%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO012^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO012^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n011.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:21:32 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.08/0.26 % (288869)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (288877)dis+10_1_sil=32000:sp=arity:random_seed=1369818917:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.08/0.26 % (288877) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-288869-288877"...
% 0.08/0.26 % (288877)...printing done.
% 0.08/0.26 % (288877)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_0, type, a: $o).
% 0.08/0.26 thf(func_def_1, type, b: $o).
% 0.08/0.26 thf(func_def_2, type, p: ($o > $o)).
% 0.08/0.26 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.08/0.26 thf(f1,conjecture,(
% 0.08/0.26 (p @ b & a) => (p @ a & b)),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.08/0.26 thf(f2,negated_conjecture,(
% 0.08/0.26 ~((p @ b & a) => (p @ a & b))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.26 thf(f3,plain,(
% 0.08/0.26 ~((p @ b & a) => (p @ a & b))),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f4,plain,(
% 0.08/0.26 ~((((p @ (a & b))) = $true) => ($true = ((p @ (b & a)))))),
% 0.08/0.26 inference(fool_elimination,[],[f3])).
% 0.08/0.26 thf(f5,plain,(
% 0.08/0.26 ($true != ((p @ (b & a)))) & (((p @ (a & b))) = $true)),
% 0.08/0.26 inference(ennf_transformation,[],[f4])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 (((p @ (a & b))) = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f5])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 ($true != ((p @ (b & a))))),
% 0.08/0.26 inference(cnf_transformation,[],[f5])).
% 0.08/0.26 thf(f9,definition,(
% 0.08/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.26 thf(f14,plain,(
% 0.08/0.26 ($true != ((p @ ($true & a)))) | (b = $false)),
% 0.08/0.26 inference(constrained_superposition,[],[f7,f9])).
% 0.08/0.26 thf(f15,plain,(
% 0.08/0.26 ($true = ((p @ (a & $true)))) | (b = $false)),
% 0.08/0.26 inference(constrained_superposition,[],[f6,f9])).
% 0.08/0.26 thf(f18,plain,(
% 0.08/0.26 ($true != $true) | (((p @ (b & a))) = $false)),
% 0.08/0.26 inference(constrained_superposition,[],[f7,f9])).
% 0.08/0.26 thf(f20,plain,(
% 0.08/0.26 (((p @ (b & a))) = $false)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f18])).
% 0.08/0.26 thf(f23,plain,(
% 0.08/0.26 ($true = ((p @ a))) | (b = $false)),
% 0.08/0.26 inference(boolean_simplification,[],[f15])).
% 0.08/0.26 thf(f24,plain,(
% 0.08/0.26 ($true != ((p @ a))) | (b = $false)),
% 0.08/0.26 inference(boolean_simplification,[],[f14])).
% 0.08/0.26 thf(f32,definition,(
% 0.08/0.26 spl0_1 <=> (b = $false)),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.08/0.26 thf(f34,plain,(
% 0.08/0.26 (b = $false) | ~spl0_1),
% 0.08/0.26 inference(avatar_component_clause,[],[f32])).
% 0.08/0.26 thf(f46,definition,(
% 0.08/0.26 spl0_4 <=> ($true = ((p @ a)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.08/0.26 thf(f49,plain,(
% 0.08/0.26 spl0_1 | spl0_4),
% 0.08/0.26 inference(avatar_split_clause,[],[f23,f46,f32])).
% 0.08/0.26 thf(f50,plain,(
% 0.08/0.26 spl0_1 | ~spl0_4),
% 0.08/0.26 inference(avatar_split_clause,[],[f24,f46,f32])).
% 0.08/0.26 thf(f59,plain,(
% 0.08/0.26 ($true = ((p @ (a & $false)))) | ~spl0_1),
% 0.08/0.26 inference(constrained_superposition,[],[f6,f34])).
% 0.08/0.26 thf(f60,plain,(
% 0.08/0.26 ($true = ((p @ $false))) | ~spl0_1),
% 0.08/0.26 inference(boolean_simplification,[],[f59])).
% 0.08/0.26 thf(f69,plain,(
% 0.08/0.26 ($false = ((p @ ($false & a)))) | ~spl0_1),
% 0.08/0.26 inference(forward_demodulation,[],[f20,f34])).
% 0.08/0.26 thf(f70,plain,(
% 0.08/0.26 ($false = ((p @ $false))) | ~spl0_1),
% 0.08/0.26 inference(boolean_simplification,[],[f69])).
% 0.08/0.26 thf(f72,plain,(
% 0.08/0.26 ($true = $false) | ~spl0_1),
% 0.08/0.26 inference(constrained_superposition,[],[f70,f60])).
% 0.08/0.26 thf(f76,plain,(
% 0.08/0.26 $false | ~spl0_1),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f72])).
% 0.08/0.26 thf(f77,plain,(
% 0.08/0.26 ~spl0_1),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f76])).
% 0.08/0.26 cnf(s3, plain, spl0_1 | spl0_4, inference(sat_conversion,[],[f49])).
% 0.08/0.26 cnf(s4, plain, spl0_1 | ~spl0_4, inference(sat_conversion,[],[f50])).
% 0.08/0.26 cnf(s8, plain, ~spl0_1, inference(sat_conversion,[],[f77])).
% 0.08/0.26 cnf(s9, plain, ~spl0_4, inference(rat,[],[s4,s8])).
% 0.08/0.26 cnf(s10, plain, $false, inference(rat,[],[s3,s9,s8])).
% 0.08/0.26 thf(f79,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(avatar_sat_refutation,[],[s10])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (288877)------------------------------
% 0.08/0.26 % (288877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (288877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (288877)CaDiCaL version: 2.1.3
% 0.08/0.26 % (288877)Termination reason: Refutation
% 0.08/0.26 % (288877)Time elapsed: 0.002 s
% 0.08/0.26 % (288877)Peak memory usage: 12 MB
% 0.08/0.26 % (288877)Instructions burned: 3 (million)
% 0.08/0.26 % (288869)Success in time 0.017 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------