definition,(
% 0.20/0.30 (sF5 = ((c @ sF4 @ sK0 @ sK1)))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.20/0.30 thf(f21,plain,(
% 0.20/0.30 (((c @ sF4 @ sK0 @ sK1)) = sF5)),
% 0.20/0.30 inference(reorient_equations,[],[f20])).
% 0.20/0.30 thf(f22,plain,(
% 0.20/0.30 (sK1 != sF5)),
% 0.20/0.30 inference(definition_folding,[],[f7,f21,f19])).
% 0.20/0.30 thf(f23,plain,(
% 0.20/0.30 ($true = ((sK0 = sK1))) | ($false = sF4)),
% 0.20/0.30 inference(iff_proxy_clausification,[],[f19])).
% 0.20/0.30 thf(f24,plain,(
% 0.20/0.30 ($false = ((sK0 = sK1))) | ($true = sF4)),
% 0.20/0.30 inference(iff_proxy_clausification,[],[f19])).
% 0.20/0.30 thf(f25,plain,(
% 0.20/0.30 (sK0 != sK1) | ($true = sF4)),
% 0.20/0.30 inference(equality_proxy_clausification,[],[f24])).
% 0.20/0.30 thf(f26,plain,(
% 0.20/0.30 (sK0 = sK1) | ($false = sF4)),
% 0.20/0.30 inference(equality_proxy_clausification,[],[f23])).
% 0.20/0.30 thf(f27,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((c @ $false @ X0 @ X1)) = X1)) )),
% 0.20/0.30 inference(forward_demodulation,[],[f13,f14])).
% 0.20/0.30 thf(f28,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i] : ((((c @ $true @ X2 @ X3)) = X2)) )),
% 0.20/0.30 inference(forward_demodulation,[],[f16,f17])).
% 0.20/0.30 thf(f30,definition,(
% 0.20/0.30 spl6_1 <=> ($true = sF4)),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.20/0.30 thf(f32,plain,(
% 0.20/0.30 ($true = sF4) | ~spl6_1),
% 0.20/0.30 inference(avatar_component_clause,[],[f30])).
% 0.20/0.30 thf(f34,definition,(
% 0.20/0.30 spl6_2 <=> (sK0 = sK1)),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.20/0.30 thf(f35,plain,(
% 0.20/0.30 (sK0 = sK1) | ~spl6_2),
% 0.20/0.30 inference(avatar_component_clause,[],[f34])).
% 0.20/0.30 thf(f37,plain,(
% 0.20/0.30 spl6_1 | ~spl6_2),
% 0.20/0.30 inference(avatar_split_clause,[],[f25,f34,f30])).
% 0.20/0.30 thf(f39,definition,(
% 0.20/0.30 spl6_3 <=> ($false = sF4)),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.20/0.30 thf(f41,plain,(
% 0.20/0.30 ($false = sF4) | ~spl6_3),
% 0.20/0.30 inference(avatar_component_clause,[],[f39])).
% 0.20/0.30 thf(f42,plain,(
% 0.20/0.30 spl6_3 | spl6_2),
% 0.20/0.30 inference(avatar_split_clause,[],[f26,f34,f39])).
% 0.20/0.30 thf(f45,plain,(
% 0.20/0.30 ( ! [X2 : $i,X0 : $o,X1 : $i] : ((((c @ X0 @ X1 @ X2)) = X1) | ($false = X0)) )),
% 0.20/0.30 inference(constrained_superposition,[],[f28,f11])).
% 0.20/0.30 thf(f53,plain,(
% 0.20/0.30 (sK0 = sF5) | ($false = sF4)),
% 0.20/0.30 inference(constrained_superposition,[],[f45,f21])).
% 0.20/0.30 thf(f55,plain,(
% 0.20/0.30 (sF5 = ((c @ $false @ sK0 @ sK1))) | ~spl6_3),
% 0.20/0.30 inference(constrained_superposition,[],[f21,f41])).
% 0.20/0.30 thf(f57,plain,(
% 0.20/0.30 (sK1 = sF5) | ~spl6_3),
% 0.20/0.30 inference(forward_demodulation,[],[f55,f27])).
% 0.20/0.30 thf(f58,plain,(
% 0.20/0.30 $false | ~spl6_3),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f57,f22])).
% 0.20/0.30 thf(f59,plain,(
% 0.20/0.30 ~spl6_3),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f58])).
% 0.20/0.30 thf(f61,plain,(
% 0.20/0.30 ($true = $false) | (sK0 = sF5) | ~spl6_1),
% 0.20/0.30 inference(forward_demodulation,[],[f53,f32])).
% 0.20/0.30 thf(f62,plain,(
% 0.20/0.30 (sK0 = sF5) | ~spl6_1),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f61])).
% 0.20/0.30 thf(f68,plain,(
% 0.20/0.30 (sK0 != sK1) | ~spl6_1),
% 0.20/0.30 inference(constrained_superposition,[],[f22,f62])).
% 0.20/0.30 thf(f69,plain,(
% 0.20/0.30 $false | (~spl6_1 | ~spl6_2)),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f68,f35])).
% 0.20/0.30 thf(f70,plain,(
% 0.20/0.30 ~spl6_1 | ~spl6_2),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f69])).
% 0.20/0.30 cnf(s1, plain, spl6_1 | ~spl6_2, inference(sat_conversion,[],[f37])).
% 0.20/0.30 cnf(s2, plain, spl6_2 | spl6_3, inference(sat_conversion,[],[f42])).
% 0.20/0.30 cnf(s3, plain, ~spl6_3, inference(sat_conversion,[],[f59])).
% 0.20/0.30 cnf(s4, plain, ~spl6_1 | ~spl6_2, inference(sat_conversion,[],[f70])).
% 0.20/0.30 cnf(s5, plain, spl6_2, inference(rat,[],[s2,s3])).
% 0.20/0.30 cnf(s6, plain, ~spl6_1, inference(rat,[],[s4,s5])).
% 0.20/0.30 cnf(s7, plain, $false, inference(rat,[],[s1,s5,s6])).
% 0.20/0.30 thf(f71,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(avatar_sat_refutation,[],[s7])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (3662251)------------------------------
% 0.20/0.30 % (3662251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3662251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3662251)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3662251)Termination reason: Refutation
% 0.20/0.30 % (3662251)Time elapsed: 0.004 s
% 0.20/0.30 % (3662251)Peak memory usage: 12 MB
% 0.20/0.30 % (3662251)Instructions burned: 4 (million)
% 0.20/0.30 % (3662226)Success in time 0.076 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------