%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO018^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:48:43 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO018^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n019.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 16:22:38 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.07/0.23 % (995961)Will run a generic schedule for satisfiability detection.
% 0.07/0.23 % (995968)% WARNING: option uhcvi not known.
% 0.07/0.23 % (995967)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2455003624_3000 on theBenchmark for (3000ds/0Mi)
% 0.07/0.23 % (995969)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3507988701:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.07/0.23 % (995973)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3625059460:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.07/0.23 % (995968)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2508388660:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.07/0.23 % (995971)dis+10_1_sil=32000:sp=arity:random_seed=791440381:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.07/0.23 % Exception at run slice level
% 0.07/0.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs% (995972)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3457693832:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.07/0.23
% 0.07/0.23 % (995968)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.23 % (995968)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.23 % (995972)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.23 % (995974)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3749884485:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.07/0.23 % (995969) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-995961-995969"...
% 0.07/0.23 % (995973) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-995961-995973"...
% 0.07/0.23 % (995972) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-995961-995972"...
% 0.07/0.23 % (995968) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-995961-995968"...
% 0.07/0.23 % (995971) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-995961-995971"...
% 0.07/0.23 % (995974) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-995961-995974"...
% 0.07/0.23 % (995973)...printing done.
% 0.07/0.23 % (995969)...printing done.
% 0.07/0.23 % (995972)...printing done.
% 0.07/0.23 % (995968)...printing done.
% 0.07/0.23 % (995971)...printing done.
% 0.07/0.23 % (995973)Refutation found. Thanks to Tanya!
% 0.07/0.23 % SZS status Theorem for theBenchmark
% 0.07/0.23 % SZS output start Proof for theBenchmark
% 0.07/0.23 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.23 thf(func_def_0, type, f: ($o > $i > $i)).
% 0.07/0.23 thf(func_def_1, type, p: (($i > $i) > $o)).
% 0.07/0.23 thf(func_def_2, type, a: (($i > $i) > $o)).
% 0.07/0.23 thf(func_def_3, type, b: $o).
% 0.07/0.23 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.07/0.23 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.23 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.23 thf(f1,conjecture,(
% 0.07/0.23 (p @ (^[X0 : $i] : ((f @ b & (a @ (^[X0 : $i] : ((f @ b @ X0)))) @ X0)))) => (p @ (f @ (a @ (f @ b)) & b))),
% 0.07/0.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.07/0.23 thf(f2,negated_conjecture,(
% 0.07/0.23 ~((p @ (^[X0 : $i] : ((f @ b & (a @ (^[X0 : $i] : ((f @ b @ X0)))) @ X0)))) => (p @ (f @ (a @ (f @ b)) & b)))),
% 0.07/0.23 inference(negated_conjecture,[status(cth)],[f1])).
% 0.07/0.23 thf(f3,plain,(
% 0.07/0.23 ~((p @ (^[X0 : $i] : ((f @ b & (a @ (^[X1 : $i] : ((f @ b @ X1)))) @ X0)))) => (p @ (f @ (a @ (f @ b)) & b)))),
% 0.07/0.23 inference(rectify,[],[f2])).
% 0.07/0.23 thf(f4,plain,(
% 0.07/0.23 ~((((p @ (^[Y0 : $i]: (f @ ((a @ (^[Y1 : $i]: (f @ b @ Y1))) & b) @ Y0)))) = $true) => ($true = ((p @ (f @ (b & (a @ (f @ b))))))))),
% 0.07/0.23 inference(fool_elimination,[],[f3])).
% 0.07/0.23 thf(f5,plain,(
% 0.07/0.23 ($true != ((p @ (f @ (b & (a @ (f @ b))))))) & (((p @ (^[Y0 : $i]: (f @ ((a @ (^[Y1 : $i]: (f @ b @ Y1))) & b) @ Y0)))) = $true)),
% 0.07/0.23 inference(ennf_transformation,[],[f4])).
% 0.07/0.23 thf(f6,plain,(
% 0.07/0.23 (((p @ (^[Y0 : $i]: (f @ ((a @ (^[Y1 : $i]: (f @ b @ Y1))) & b) @ Y0)))) = $true)),
% 0.07/0.23 inference(cnf_transformation,[],[f5])).
% 0.07/0.23 thf(f7,plain,(
% 0.07/0.23 ($true != ((p @ (f @ (b & (a @ (f @ b)))))))),
% 0.07/0.23 inference(cnf_transformation,[],[f5])).
% 0.07/0.23 thf(f9,definition,(
% 0.07/0.23 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.23 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.23 thf(f10,plain,(
% 0.07/0.23 ($true = ((p @ (f @ ((a @ (f @ b)) & b)))))),
% 0.07/0.23 inference(beta-eta_normalization,[],[f6])).
% 0.07/0.23 thf(f18,plain,(
% 0.07/0.23 ($true = ((p @ (f @ ((a @ (f @ $true)) & $true))))) | (b = $false)),
% 0.07/0.23 inference(constrained_superposition,[],[f10,f9])).
% 0.07/0.23 thf(f19,plain,(
% 0.07/0.23 ($true != ((p @ (f @ ($true & (a @ (f @ $true))))))) | (b = $false)),
% 0.07/0.23 inference(constrained_superposition,[],[f7,f9])).
% 0.07/0.23 thf(f21,plain,(
% 0.07/0.23 ($true != ((p @ (f @ (a @ (f @ $true)))))) | (b = $false)),
% 0.07/0.23 inference(boolean_simplification,[],[f19])).
% 0.07/0.23 thf(f22,plain,(
% 0.07/0.23 ($true = ((p @ (f @ (a @ (f @ $true)))))) | (b = $false)),
% 0.07/0.23 inference(boolean_simplification,[],[f18])).
% 0.07/0.23 thf(f33,definition,(
% 0.07/0.23 spl0_1 <=> (b = $false)),
% 0.07/0.23 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.07/0.23 thf(f35,plain,(
% 0.07/0.23 (b = $false) | ~spl0_1),
% 0.07/0.23 inference(avatar_component_clause,[],[f33])).
% 0.07/0.23 thf(f37,definition,(
% 0.07/0.23 spl0_2 <=> ($true = ((p @ (f @ (a @ (f @ $true))))))),
% 0.07/0.23 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.07/0.23 thf(f40,plain,(
% 0.07/0.23 spl0_1 | ~spl0_2),
% 0.07/0.23 inference(avatar_split_clause,[],[f21,f37,f33])).
% 0.07/0.23 thf(f41,plain,(
% 0.07/0.23 spl0_1 | spl0_2),
% 0.07/0.23 inference(avatar_split_clause,[],[f22,f37,f33])).
% 0.07/0.23 thf(f60,plain,(
% 0.07/0.23 ($true = ((p @ (f @ ((a @ (f @ $false)) & $false))))) | ~spl0_1),
% 0.07/0.23 inference(constrained_superposition,[],[f10,f35])).
% 0.07/0.23 thf(f61,plain,(
% 0.07/0.23 ($true != ((p @ (f @ ($false & (a @ (f @ $false))))))) | ~spl0_1),
% 0.07/0.23 inference(constrained_superposition,[],[f7,f35])).
% 0.07/0.23 thf(f62,plain,(
% 0.07/0.23 ($true != ((p @ (f @ $false)))) | ~spl0_1),
% 0.07/0.23 inference(boolean_simplification,[],[f61])).
% 0.07/0.23 thf(f63,plain,(
% 0.07/0.23 ($true = ((p @ (f @ $false)))) | ~spl0_1),
% 0.07/0.23 inference(boolean_simplification,[],[f60])).
% 0.07/0.23 thf(f65,plain,(
% 0.07/0.23 $false | ~spl0_1),
% 0.07/0.23 inference(forward_subsumption_resolution,[],[f63,f62])).
% 0.07/0.23 thf(f66,plain,(
% 0.07/0.23 ~spl0_1),
% 0.07/0.23 inference(avatar_contradiction_clause,[],[f65])).
% 0.07/0.23 cnf(s1, plain, spl0_1 | ~spl0_2, inference(sat_conversion,[],[f40])).
% 0.07/0.23 cnf(s2, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f41])).
% 0.07/0.23 cnf(s7, plain, ~spl0_1, inference(sat_conversion,[],[f66])).
% 0.07/0.23 cnf(s10, plain, spl0_2, inference(rat,[],[s2,s7])).
% 0.07/0.23 cnf(s11, plain, $false, inference(rat,[],[s1,s10,s7])).
% 0.07/0.23 thf(f67,plain,(
% 0.07/0.23 $false),
% 0.07/0.23 inference(avatar_sat_refutation,[],[s11])).
% 0.07/0.23 % SZS output end Proof for theBenchmark
% 0.07/0.23 % (995973)------------------------------
% 0.07/0.23 % (995973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.23 % (995973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.23 % (995973)CaDiCaL version: 2.1.3
% 0.07/0.23 % (995973)Termination reason: Refutation
% 0.07/0.23 % (995973)Time elapsed: 0.003 s
% 0.07/0.23 % (995973)Peak memory usage: 12 MB
% 0.07/0.23 % (995973)Instructions burned: 3 (million)
% 0.07/0.23 % (995961)Success in time 0.026 s
% 0.07/0.23 % Vampire exiting
%------------------------------------------------------------------------------