%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO301^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:49:41 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO301^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n009.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 16:44:30 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.21 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
% 0.10/0.26 % (48401)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (48413)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=430671330_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.26 % Exception at run slice level
% 0.10/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.26 % (48414)% WARNING: option uhcvi not known.
% 0.10/0.26 % (48414)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1335152668:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.26 % (48414)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (48415)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=614023216:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.26 % (48416)dis+10_1_sil=32000:sp=arity:random_seed=1669875449:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.26 % (48414)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.26 % (48417)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=220466978:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.26 % (48418)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=305861939:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.26 % (48419)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3928057977:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.26 % (48417)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (48422)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2193421924:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.10/0.26 % Exception at run slice level
% 0.10/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.26 % (48416) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-48401-48416"...
% 0.10/0.26 % (48419) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-48401-48419"...
% 0.10/0.26 % (48418) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-48401-48418"...
% 0.10/0.26 % (48417) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-48401-48417"...
% 0.10/0.26 % (48415) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-48401-48415"...
% 0.10/0.26 % (48416)...printing done.
% 0.10/0.26 % (48419)...printing done.
% 0.10/0.26 % (48418)...printing done.
% 0.10/0.26 % (48417)...printing done.
% 0.10/0.26 % (48416)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% 0.10/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.26 thf(func_def_0, type, f: ($i > $i)).
% 0.10/0.26 thf(func_def_1, type, cP: ($i > $o)).
% 0.10/0.26 thf(func_def_6, type, sK0: (($i > $o) > $i)).
% 0.10/0.26 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.10/0.26 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.10/0.26 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.10/0.26 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.10/0.26 thf(f1,conjecture,(
% 0.10/0.26 (cP @ (f @ b)) => ? [X0 : $i,X1 : ($i > $o)] : ((X1 @ (f @ X0)) & ! [X2 : $i] : ((X1 @ X2) => (cP @ X2)))),
% 0.10/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE5)).
% 0.10/0.26 thf(f2,negated_conjecture,(
% 0.10/0.26 ~((cP @ (f @ b)) => ? [X0 : $i,X1 : ($i > $o)] : ((X1 @ (f @ X0)) & ! [X2 : $i] : ((X1 @ X2) => (cP @ X2))))),
% 0.10/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.10/0.26 thf(f3,plain,(
% 0.10/0.26 ~((cP @ (f @ b)) => ? [X0 : $i,X1 : ($i > $o)] : ((X1 @ (f @ X0)) & ! [X2 : $i] : ((X1 @ X2) => (cP @ X2))))),
% 0.10/0.26 inference(rectify,[],[f2])).
% 0.10/0.26 thf(f4,plain,(
% 0.10/0.26 ~((((cP @ (f @ b))) = $true) => ? [X0 : $i,X1 : ($i > $o)] : ((((X1 @ (f @ X0))) = $true) & ! [X2 : $i] : ((((X1 @ X2)) = $true) => (((cP @ X2)) = $true))))),
% 0.10/0.26 inference(fool_elimination,[],[f3])).
% 0.10/0.26 thf(f5,plain,(
% 0.10/0.26 ! [X0 : $i,X1 : ($i > $o)] : ((((X1 @ (f @ X0))) != $true) | ? [X2 : $i] : ((((cP @ X2)) != $true) & (((X1 @ X2)) = $true))) & (((cP @ (f @ b))) = $true)),
% 0.10/0.26 inference(ennf_transformation,[],[f4])).
% 0.10/0.26 thf(f6,plain,(
% 0.10/0.26 ! [X0 : $i,X1 : ($i > $o)] : ((((X1 @ (f @ X0))) != $true) | (($true != ((cP @ (sK0 @ X1)))) & ($true = ((X1 @ (sK0 @ X1)))))) & (((cP @ (f @ b))) = $true)),
% 0.10/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1)],[f5])).
% 0.10/0.26 thf(f7,plain,(
% 0.10/0.26 (((cP @ (f @ b))) = $true)),
% 0.10/0.26 inference(cnf_transformation,[],[f6])).
% 0.10/0.26 thf(f8,plain,(
% 0.10/0.26 ( ! [X0 : $i,X1 : ($i > $o)] : ((((X1 @ (f @ X0))) != $true) | ($true = ((X1 @ (sK0 @ X1))))) )),
% 0.10/0.26 inference(cnf_transformation,[],[f6])).
% 0.10/0.26 thf(f9,plain,(
% 0.10/0.26 ( ! [X0 : $i,X1 : ($i > $o)] : (($true != ((cP @ (sK0 @ X1)))) | (((X1 @ (f @ X0))) != $true)) )),
% 0.10/0.26 inference(cnf_transformation,[],[f6])).
% 0.10/0.26 thf(f16,plain,(
% 0.10/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (b != X0)) )),
% 0.10/0.26 inference(constrained_superposition,[],[f8,f7])).
% 0.10/0.26 thf(f22,plain,(
% 0.10/0.26 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (b != X0)) )),
% 0.10/0.26 inference(trivial_inequality_removal,[],[f16])).
% 0.10/0.26 thf(f23,plain,(
% 0.10/0.26 ( ! [X0 : $i] : (($true = ((cP @ (sK0 @ cP)))) | (b != X0)) )),
% 0.10/0.26 inference(beta-eta_normalization,[],[f22])).
% 0.10/0.26 thf(f30,definition,(
% 0.10/0.26 spl1_1 <=> ! [X0 : $i] : (b != X0)),
% 0.10/0.26 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.10/0.26 thf(f31,plain,(
% 0.10/0.26 ( ! [X0 : $i] : ((b != X0)) ) | ~spl1_1),
% 0.10/0.26 inference(avatar_component_clause,[],[f30])).
% 0.10/0.26 thf(f33,definition,(
% 0.10/0.26 spl1_2 <=> ($true = ((cP @ (sK0 @ cP))))),
% 0.10/0.26 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.10/0.26 thf(f35,plain,(
% 0.10/0.26 ($true = ((cP @ (sK0 @ cP)))) | ~spl1_2),
% 0.10/0.26 inference(avatar_component_clause,[],[f33])).
% 0.10/0.26 thf(f36,plain,(
% 0.10/0.26 spl1_1 | spl1_2),
% 0.10/0.26 inference(avatar_split_clause,[],[f23,f33,f30])).
% 0.10/0.26 thf(f40,plain,(
% 0.10/0.26 ( ! [X0 : $i] : (($true != $true) | ($true != ((cP @ (f @ X0))))) ) | ~spl1_2),
% 0.10/0.26 inference(constrained_superposition,[],[f9,f35])).
% 0.10/0.26 thf(f41,plain,(
% 0.10/0.26 ( ! [X0 : $i] : (($true != ((cP @ (f @ X0))))) ) | ~spl1_2),
% 0.10/0.26 inference(trivial_inequality_removal,[],[f40])).
% 0.10/0.26 thf(f42,plain,(
% 0.10/0.26 ($true != $true) | ~spl1_2),
% 0.10/0.26 inference(constrained_superposition,[],[f41,f7])).
% 0.10/0.26 thf(f43,plain,(
% 0.10/0.26 $false | ~spl1_2),
% 0.10/0.26 inference(trivial_inequality_removal,[],[f42])).
% 0.10/0.26 thf(f44,plain,(
% 0.10/0.26 ~spl1_2),
% 0.10/0.26 inference(avatar_contradiction_clause,[],[f43])).
% 0.10/0.26 thf(f45,plain,(
% 0.10/0.26 $false | ~spl1_1),
% 0.10/0.26 inference(equality_resolution,[],[f31])).
% 0.10/0.26 thf(f46,plain,(
% 0.10/0.26 ~spl1_1),
% 0.10/0.26 inference(avatar_contradiction_clause,[],[f45])).
% 0.10/0.26 cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f36])).
% 0.10/0.26 cnf(s2, plain, ~spl1_2, inference(sat_conversion,[],[f44])).
% 0.10/0.26 cnf(s3, plain, ~spl1_1, inference(sat_conversion,[],[f46])).
% 0.10/0.26 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.10/0.26 thf(f47,plain,(
% 0.10/0.26 $false),
% 0.10/0.26 inference(avatar_sat_refutation,[],[s4])).
% 0.10/0.26 % SZS output end Proof for theBenchmark
% 0.10/0.26 % (48416)------------------------------
% 0.10/0.26 % (48416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (48416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (48416)CaDiCaL version: 2.1.3
% 0.10/0.26 % (48416)Termination reason: Refutation
% 0.10/0.26 % (48416)Time elapsed: 0.003 s
% 0.10/0.26 % (48416)Peak memory usage: 12 MB
% 0.10/0.26 % (48416)Instructions burned: 3 (million)
% 0.10/0.26 % (48401)Success in time 0.042 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------