%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO039^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:46 AM UTC 2026
% Result : Theorem 0.73s 0.38s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO039^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 % Computer : n010.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 16:24:03 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.28 Running first-order model finding
% 0.09/0.28 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
% 0.27/0.38 % (3076734)Will run a generic schedule for satisfiability detection.
% 0.27/0.38 % (3076740)% WARNING: option uhcvi not known.
% 0.27/0.38 % (3076740)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2561928352:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.27/0.38 % (3076740)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.27/0.38 % (3076740)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.27/0.38 % (3076739)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2325998278_2999 on theBenchmark for (2999ds/0Mi)
% 0.27/0.38 % (3076740)Refutation not found, incomplete strategy
% 0.27/0.38 % (3076740)------------------------------
% 0.27/0.38 % (3076740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.38 % (3076740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.38 % (3076740)CaDiCaL version: 2.1.3
% 0.27/0.38 % (3076740)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.38 % (3076740)Time elapsed: 0.001 s
% 0.27/0.38 % (3076740)Peak memory usage: 12 MB
% 0.27/0.38 % (3076740)Instructions burned: 1 (million)
% 0.27/0.38 % Exception at run slice level
% 0.27/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.27/0.38 % (3076740)------------------------------
% 0.27/0.38 % (3076740)------------------------------
% 0.27/0.38 % (3076741)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2004110:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.27/0.38 % (3076742)dis+10_1_sil=32000:sp=arity:random_seed=1679741358:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.27/0.38 % (3076744)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1926594096:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.27/0.38 % (3076743)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2038727486:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.27/0.38 % (3076745)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1185738449:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.27/0.38 % (3076743)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.27/0.38 % (3076742)Refutation not found, incomplete strategy
% 0.27/0.38 % (3076742)------------------------------
% 0.27/0.38 % (3076742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.38 % (3076742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.38 % (3076744)Refutation not found, incomplete strategy
% 0.27/0.38 % (3076744)------------------------------
% 0.27/0.38 % (3076744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.38 % (3076742)CaDiCaL version: 2.1.3
% 0.27/0.38 % (3076742)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.38 % (3076742)Time elapsed: 0.002 s
% 0.27/0.38 % (3076742)Peak memory usage: 12 MB
% 0.27/0.38 % (3076744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.38 % (3076742)Instructions burned: 1 (million)
% 0.27/0.38 % (3076744)CaDiCaL version: 2.1.3
% 0.27/0.38 % (3076744)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.38 % (3076744)Time elapsed: 0.002 s
% 0.27/0.38 % (3076744)Peak memory usage: 12 MB
% 0.27/0.38 % (3076744)Instructions burned: 1 (million)
% 0.27/0.38 % (3076743)Refutation not found, incomplete strategy
% 0.27/0.38 % (3076743)------------------------------
% 0.27/0.38 % (3076743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.38 % (3076743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.38 % (3076743)CaDiCaL version: 2.1.3
% 0.27/0.38 % (3076743)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.38 % (3076743)Time elapsed: 0.002 s
% 0.27/0.38 % (3076743)Peak memory usage: 12 MB
% 0.27/0.38 % (3076743)Instructions burned: 1 (million)
% 0.27/0.38 % (3076745)Refutation not found, incomplete strategy
% 0.27/0.38 % (3076745)------------------------------
% 0.27/0.38 % (3076745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.38 % (3076745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.38 % (3076745)CaDiCaL version: 2.1.3
% 0.27/0.38 % (3076745)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.38 % (3076745)Time elapsed: 0.002 s
% 0.27/0.38 % (3076745)Peak memory usage: 12 MB
% 0.27/0.38 % (3076745)Instructions burned: 1 (million)
% 0.27/0.38 % (3076742)------------------------------
% 0.27/0.38 % (3076742)------------------------------
% 0.27/0.38 % (3076744)------------------------------
% 0.27/0.38 % (3076744)------------------------------
% 0.27/0.38 % (3076743)------------------------------
% 0.27/0.38 % (3076743)------------------------------
% 0.27/0.38 % (3076741)Refutation not found, incomplete strategy
% 0.27/0.38 % (3076741)------------------------------
% 0.27/0.38 % (3076741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.38 % (3076741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.38 % (3076741)CaDiCaL version: 2.1.3
% 0.27/0.38 % (3076741)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.38 % (3076741)Time elapsed: 0.004 s
% 0.27/0.38 % (3076741)Peak memory usage: 12 MB
% 0.27/0.38 % (3076741)Instructions burned: 2 (million)
% 0.27/0.38 % (3076745)------------------------------
% 0.27/0.38 % (3076745)------------------------------
% 0.27/0.38 % (3076741)------------------------------
% 0.27/0.38 % (3076741)------------------------------
% 0.27/0.38 % (3076749)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=970489809:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.27/0.38 % (3076749)Refutation not found, incomplete strategy
% 0.27/0.38 % (3076749)------------------------------
% 0.27/0.38 % (3076749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.38 % (3076749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.38 % (3076749)CaDiCaL version: 2.1.3
% 0.27/0.38 % (3076749)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.38 % (3076749)Time elapsed: 0.001 s
% 0.27/0.38 % (3076749)Peak memory usage: 12 MB
% 0.27/0.38 % (3076749)Instructions burned: 1 (million)
% 0.27/0.38 % (3076749)------------------------------
% 0.27/0.38 % (3076749)------------------------------
% 0.27/0.38 % (3076748)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1400291037:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.27/0.38 % Exception at run slice level
% 0.27/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.27/0.38 % (3076762)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1891441349:i=889:ins=1_2999 on theBenchmark for (2999ds/889Mi)
% 0.27/0.38 % Exception at run slice level
% 0.27/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.27/0.38 % (3076756)ott-21_1_sil=16000:fs=off:random_seed=1097502785:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.27/0.38 % (3076755)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=1901318820:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.27/0.38 % (3076755)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.27/0.38 % (3076759)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2158721010:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 0.27/0.38 % (3076755)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.27/0.38 % (3076758)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2238017744:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.27/0.38 % (3076757)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3461253779:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.27/0.38 % Exception at run slice level
% 0.27/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.27/0.38 % (3076755)Refutation not found, incomplete strategy
% 0.27/0.38 % (3076755)------------------------------
% 0.27/0.38 % (3076755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.38 % (3076755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.38 % (3076755)CaDiCaL version: 2.1.3
% 0.27/0.38 % (3076755)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.38 % (3076755)Time elapsed: 0.002 s
% 0.27/0.38 % (3076755)Peak memory usage: 12 MB
% 0.27/0.38 % (3076755)Instructions burned: 1 (million)
% 0.27/0.38 % (3076755)------------------------------
% 0.27/0.38 % (3076755)------------------------------
% 0.27/0.38 % (3076759) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3076734-3076759"...
% 0.73/0.38 % (3076757)Refutation not found, incomplete strategy
% 0.73/0.38 % (3076757)------------------------------
% 0.73/0.38 % (3076757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.38 % (3076757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.38 % (3076757)CaDiCaL version: 2.1.3
% 0.73/0.38 % (3076757)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.38 % (3076757)Time elapsed: 0.005 s
% 0.73/0.38 % (3076757)Peak memory usage: 12 MB
% 0.73/0.38 % (3076757)Instructions burned: 3 (million)
% 0.73/0.38 % (3076759)...printing done.
% 0.73/0.38 % (3076763)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=4212437282: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)
% 0.73/0.38 % (3076763)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.73/0.38 % (3076757)------------------------------
% 0.73/0.38 % (3076757)------------------------------
% 0.73/0.38 % (3076765)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1790780422:i=879:kws=inv_precedence:fsr=off_2999 on theBenchmark for (2999ds/879Mi)
% 0.73/0.38 % (3076765)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.73/0.38 % (3076763)Refutation not found, incomplete strategy
% 0.73/0.38 % (3076763)------------------------------
% 0.73/0.38 % (3076763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.38 % (3076763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.38 % (3076763)CaDiCaL version: 2.1.3
% 0.73/0.38 % (3076763)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.38 % (3076763)Time elapsed: 0.002 s
% 0.73/0.38 % (3076763)Peak memory usage: 13 MB
% 0.73/0.38 % (3076763)Instructions burned: 1 (million)
% 0.73/0.38 % (3076765)Refutation not found, incomplete strategy
% 0.73/0.38 % (3076765)------------------------------
% 0.73/0.38 % (3076765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.38 % (3076765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.38 % (3076765)CaDiCaL version: 2.1.3
% 0.73/0.38 % (3076765)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.38 % (3076765)Time elapsed: 0.001 s
% 0.73/0.38 % (3076765)Peak memory usage: 12 MB
% 0.73/0.38 % (3076765)Instructions burned: 2 (million)
% 0.73/0.38 % (3076765)------------------------------
% 0.73/0.38 % (3076765)------------------------------
% 0.73/0.38 % (3076763)------------------------------
% 0.73/0.38 % (3076763)------------------------------
% 0.73/0.38 % (3076759)Refutation found. Thanks to Tanya!
% 0.73/0.38 % SZS status Theorem for theBenchmark
% 0.73/0.38 % SZS output start Proof for theBenchmark
% 0.73/0.38 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.73/0.38 thf(func_def_0, type, h: ($o > $i)).
% 0.73/0.38 thf(func_def_4, type, vNOT: ($o > $o)).
% 0.73/0.38 thf(func_def_5, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.73/0.38 thf(func_def_7, type, sF1: $o).
% 0.73/0.38 thf(func_def_9, type, sF3: $o).
% 0.73/0.38 thf(f1,conjecture,(
% 0.73/0.38 (((h @ (((h @ $false)) = ((h @ ~$false))))) = ((h @ $false)))),
% 0.73/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',1)).
% 0.73/0.38 thf(f2,negated_conjecture,(
% 0.73/0.38 ~ (((h @ (((h @ $false)) = ((h @ ~$false))))) = ((h @ $false)))),
% 0.73/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.73/0.38 thf(f3,plain,(
% 0.73/0.38 ~ (((h @ (((h @ $false)) = ((h @ ~$false))))) = ((h @ $false)))),
% 0.73/0.38 inference(rectify,[],[f2])).
% 0.73/0.38 thf(f4,plain,(
% 0.73/0.38 ~ (((h @ $false)) = ((h @ ((h @ $false) = (h @ (~ $false))))))),
% 0.73/0.38 inference(fool_elimination,[],[f3])).
% 0.73/0.38 thf(f5,plain,(
% 0.73/0.38 (((h @ $false)) != ((h @ ((h @ $false) = (h @ (~ $false))))))),
% 0.73/0.38 inference(flattening,[],[f4])).
% 0.73/0.38 thf(f6,plain,(
% 0.73/0.38 (((h @ $false)) != ((h @ ((h @ $false) = (h @ (~ $false))))))),
% 0.73/0.38 inference(cnf_transformation,[],[f5])).
% 0.73/0.38 thf(f8,definition,(
% 0.73/0.38 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.73/0.38 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.73/0.38 thf(f9,definition,(
% 0.73/0.38 (sF0 = ((h @ $false)))),
% 0.73/0.38 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 0.73/0.38 thf(f10,plain,(
% 0.73/0.38 (((h @ $false)) = sF0)),
% 0.73/0.38 inference(reorient_equations,[],[f9])).
% 0.73/0.38 thf(f11,definition,(
% 0.73/0.38 (sF1 = ((~ $false)))),
% 0.73/0.38 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 0.73/0.38 thf(f12,plain,(
% 0.73/0.38 (((~ $false)) = sF1)),
% 0.73/0.38 inference(reorient_equations,[],[f11])).
% 0.73/0.38 thf(f13,definition,(
% 0.73/0.38 (sF2 = ((h @ sF1)))),
% 0.73/0.38 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.73/0.38 thf(f14,plain,(
% 0.73/0.38 (((h @ sF1)) = sF2)),
% 0.73/0.38 inference(reorient_equations,[],[f13])).
% 0.73/0.38 thf(f15,definition,(
% 0.73/0.38 (sF3 = ((sF0 = sF2)))),
% 0.73/0.38 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.73/0.38 thf(f16,plain,(
% 0.73/0.38 (((sF0 = sF2)) = sF3)),
% 0.73/0.38 inference(reorient_equations,[],[f15])).
% 0.73/0.38 thf(f17,definition,(
% 0.73/0.38 (sF4 = ((h @ sF3)))),
% 0.73/0.38 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.73/0.38 thf(f18,plain,(
% 0.73/0.38 (((h @ sF3)) = sF4)),
% 0.73/0.38 inference(reorient_equations,[],[f17])).
% 0.73/0.38 thf(f19,plain,(
% 0.73/0.38 (sF0 != sF4)),
% 0.73/0.38 inference(definition_folding,[],[f6,f18,f16,f14,f12,f10,f10])).
% 0.73/0.38 thf(f21,plain,(
% 0.73/0.38 ($false = ((~ $false))) | ($true = sF1)),
% 0.73/0.38 inference(iff_proxy_clausification,[],[f12])).
% 0.73/0.38 thf(f22,plain,(
% 0.73/0.38 ($false = $true) | ($true = sF1)),
% 0.73/0.38 inference(not_proxy_clausification,[],[f21])).
% 0.73/0.38 thf(f23,plain,(
% 0.73/0.38 ($true = sF1)),
% 0.73/0.38 inference(trivial_inequality_removal,[],[f22])).
% 0.73/0.38 thf(f25,plain,(
% 0.73/0.38 ($true = ((sF0 = sF2))) | ($false = sF3)),
% 0.73/0.38 inference(iff_proxy_clausification,[],[f16])).
% 0.73/0.38 thf(f26,plain,(
% 0.73/0.38 ($false = ((sF0 = sF2))) | ($true = sF3)),
% 0.73/0.38 inference(iff_proxy_clausification,[],[f16])).
% 0.73/0.38 thf(f27,plain,(
% 0.73/0.38 (sF0 != sF2) | ($true = sF3)),
% 0.73/0.38 inference(equality_proxy_clausification,[],[f26])).
% 0.73/0.38 thf(f28,plain,(
% 0.73/0.38 (sF0 = sF2) | ($false = sF3)),
% 0.73/0.38 inference(equality_proxy_clausification,[],[f25])).
% 0.73/0.38 thf(f29,plain,(
% 0.73/0.38 (sF2 = ((h @ $true)))),
% 0.73/0.38 inference(forward_demodulation,[],[f14,f23])).
% 0.73/0.38 thf(f31,definition,(
% 0.73/0.38 spl5_1 <=> ($true = sF3)),
% 0.73/0.38 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.73/0.38 thf(f33,plain,(
% 0.73/0.38 ($true = sF3) | ~spl5_1),
% 0.73/0.38 inference(avatar_component_clause,[],[f31])).
% 0.73/0.38 thf(f35,definition,(
% 0.73/0.38 spl5_2 <=> (sF0 = sF2)),
% 0.73/0.38 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.73/0.38 thf(f36,plain,(
% 0.73/0.38 (sF0 = sF2) | ~spl5_2),
% 0.73/0.38 inference(avatar_component_clause,[],[f35])).
% 0.73/0.38 thf(f38,plain,(
% 0.73/0.38 spl5_1 | ~spl5_2),
% 0.73/0.38 inference(avatar_split_clause,[],[f27,f35,f31])).
% 0.73/0.38 thf(f40,definition,(
% 0.73/0.38 spl5_3 <=> ($false = sF3)),
% 0.73/0.38 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.73/0.38 thf(f42,plain,(
% 0.73/0.38 ($false = sF3) | ~spl5_3),
% 0.73/0.38 inference(avatar_component_clause,[],[f40])).
% 0.73/0.38 thf(f43,plain,(
% 0.73/0.38 spl5_3 | spl5_2),
% 0.73/0.38 inference(avatar_split_clause,[],[f28,f35,f40])).
% 0.73/0.38 thf(f53,plain,(
% 0.73/0.38 (sF4 = ((h @ $true))) | ($false = sF3)),
% 0.73/0.38 inference(constrained_superposition,[],[f18,f8])).
% 0.73/0.38 thf(f54,plain,(
% 0.73/0.38 (((h @ $false)) = sF4) | ~spl5_3),
% 0.73/0.38 inference(constrained_superposition,[],[f18,f42])).
% 0.73/0.38 thf(f55,plain,(
% 0.73/0.38 (sF0 = sF4) | ~spl5_3),
% 0.73/0.38 inference(forward_demodulation,[],[f54,f10])).
% 0.73/0.38 thf(f56,plain,(
% 0.73/0.38 $false | ~spl5_3),
% 0.73/0.38 inference(forward_subsumption_resolution,[],[f55,f19])).
% 0.73/0.38 thf(f57,plain,(
% 0.73/0.38 ~spl5_3),
% 0.73/0.38 inference(avatar_contradiction_clause,[],[f56])).
% 0.73/0.38 thf(f59,plain,(
% 0.73/0.38 (sF2 = sF4) | ($false = sF3)),
% 0.73/0.38 inference(forward_demodulation,[],[f53,f29])).
% 0.73/0.38 thf(f60,plain,(
% 0.73/0.38 ($false = $true) | (sF2 = sF4) | ~spl5_1),
% 0.73/0.38 inference(forward_demodulation,[],[f59,f33])).
% 0.73/0.38 thf(f61,plain,(
% 0.73/0.38 (sF2 = sF4) | ~spl5_1),
% 0.73/0.38 inference(trivial_inequality_removal,[],[f60])).
% 0.73/0.38 thf(f65,plain,(
% 0.73/0.38 (sF0 != sF2) | ~spl5_1),
% 0.73/0.38 inference(constrained_superposition,[],[f19,f61])).
% 0.73/0.38 thf(f66,plain,(
% 0.73/0.38 $false | (~spl5_1 | ~spl5_2)),
% 0.73/0.38 inference(forward_subsumption_resolution,[],[f65,f36])).
% 0.73/0.38 thf(f67,plain,(
% 0.73/0.38 ~spl5_1 | ~spl5_2),
% 0.73/0.38 inference(avatar_contradiction_clause,[],[f66])).
% 0.73/0.38 cnf(s1, plain, spl5_1 | ~spl5_2, inference(sat_conversion,[],[f38])).
% 0.73/0.38 cnf(s2, plain, spl5_2 | spl5_3, inference(sat_conversion,[],[f43])).
% 0.73/0.38 cnf(s3, plain, ~spl5_3, inference(sat_conversion,[],[f57])).
% 0.73/0.38 cnf(s4, plain, ~spl5_1 | ~spl5_2, inference(sat_conversion,[],[f67])).
% 0.73/0.38 cnf(s5, plain, spl5_2, inference(rat,[],[s2,s3])).
% 0.73/0.38 cnf(s6, plain, ~spl5_1, inference(rat,[],[s4,s5])).
% 0.73/0.38 cnf(s7, plain, $false, inference(rat,[],[s1,s5,s6])).
% 0.73/0.38 thf(f68,plain,(
% 0.73/0.38 $false),
% 0.73/0.38 inference(avatar_sat_refutation,[],[s7])).
% 0.73/0.38 % SZS output end Proof for theBenchmark
% 0.73/0.38 % (3076759)------------------------------
% 0.73/0.38 % (3076759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.38 % (3076759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.38 % (3076759)CaDiCaL version: 2.1.3
% 0.73/0.38 % (3076759)Termination reason: Refutation
% 0.73/0.38 % (3076759)Time elapsed: 0.005 s
% 0.73/0.38 % (3076759)Peak memory usage: 12 MB
% 0.73/0.38 % (3076759)Instructions burned: 3 (million)
% 0.73/0.38 % (3076734)Success in time 0.083 s
% 0.73/0.38 % Vampire exiting
%------------------------------------------------------------------------------