%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MSC025^2 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:15:38 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC025^2 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 % Computer : n005.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 11:22:46 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 Running first-order model finding
% 0.10/0.24 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
% 0.21/0.31 % (1550513)Will run a generic schedule for satisfiability detection.
% 0.21/0.31 % (1550522)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1602929958:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.31 % (1550522)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.31 % (1550518)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3700602077_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.31 % (1550521)dis+10_1_sil=32000:sp=arity:random_seed=3278153924:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.31 % (1550520)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3965914070:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.31 % Exception at run slice level
% 0.21/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.31 % (1550519)% WARNING: option uhcvi not known.
% 0.21/0.31 % (1550523)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=936188181:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.31 % (1550521) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1550513-1550521"...
% 0.21/0.31 % (1550522) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1550513-1550522"...
% 0.21/0.31 % (1550519)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2907397548:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.31 % (1550519)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.31 % (1550521)...printing done.
% 0.21/0.31 % (1550519)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.31 % (1550522)...printing done.
% 0.21/0.31 % (1550521)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% 0.21/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.31 thf(func_def_2, type, b1: ($o > $i)).
% 0.21/0.31 thf(func_def_4, type, b2: ($o > $i)).
% 0.21/0.31 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.21/0.31 thf(func_def_8, type, sK0: ($o > $i)).
% 0.21/0.31 thf(func_def_9, type, sK1: $o).
% 0.21/0.31 thf(func_def_10, type, sK2: $o).
% 0.21/0.31 thf(f1,axiom,(
% 0.21/0.31 ! [X0 : $i] : ((X0 = two) | (X0 = one))),
% 0.21/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binarity_exhaust)).
% 0.21/0.31 thf(f2,axiom,(
% 0.21/0.31 (one != two)),
% 0.21/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binarity_distinc)).
% 0.21/0.31 thf(f3,axiom,(
% 0.21/0.31 ! [X0 : $o] : ((~X0 => (((b1 @ X0)) = two)) & (X0 => (((b1 @ X0)) = one)))),
% 0.21/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1)).
% 0.21/0.31 thf(f4,axiom,(
% 0.21/0.31 ! [X0 : $o] : ((~X0 => (((b2 @ X0)) = one)) & (X0 => (((b2 @ X0)) = two)))),
% 0.21/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2)).
% 0.21/0.31 thf(f5,conjecture,(
% 0.21/0.31 ! [X0 : ($o > $i)] : (! [X1 : $o] : (((X0 @ X1)) != ((X0 @ ~X1))) => ((X0 = b2) | (X0 = b1)))),
% 0.21/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal)).
% 0.21/0.31 thf(f6,negated_conjecture,(
% 0.21/0.31 ~ ! [X0 : ($o > $i)] : (! [X1 : $o] : (((X0 @ X1)) != ((X0 @ ~X1))) => ((X0 = b2) | (X0 = b1)))),
% 0.21/0.31 inference(negated_conjecture,[status(cth)],[f5])).
% 0.21/0.31 thf(f7,plain,(
% 0.21/0.31 ! [X0 : $o] : ((~X0 => (((b1 @ X0)) = two)) & (X0 => (((b1 @ X0)) = one)))),
% 0.21/0.31 inference(rectify,[],[f3])).
% 0.21/0.31 thf(f8,plain,(
% 0.21/0.31 ! [X0 : $o] : ((~ ($true = X0) => (two = ((b1 @ X0)))) & (($true = X0) => (one = ((b1 @ X0)))))),
% 0.21/0.31 inference(fool_elimination,[],[f7])).
% 0.21/0.31 thf(f9,plain,(
% 0.21/0.31 ! [X0 : $o] : ((~X0 => (((b2 @ X0)) = one)) & (X0 => (((b2 @ X0)) = two)))),
% 0.21/0.31 inference(rectify,[],[f4])).
% 0.21/0.31 thf(f10,plain,(
% 0.21/0.31 ! [X0 : $o] : ((~ ($true = X0) => (one = ((b2 @ X0)))) & (($true = X0) => (two = ((b2 @ X0)))))),
% 0.21/0.31 inference(fool_elimination,[],[f9])).
% 0.21/0.31 thf(f11,plain,(
% 0.21/0.31 ~ ! [X0 : ($o > $i)] : (! [X1 : $o] : (((X0 @ X1)) != ((X0 @ ~X1))) => ((X0 = b2) | (X0 = b1)))),
% 0.21/0.31 inference(rectify,[],[f6])).
% 0.21/0.31 thf(f12,plain,(
% 0.21/0.31 ~ ! [X0 : ($o > $i)] : (! [X1 : $o] : (((X0 @ X1)) != ((X0 @ (~ X1)))) => ((b2 = X0) | (b1 = X0)))),
% 0.21/0.31 inference(fool_elimination,[],[f11])).
% 0.21/0.31 thf(f13,plain,(
% 0.21/0.31 ! [X0 : $o] : ((($true != X0) => (two = ((b1 @ X0)))) & (($true = X0) => (one = ((b1 @ X0)))))),
% 0.21/0.31 inference(flattening,[],[f8])).
% 0.21/0.31 thf(f14,plain,(
% 0.21/0.31 ! [X0 : $o] : ((($true != X0) => (one = ((b2 @ X0)))) & (($true = X0) => (two = ((b2 @ X0)))))),
% 0.21/0.31 inference(flattening,[],[f10])).
% 0.21/0.31 thf(f15,plain,(
% 0.21/0.31 ! [X0 : $o] : (((two = ((b1 @ X0))) | ($true = X0)) & ((one = ((b1 @ X0))) | ($true != X0)))),
% 0.21/0.31 inference(ennf_transformation,[],[f13])).
% 0.21/0.31 thf(f16,plain,(
% 0.21/0.31 ! [X0 : $o] : (((one = ((b2 @ X0))) | ($true = X0)) & ((two = ((b2 @ X0))) | ($true != X0)))),
% 0.21/0.31 inference(ennf_transformation,[],[f14])).
% 0.21/0.31 thf(f17,plain,(
% 0.21/0.31 ? [X0 : ($o > $i)] : (((b2 != X0) & (b1 != X0)) & ! [X1 : $o] : (((X0 @ X1)) != ((X0 @ (~ X1)))))),
% 0.21/0.31 inference(ennf_transformation,[],[f12])).
% 0.21/0.31 thf(f18,plain,(
% 0.21/0.31 ? [X0 : ($o > $i)] : ((b2 != X0) & (b1 != X0) & ! [X1 : $o] : (((X0 @ X1)) != ((X0 @ (~ X1)))))),
% 0.21/0.31 inference(flattening,[],[f17])).
% 0.21/0.31 thf(f19,plain,(
% 0.21/0.31 (b2 != sK0) & (b1 != sK0) & ! [X1 : $o] : (((sK0 @ X1)) != ((sK0 @ (~ X1))))),
% 0.21/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f18])).
% 0.21/0.31 thf(f20,plain,(
% 0.21/0.31 ( ! [X0 : $i] : ((two = X0) | (one = X0)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f1])).
% 0.21/0.31 thf(f21,plain,(
% 0.21/0.31 (one != two)),
% 0.21/0.31 inference(cnf_transformation,[],[f2])).
% 0.21/0.31 thf(f22,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((one = ((b1 @ X0))) | ($true != X0)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f15])).
% 0.21/0.31 thf(f23,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((two = ((b1 @ X0))) | ($true = X0)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f15])).
% 0.21/0.31 thf(f24,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((two = ((b2 @ X0))) | ($true != X0)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f16])).
% 0.21/0.31 thf(f25,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((one = ((b2 @ X0))) | ($true = X0)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f16])).
% 0.21/0.31 thf(f26,plain,(
% 0.21/0.31 ( ! [X1 : $o] : ((((sK0 @ X1)) != ((sK0 @ (~ X1))))) )),
% 0.21/0.31 inference(cnf_transformation,[],[f19])).
% 0.21/0.31 thf(f27,plain,(
% 0.21/0.31 (b1 != sK0)),
% 0.21/0.31 inference(cnf_transformation,[],[f19])).
% 0.21/0.31 thf(f28,plain,(
% 0.21/0.31 (b2 != sK0)),
% 0.21/0.31 inference(cnf_transformation,[],[f19])).
% 0.21/0.31 thf(f30,definition,(
% 0.21/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.31 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.31 thf(f31,plain,(
% 0.21/0.31 (one = ((b1 @ $true)))),
% 0.21/0.31 inference(equality_resolution,[],[f22])).
% 0.21/0.31 thf(f32,plain,(
% 0.21/0.31 (two = ((b2 @ $true)))),
% 0.21/0.31 inference(equality_resolution,[],[f24])).
% 0.21/0.31 thf(f33,plain,(
% 0.21/0.31 (((b1 @ sK1)) != ((sK0 @ sK1)))),
% 0.21/0.31 inference(negative_extensionality,[],[f27])).
% 0.21/0.31 thf(f34,plain,(
% 0.21/0.31 (((b2 @ sK2)) != ((sK0 @ sK2)))),
% 0.21/0.31 inference(negative_extensionality,[],[f28])).
% 0.21/0.31 thf(f35,plain,(
% 0.21/0.31 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | (one = X1) | (one = X0)) )),
% 0.21/0.31 inference(constrained_superposition,[],[f20,f20])).
% 0.21/0.31 thf(f37,plain,(
% 0.21/0.31 (two != ((b1 @ sK1))) | (one = ((sK0 @ sK1)))),
% 0.21/0.31 inference(constrained_superposition,[],[f33,f20])).
% 0.21/0.31 thf(f51,definition,(
% 0.21/0.31 spl3_3 <=> (one = ((sK0 @ sK1)))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.21/0.31 thf(f53,plain,(
% 0.21/0.31 (one = ((sK0 @ sK1))) | ~spl3_3),
% 0.21/0.31 inference(avatar_component_clause,[],[f51])).
% 0.21/0.31 thf(f55,definition,(
% 0.21/0.31 spl3_4 <=> (two = ((b1 @ sK1)))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.21/0.31 thf(f56,plain,(
% 0.21/0.31 (two = ((b1 @ sK1))) | ~spl3_4),
% 0.21/0.31 inference(avatar_component_clause,[],[f55])).
% 0.21/0.31 thf(f57,plain,(
% 0.21/0.31 (two != ((b1 @ sK1))) | spl3_4),
% 0.21/0.31 inference(avatar_component_clause,[],[f55])).
% 0.21/0.31 thf(f58,plain,(
% 0.21/0.31 spl3_3 | ~spl3_4),
% 0.21/0.31 inference(avatar_split_clause,[],[f37,f55,f51])).
% 0.21/0.31 thf(f63,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((((sK0 @ X0)) != ((sK0 @ $true))) | ($false = ((~ X0)))) )),
% 0.21/0.31 inference(constrained_superposition,[],[f26,f30])).
% 0.21/0.31 thf(f68,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((((sK0 @ X0)) != ((sK0 @ $true))) | ($true = X0)) )),
% 0.21/0.31 inference(not_proxy_clausification,[],[f63])).
% 0.21/0.31 thf(f83,definition,(
% 0.21/0.31 spl3_7 <=> (two = ((b2 @ $true)))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition])).
% 0.21/0.31 thf(f84,plain,(
% 0.21/0.31 (two = ((b2 @ $true))) | ~spl3_7),
% 0.21/0.31 inference(avatar_component_clause,[],[f83])).
% 0.21/0.31 thf(f88,definition,(
% 0.21/0.31 spl3_8 <=> ($false = sK1)),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition])).
% 0.21/0.31 thf(f90,plain,(
% 0.21/0.31 ($false = sK1) | ~spl3_8),
% 0.21/0.31 inference(avatar_component_clause,[],[f88])).
% 0.21/0.31 thf(f104,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((one = ((b1 @ X0))) | ($false = X0)) )),
% 0.21/0.31 inference(constrained_superposition,[],[f31,f30])).
% 0.21/0.31 thf(f114,plain,(
% 0.21/0.31 spl3_7),
% 0.21/0.31 inference(avatar_split_clause,[],[f32,f83])).
% 0.21/0.31 thf(f120,plain,(
% 0.21/0.31 (two != two) | ($true = sK1) | spl3_4),
% 0.21/0.31 inference(constrained_superposition,[],[f57,f23])).
% 0.21/0.31 thf(f121,plain,(
% 0.21/0.31 ($true = sK1) | spl3_4),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f120])).
% 0.21/0.31 thf(f129,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((two != ((sK0 @ $true))) | ($true = X0) | (one = ((sK0 @ X0)))) )),
% 0.21/0.31 inference(constrained_superposition,[],[f68,f20])).
% 0.21/0.31 thf(f137,definition,(
% 0.21/0.31 spl3_12 <=> (one = ((sK0 @ $true)))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition])).
% 0.21/0.31 thf(f139,plain,(
% 0.21/0.31 (one = ((sK0 @ $true))) | ~spl3_12),
% 0.21/0.31 inference(avatar_component_clause,[],[f137])).
% 0.21/0.31 thf(f145,definition,(
% 0.21/0.31 spl3_14 <=> ! [X0 : $o] : (($true = X0) | (one = ((sK0 @ X0))))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition])).
% 0.21/0.31 thf(f146,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((one = ((sK0 @ X0))) | ($true = X0)) ) | ~spl3_14),
% 0.21/0.31 inference(avatar_component_clause,[],[f145])).
% 0.21/0.31 thf(f148,definition,(
% 0.21/0.31 spl3_15 <=> (two = ((sK0 @ $true)))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_15])],[avatar_definition])).
% 0.21/0.31 thf(f150,plain,(
% 0.21/0.31 (two != ((sK0 @ $true))) | spl3_15),
% 0.21/0.31 inference(avatar_component_clause,[],[f148])).
% 0.21/0.31 thf(f151,plain,(
% 0.21/0.31 spl3_14 | ~spl3_15),
% 0.21/0.31 inference(avatar_split_clause,[],[f129,f148,f145])).
% 0.21/0.31 thf(f214,plain,(
% 0.21/0.31 ( ! [X0 : $i] : ((one != ((b1 @ sK1))) | (((sK0 @ sK1)) = X0) | (one = X0)) )),
% 0.21/0.31 inference(constrained_superposition,[],[f33,f35])).
% 0.21/0.31 thf(f247,plain,(
% 0.21/0.31 ( ! [X0 : $i] : ((one != ((b1 @ $true))) | (((sK0 @ sK1)) = X0) | (one = X0)) ) | spl3_4),
% 0.21/0.31 inference(forward_demodulation,[],[f214,f121])).
% 0.21/0.31 thf(f272,plain,(
% 0.21/0.31 ( ! [X0 : $i] : ((((sK0 @ sK1)) = X0) | (one = X0)) ) | spl3_4),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f247,f31])).
% 0.21/0.31 thf(f277,definition,(
% 0.21/0.31 spl3_17 <=> ! [X1 : $i] : (one = X1)),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition])).
% 0.21/0.31 thf(f278,plain,(
% 0.21/0.31 ( ! [X1 : $i] : ((one = X1)) ) | ~spl3_17),
% 0.21/0.31 inference(avatar_component_clause,[],[f277])).
% 0.21/0.31 thf(f293,plain,(
% 0.21/0.31 ( ! [X0 : $i] : ((((sK0 @ $true)) = X0) | (one = X0)) ) | spl3_4),
% 0.21/0.31 inference(forward_demodulation,[],[f272,f121])).
% 0.21/0.31 thf(f295,plain,(
% 0.21/0.31 ( ! [X0 : $i] : ((one = X0) | (one = X0)) ) | (spl3_4 | ~spl3_12)),
% 0.21/0.31 inference(forward_demodulation,[],[f293,f139])).
% 0.21/0.31 thf(f296,plain,(
% 0.21/0.31 ( ! [X0 : $i] : ((one = X0)) ) | (spl3_4 | ~spl3_12)),
% 0.21/0.31 inference(duplicate_literal_removal,[],[f295])).
% 0.21/0.31 thf(f299,plain,(
% 0.21/0.31 spl3_17 | spl3_4 | ~spl3_12),
% 0.21/0.31 inference(avatar_split_clause,[],[f296,f137,f55,f277])).
% 0.21/0.31 thf(f309,plain,(
% 0.21/0.31 ( ! [X0 : $o] : ((one != ((sK0 @ X0)))) ) | ~spl3_17),
% 0.21/0.31 inference(constrained_superposition,[],[f26,f278])).
% 0.21/0.31 thf(f325,plain,(
% 0.21/0.31 $false | ~spl3_17),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f309,f278])).
% 0.21/0.31 thf(f326,plain,(
% 0.21/0.31 ~spl3_17),
% 0.21/0.31 inference(avatar_contradiction_clause,[],[f325])).
% 0.21/0.31 thf(f371,plain,(
% 0.21/0.31 (two != two) | (one = ((sK0 @ $true))) | spl3_15),
% 0.21/0.31 inference(constrained_superposition,[],[f150,f20])).
% 0.21/0.31 thf(f372,plain,(
% 0.21/0.31 (one = ((sK0 @ $true))) | spl3_15),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f371])).
% 0.21/0.31 thf(f415,plain,(
% 0.21/0.31 (one != ((b2 @ sK2))) | ($true = sK2) | ~spl3_14),
% 0.21/0.31 inference(constrained_superposition,[],[f34,f146])).
% 0.21/0.31 thf(f421,plain,(
% 0.21/0.31 ($true = sK2) | ~spl3_14),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f415,f25])).
% 0.21/0.31 thf(f425,plain,(
% 0.21/0.31 spl3_12 | spl3_15),
% 0.21/0.31 inference(avatar_split_clause,[],[f372,f148,f137])).
% 0.21/0.31 thf(f445,plain,(
% 0.21/0.31 (one != ((sK0 @ $true))) | ($true = sK1) | ~spl3_3),
% 0.21/0.31 inference(constrained_superposition,[],[f68,f53])).
% 0.21/0.31 thf(f451,definition,(
% 0.21/0.31 spl3_26 <=> ($true = sK1)),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_26])],[avatar_definition])).
% 0.21/0.31 thf(f453,plain,(
% 0.21/0.31 ($true = sK1) | ~spl3_26),
% 0.21/0.31 inference(avatar_component_clause,[],[f451])).
% 0.21/0.31 thf(f454,plain,(
% 0.21/0.31 spl3_26 | ~spl3_12 | ~spl3_3),
% 0.21/0.31 inference(avatar_split_clause,[],[f445,f51,f137,f451])).
% 0.21/0.31 thf(f462,plain,(
% 0.21/0.31 (one = two) | ($false = sK1) | ~spl3_4),
% 0.21/0.31 inference(constrained_superposition,[],[f104,f56])).
% 0.21/0.31 thf(f463,plain,(
% 0.21/0.31 ($false = sK1) | ~spl3_4),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f462,f21])).
% 0.21/0.31 thf(f468,plain,(
% 0.21/0.31 spl3_8 | ~spl3_4),
% 0.21/0.31 inference(avatar_split_clause,[],[f463,f55,f88])).
% 0.21/0.31 thf(f487,plain,(
% 0.21/0.31 ($true = $false) | (~spl3_8 | ~spl3_26)),
% 0.21/0.31 inference(forward_demodulation,[],[f453,f90])).
% 0.21/0.31 thf(f488,plain,(
% 0.21/0.31 $false | (~spl3_8 | ~spl3_26)),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f487])).
% 0.21/0.31 thf(f489,plain,(
% 0.21/0.31 ~spl3_8 | ~spl3_26),
% 0.21/0.31 inference(avatar_contradiction_clause,[],[f488])).
% 0.21/0.31 thf(f513,plain,(
% 0.21/0.31 (((b2 @ $true)) != ((sK0 @ $true))) | ~spl3_14),
% 0.21/0.31 inference(constrained_superposition,[],[f34,f421])).
% 0.21/0.31 thf(f514,plain,(
% 0.21/0.31 (two != ((sK0 @ $true))) | (~spl3_7 | ~spl3_14)),
% 0.21/0.31 inference(forward_demodulation,[],[f513,f84])).
% 0.21/0.31 thf(f515,plain,(
% 0.21/0.31 ~spl3_15 | ~spl3_7 | ~spl3_14),
% 0.21/0.31 inference(avatar_split_clause,[],[f514,f145,f83,f148])).
% 0.21/0.31 cnf(s2, plain, spl3_3 | ~spl3_4, inference(sat_conversion,[],[f58])).
% 0.21/0.31 cnf(s8, plain, spl3_7, inference(sat_conversion,[],[f114])).
% 0.21/0.31 cnf(s10, plain, spl3_14 | ~spl3_15, inference(sat_conversion,[],[f151])).
% 0.21/0.31 cnf(s15, plain, spl3_4 | ~spl3_12 | spl3_17, inference(sat_conversion,[],[f299])).
% 0.21/0.31 cnf(s20, plain, ~spl3_17, inference(sat_conversion,[],[f326])).
% 0.21/0.31 cnf(s41, plain, spl3_12 | spl3_15, inference(sat_conversion,[],[f425])).
% 0.21/0.31 cnf(s47, plain, ~spl3_3 | ~spl3_12 | spl3_26, inference(sat_conversion,[],[f454])).
% 0.21/0.31 cnf(s49, plain, ~spl3_4 | spl3_8, inference(sat_conversion,[],[f468])).
% 0.21/0.31 cnf(s53, plain, ~spl3_8 | ~spl3_26, inference(sat_conversion,[],[f489])).
% 0.21/0.31 cnf(s60, plain, ~spl3_7 | ~spl3_14 | ~spl3_15, inference(sat_conversion,[],[f515])).
% 0.21/0.31 cnf(s61, plain, spl3_4 | ~spl3_12, inference(rat,[],[s15,s20])).
% 0.21/0.31 cnf(s66, plain, ~spl3_12, inference(rat,[],[s47,s53,s2,s49,s61])).
% 0.21/0.31 cnf(s67, plain, spl3_15, inference(rat,[],[s41,s66])).
% 0.21/0.31 cnf(s71, plain, spl3_14, inference(rat,[],[s10,s67])).
% 0.21/0.31 cnf(s72, plain, $false, inference(rat,[],[s60,s8,s67,s71])).
% 0.21/0.31 thf(f516,plain,(
% 0.21/0.31 $false),
% 0.21/0.31 inference(avatar_sat_refutation,[],[s72])).
% 0.21/0.31 % SZS output end Proof for theBenchmark
% 0.21/0.31 % (1550521)------------------------------
% 0.21/0.31 % (1550521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1550521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1550521)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1550521)Termination reason: Refutation
% 0.21/0.31 % (1550521)Time elapsed: 0.013 s
% 0.21/0.31 % (1550521)Peak memory usage: 13 MB
% 0.21/0.31 % (1550521)Instructions burned: 20 (million)
% 0.21/0.31 % (1550513)Success in time 0.056 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------