%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO310^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:49:43 AM UTC 2026
% Result : Theorem 0.11s 0.26s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO310^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.17 % Computer : n009.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 16:45:00 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.20 Running first-order model finding
% 0.11/0.20 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
% 0.11/0.26 % (50307)Will run a generic schedule for satisfiability detection.
% 0.11/0.26 % (50312)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2319503888_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.26 % Exception at run slice level
% 0.11/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.26 % (50313)% WARNING: option uhcvi not known.
% 0.11/0.26 % (50313)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=598094369:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.26 % (50315)dis+10_1_sil=32000:sp=arity:random_seed=189991183:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.26 % (50314)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3197789455:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.26 % (50313)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.26 % (50313)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.11/0.26 % (50316)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2100862061:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.26 % (50316)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.26 % (50320)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=22359832:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.11/0.26 % Exception at run slice level
% 0.11/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.26 % (50315) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-50307-50315"...
% 0.11/0.26 % (50313) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-50307-50313"...
% 0.11/0.26 % (50314) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-50307-50314"...
% 0.11/0.26 % (50316) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-50307-50316"...
% 0.11/0.26 % (50318)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3019029806:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.26 % (50315)...printing done.
% 0.11/0.26 % (50314)...printing done.
% 0.11/0.26 % (50313)...printing done.
% 0.11/0.26 % (50316)...printing done.
% 0.11/0.26 % (50313)Refutation found. Thanks to Tanya!
% 0.11/0.26 % SZS status Theorem for theBenchmark
% 0.11/0.26 % SZS output start Proof for theBenchmark
% 0.11/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.11/0.26 thf(func_def_3, type, vIMP: ($o > $o > $o)).
% 0.11/0.26 thf(func_def_4, type, sK0: ($o > $o)).
% 0.11/0.26 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.11/0.26 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.11/0.26 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.11/0.26 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.11/0.26 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.11/0.26 thf(func_def_11, type, vOR: ($o > $o > $o)).
% 0.11/0.26 thf(func_def_12, type, vAND: ($o > $o > $o)).
% 0.11/0.26 thf(f1,conjecture,(
% 0.11/0.26 ! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true)) & ? [X0 : ($o > $o > $o)] : (~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & (X0 @ $false @ $false) & (X0 @ $true @ $true))),
% 0.11/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cOMEGA_EXAMPLE)).
% 0.11/0.26 thf(f2,negated_conjecture,(
% 0.11/0.26 ~(! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true)) & ? [X0 : ($o > $o > $o)] : (~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & (X0 @ $false @ $false) & (X0 @ $true @ $true)))),
% 0.11/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.11/0.26 thf(f3,plain,(
% 0.11/0.26 ~(! [X0 : ($o > $o)] : ((X0 @ $true) <=> (X0 @ $true => $true)) & ? [X1 : ($o > $o > $o)] : (~(X1 @ $true @ $false) & ~(X1 @ $false @ $true) & (X1 @ $false @ $false) & (X1 @ $true @ $true)))),
% 0.11/0.26 inference(rectify,[],[f2])).
% 0.11/0.26 thf(f4,plain,(
% 0.11/0.26 ~(! [X0 : ($o > $o)] : (((X0 @ $true)) = ((X0 @ ($true => $true)))) & ? [X1 : ($o > $o > $o)] : (~ ($true = ((X1 @ $true @ $false))) & ~ ($true = ((X1 @ $false @ $true))) & ($true = ((X1 @ $false @ $false))) & ($true = ((X1 @ $true @ $true)))))),
% 0.11/0.26 inference(fool_elimination,[],[f3])).
% 0.11/0.26 thf(f5,plain,(
% 0.11/0.26 ~(! [X0 : ($o > $o)] : (((X0 @ $true)) = ((X0 @ ($true => $true)))) & ? [X1 : ($o > $o > $o)] : (($true != ((X1 @ $true @ $false))) & ($true != ((X1 @ $false @ $true))) & ($true = ((X1 @ $false @ $false))) & ($true = ((X1 @ $true @ $true)))))),
% 0.11/0.26 inference(flattening,[],[f4])).
% 0.11/0.26 thf(f6,plain,(
% 0.11/0.26 ? [X0 : ($o > $o)] : (((X0 @ $true)) != ((X0 @ ($true => $true)))) | ! [X1 : ($o > $o > $o)] : (($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))))),
% 0.11/0.26 inference(ennf_transformation,[],[f5])).
% 0.11/0.26 thf(f7,plain,(
% 0.11/0.26 (((sK0 @ $true)) != ((sK0 @ ($true => $true)))) | ! [X1 : ($o > $o > $o)] : (($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))))),
% 0.11/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6])).
% 0.11/0.26 thf(f8,plain,(
% 0.11/0.26 ( ! [X1 : ($o > $o > $o)] : ((((sK0 @ $true)) != ((sK0 @ ($true => $true)))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true)))) )),
% 0.11/0.26 inference(cnf_transformation,[],[f7])).
% 0.11/0.26 thf(f11,plain,(
% 0.11/0.26 ( ! [X1 : ($o > $o > $o)] : (($true = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))) | ($true = ((sK0 @ ($true => $true))))) )),
% 0.11/0.26 inference(xor_proxy_clausification,[],[f8])).
% 0.11/0.26 thf(f12,plain,(
% 0.11/0.26 ( ! [X1 : ($o > $o > $o)] : (($false = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))) | ($false = ((sK0 @ ($true => $true))))) )),
% 0.11/0.26 inference(xor_proxy_clausification,[],[f8])).
% 0.11/0.26 thf(f13,plain,(
% 0.11/0.26 ( ! [X1 : ($o > $o > $o)] : (($false = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))) | ($false = ((sK0 @ $true)))) )),
% 0.11/0.26 inference(boolean_simplification,[],[f12])).
% 0.11/0.26 thf(f14,plain,(
% 0.11/0.26 ( ! [X1 : ($o > $o > $o)] : (($false = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true)))) )),
% 0.11/0.26 inference(duplicate_literal_removal,[],[f13])).
% 0.11/0.26 thf(f15,plain,(
% 0.11/0.26 ( ! [X1 : ($o > $o > $o)] : (($true = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))) | ($true = ((sK0 @ $true)))) )),
% 0.11/0.26 inference(boolean_simplification,[],[f11])).
% 0.11/0.26 thf(f16,plain,(
% 0.11/0.26 ( ! [X1 : ($o > $o > $o)] : (($true = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true)))) )),
% 0.11/0.26 inference(duplicate_literal_removal,[],[f15])).
% 0.11/0.26 thf(f18,definition,(
% 0.11/0.26 spl1_1 <=> ! [X1 : ($o > $o > $o)] : (($true = ((X1 @ $true @ $false))) | ($true != ((X1 @ $true @ $true))) | ($true != ((X1 @ $false @ $false))) | ($true = ((X1 @ $false @ $true))))),
% 0.11/0.26 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.11/0.26 thf(f19,plain,(
% 0.11/0.26 ( ! [X1 : ($o > $o > $o)] : (($true != ((X1 @ $true @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true != ((X1 @ $false @ $false))) | ($true = ((X1 @ $false @ $true)))) ) | ~spl1_1),
% 0.11/0.26 inference(avatar_component_clause,[],[f18])).
% 0.11/0.26 thf(f21,definition,(
% 0.11/0.26 spl1_2 <=> ($false = ((sK0 @ $true)))),
% 0.11/0.26 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.11/0.26 thf(f23,plain,(
% 0.11/0.26 ($false = ((sK0 @ $true))) | ~spl1_2),
% 0.11/0.26 inference(avatar_component_clause,[],[f21])).
% 0.11/0.26 thf(f24,plain,(
% 0.11/0.26 spl1_1 | spl1_2),
% 0.11/0.26 inference(avatar_split_clause,[],[f14,f21,f18])).
% 0.11/0.26 thf(f26,definition,(
% 0.11/0.26 spl1_3 <=> ($true = ((sK0 @ $true)))),
% 0.11/0.26 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.11/0.26 thf(f28,plain,(
% 0.11/0.26 ($true = ((sK0 @ $true))) | ~spl1_3),
% 0.11/0.26 inference(avatar_component_clause,[],[f26])).
% 0.11/0.26 thf(f29,plain,(
% 0.11/0.26 spl1_1 | spl1_3),
% 0.11/0.26 inference(avatar_split_clause,[],[f16,f26,f18])).
% 0.11/0.26 thf(f40,plain,(
% 0.11/0.26 ($true = $false) | (~spl1_2 | ~spl1_3)),
% 0.11/0.26 inference(forward_demodulation,[],[f28,f23])).
% 0.11/0.26 thf(f41,plain,(
% 0.11/0.26 $false | (~spl1_2 | ~spl1_3)),
% 0.11/0.26 inference(trivial_inequality_removal,[],[f40])).
% 0.11/0.26 thf(f42,plain,(
% 0.11/0.26 ~spl1_2 | ~spl1_3),
% 0.11/0.26 inference(avatar_contradiction_clause,[],[f41])).
% 0.11/0.26 thf(f52,plain,(
% 0.11/0.26 ($true != (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 = Y1)))) @ $true @ $true))) | ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 = Y1)))) @ $true @ $false))) | ($true != (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 = Y1)))) @ $false @ $false))) | ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 = Y1)))) @ $false @ $true))) | ~spl1_1),
% 0.11/0.26 inference(primitive_instantiation,[],[f19])).
% 0.11/0.26 thf(f182,plain,(
% 0.11/0.26 ($true != (($true = $true))) | ($true = (($true = $false))) | ($true != (($false = $false))) | ($true = (($false = $true))) | ~spl1_1),
% 0.11/0.26 inference(beta-eta_normalization,[],[f52])).
% 0.11/0.26 thf(f183,plain,(
% 0.11/0.26 ($true != $true) | ($true = (($true = $false))) | ($true != (($false = $false))) | ($true = (($false = $true))) | ~spl1_1),
% 0.11/0.26 inference(equality_proxy_clausification,[],[f182])).
% 0.11/0.26 thf(f184,plain,(
% 0.11/0.26 ($true != $true) | ($true = $false) | ($true != (($false = $false))) | ($true = (($false = $true))) | ~spl1_1),
% 0.11/0.26 inference(equality_proxy_clausification,[],[f183])).
% 0.11/0.26 thf(f185,plain,(
% 0.11/0.26 ($true != $true) | ($true = $false) | ($false != $false) | ($true = (($false = $true))) | ~spl1_1),
% 0.11/0.26 inference(equality_proxy_clausification,[],[f184])).
% 0.11/0.26 thf(f186,plain,(
% 0.11/0.26 ($true != $true) | ($true = $false) | ($false != $false) | ($true = $false) | ~spl1_1),
% 0.11/0.26 inference(equality_proxy_clausification,[],[f185])).
% 0.11/0.26 thf(f187,plain,(
% 0.11/0.26 ($true != $true) | ($true = $false) | ($false != $false) | ~spl1_1),
% 0.11/0.26 inference(duplicate_literal_removal,[],[f186])).
% 0.11/0.26 thf(f188,plain,(
% 0.11/0.26 $false | ~spl1_1),
% 0.11/0.26 inference(trivial_inequality_removal,[],[f187])).
% 0.11/0.26 thf(f189,plain,(
% 0.11/0.26 ~spl1_1),
% 0.11/0.26 inference(avatar_contradiction_clause,[],[f188])).
% 0.11/0.26 cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f24])).
% 0.11/0.26 cnf(s2, plain, spl1_1 | spl1_3, inference(sat_conversion,[],[f29])).
% 0.11/0.26 cnf(s3, plain, ~spl1_2 | ~spl1_3, inference(sat_conversion,[],[f42])).
% 0.11/0.26 cnf(s4, plain, ~spl1_1, inference(sat_conversion,[],[f189])).
% 0.11/0.26 cnf(s5, plain, spl1_3, inference(rat,[],[s2,s4])).
% 0.11/0.26 cnf(s6, plain, ~spl1_2, inference(rat,[],[s3,s5])).
% 0.11/0.26 cnf(s7, plain, $false, inference(rat,[],[s1,s6,s4])).
% 0.11/0.26 thf(f192,plain,(
% 0.11/0.26 $false),
% 0.11/0.26 inference(avatar_sat_refutation,[],[s7])).
% 0.11/0.26 % SZS output end Proof for theBenchmark
% 0.11/0.26 % (50313)------------------------------
% 0.11/0.26 % (50313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.26 % (50313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.26 % (50313)CaDiCaL version: 2.1.3
% 0.11/0.26 % (50313)Termination reason: Refutation
% 0.11/0.26 % (50313)Time elapsed: 0.005 s
% 0.11/0.26 % (50313)Peak memory usage: 12 MB
% 0.11/0.26 % (50313)Instructions burned: 7 (million)
% 0.11/0.26 % (50307)Success in time 0.046 s
% 0.11/0.26 % Vampire exiting
%------------------------------------------------------------------------------