%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO012_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 : Tue Sep 29 02:29:33 PM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO012_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n008.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 17:21:54 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.24 Running first-order model finding
% 0.07/0.24 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
% 0.22/0.29 % (2409012)Will run a generic schedule for satisfiability detection.
% 0.22/0.29 % (2409020)dis+10_1_sil=32000:sp=arity:random_seed=3940034796:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.22/0.29 % (2409020) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2409012-2409020"...
% 0.22/0.29 % (2409020)...printing done.
% 0.22/0.29 % (2409020)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 tff(func_def_0, type, bG0: $o).
% 0.22/0.29 tff(func_def_3, type, bG1: $o).
% 0.22/0.29 tff(pred_def_3, type, p: $o > $o).
% 0.22/0.29 tff(f1,conjecture,(
% 0.22/0.29 p(a & b) => p(b & a)),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.22/0.29 tff(f2,negated_conjecture,(
% 0.22/0.29 ~(p(a & b) => p(b & a))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.29 tff(f3,definition,(
% 0.22/0.29 (a & b) <=> (bG0 = $true)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition])).
% 0.22/0.29 tff(f4,definition,(
% 0.22/0.29 (b & a) <=> ($true = bG1)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition])).
% 0.22/0.29 tff(f5,plain,(
% 0.22/0.29 ~(p(bG0) => p(bG1))),
% 0.22/0.29 inference(fool_elimination,[],[f2,f4,f3])).
% 0.22/0.29 tff(f6,plain,(
% 0.22/0.29 ~p(bG1) & p(bG0)),
% 0.22/0.29 inference(ennf_transformation,[],[f5])).
% 0.22/0.29 tff(f7,plain,(
% 0.22/0.29 ((b & a) | ($true != bG1)) & (($true = bG1) | (~b | ~a))),
% 0.22/0.29 inference(nnf_transformation,[],[f4])).
% 0.22/0.29 tff(f8,plain,(
% 0.22/0.29 ((b & a) | ($true != bG1)) & (($true = bG1) | ~b | ~a)),
% 0.22/0.29 inference(flattening,[],[f7])).
% 0.22/0.29 tff(f9,plain,(
% 0.22/0.29 ((a & b) | (bG0 != $true)) & ((bG0 = $true) | (~a | ~b))),
% 0.22/0.29 inference(nnf_transformation,[],[f3])).
% 0.22/0.29 tff(f10,plain,(
% 0.22/0.29 ((a & b) | (bG0 != $true)) & ((bG0 = $true) | ~a | ~b)),
% 0.22/0.29 inference(flattening,[],[f9])).
% 0.22/0.29 tff(f11,plain,(
% 0.22/0.29 ($true = bG1) | ~b | ~a),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 tff(f12,plain,(
% 0.22/0.29 a | ($true != bG1)),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 tff(f13,plain,(
% 0.22/0.29 b | ($true != bG1)),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 tff(f14,plain,(
% 0.22/0.29 (bG0 = $true) | ~a | ~b),
% 0.22/0.29 inference(cnf_transformation,[],[f10])).
% 0.22/0.29 tff(f15,plain,(
% 0.22/0.29 b | (bG0 != $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f10])).
% 0.22/0.29 tff(f16,plain,(
% 0.22/0.29 a | (bG0 != $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f10])).
% 0.22/0.29 tff(f17,plain,(
% 0.22/0.29 p(bG0)),
% 0.22/0.29 inference(cnf_transformation,[],[f6])).
% 0.22/0.29 tff(f18,plain,(
% 0.22/0.29 ~p(bG1)),
% 0.22/0.29 inference(cnf_transformation,[],[f6])).
% 0.22/0.29 tff(f20,definition,(
% 0.22/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.29 tff(f22,definition,(
% 0.22/0.29 spl2_1 <=> b),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.22/0.29 tff(f26,definition,(
% 0.22/0.29 spl2_2 <=> a),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.22/0.29 tff(f30,definition,(
% 0.22/0.29 spl2_3 <=> (bG0 = $true)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.22/0.29 tff(f31,plain,(
% 0.22/0.29 (bG0 != $true) | spl2_3),
% 0.22/0.29 inference(avatar_component_clause,[],[f30])).
% 0.22/0.29 tff(f32,plain,(
% 0.22/0.29 (bG0 = $true) | ~spl2_3),
% 0.22/0.29 inference(avatar_component_clause,[],[f30])).
% 0.22/0.29 tff(f33,plain,(
% 0.22/0.29 ~spl2_1 | ~spl2_2 | spl2_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f14,f30,f26,f22])).
% 0.22/0.29 tff(f34,plain,(
% 0.22/0.29 ~spl2_3 | spl2_1),
% 0.22/0.29 inference(avatar_split_clause,[],[f15,f22,f30])).
% 0.22/0.29 tff(f35,plain,(
% 0.22/0.29 ~spl2_3 | spl2_2),
% 0.22/0.29 inference(avatar_split_clause,[],[f16,f26,f30])).
% 0.22/0.29 tff(f37,definition,(
% 0.22/0.29 spl2_4 <=> ($true = bG1)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.22/0.29 tff(f38,plain,(
% 0.22/0.29 ($true != bG1) | spl2_4),
% 0.22/0.29 inference(avatar_component_clause,[],[f37])).
% 0.22/0.29 tff(f39,plain,(
% 0.22/0.29 ($true = bG1) | ~spl2_4),
% 0.22/0.29 inference(avatar_component_clause,[],[f37])).
% 0.22/0.29 tff(f40,plain,(
% 0.22/0.29 ~spl2_2 | ~spl2_1 | spl2_4),
% 0.22/0.29 inference(avatar_split_clause,[],[f11,f37,f22,f26])).
% 0.22/0.29 tff(f41,plain,(
% 0.22/0.29 ~spl2_4 | spl2_2),
% 0.22/0.29 inference(avatar_split_clause,[],[f12,f26,f37])).
% 0.22/0.29 tff(f42,plain,(
% 0.22/0.29 ~spl2_4 | spl2_1),
% 0.22/0.29 inference(avatar_split_clause,[],[f13,f22,f37])).
% 0.22/0.29 tff(f45,plain,(
% 0.22/0.29 ($true != $true) | (bG0 = $false) | spl2_3),
% 0.22/0.29 inference(superposition,[],[f31,f20])).
% 0.22/0.29 tff(f46,plain,(
% 0.22/0.29 p($true) | (bG0 = $false)),
% 0.22/0.29 inference(superposition,[],[f17,f20])).
% 0.22/0.29 tff(f47,plain,(
% 0.22/0.29 ($true != $true) | (bG1 = $false) | spl2_4),
% 0.22/0.29 inference(superposition,[],[f38,f20])).
% 0.22/0.29 tff(f48,plain,(
% 0.22/0.29 ~p($true) | (bG1 = $false)),
% 0.22/0.29 inference(superposition,[],[f18,f20])).
% 0.22/0.29 tff(f50,plain,(
% 0.22/0.29 (bG1 = $false) | spl2_4),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f47])).
% 0.22/0.29 tff(f51,plain,(
% 0.22/0.29 (bG0 = $false) | spl2_3),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f45])).
% 0.22/0.29 tff(f53,definition,(
% 0.22/0.29 spl2_5 <=> (bG1 = $false)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.22/0.29 tff(f55,plain,(
% 0.22/0.29 (bG1 = $false) | ~spl2_5),
% 0.22/0.29 inference(avatar_component_clause,[],[f53])).
% 0.22/0.29 tff(f57,definition,(
% 0.22/0.29 spl2_6 <=> p($true)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition])).
% 0.22/0.29 tff(f60,plain,(
% 0.22/0.29 spl2_5 | ~spl2_6),
% 0.22/0.29 inference(avatar_split_clause,[],[f48,f57,f53])).
% 0.22/0.29 tff(f61,plain,(
% 0.22/0.29 spl2_5 | spl2_4),
% 0.22/0.29 inference(avatar_split_clause,[],[f50,f37,f53])).
% 0.22/0.29 tff(f63,definition,(
% 0.22/0.29 spl2_7 <=> (bG0 = $false)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition])).
% 0.22/0.29 tff(f65,plain,(
% 0.22/0.29 (bG0 = $false) | ~spl2_7),
% 0.22/0.29 inference(avatar_component_clause,[],[f63])).
% 0.22/0.29 tff(f66,plain,(
% 0.22/0.29 spl2_7 | spl2_6),
% 0.22/0.29 inference(avatar_split_clause,[],[f46,f57,f63])).
% 0.22/0.29 tff(f67,plain,(
% 0.22/0.29 spl2_7 | spl2_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f51,f30,f63])).
% 0.22/0.29 tff(f70,plain,(
% 0.22/0.29 ~p($false) | ~spl2_5),
% 0.22/0.29 inference(superposition,[],[f18,f55])).
% 0.22/0.29 tff(f74,plain,(
% 0.22/0.29 p($false) | ~spl2_7),
% 0.22/0.29 inference(superposition,[],[f17,f65])).
% 0.22/0.29 tff(f76,plain,(
% 0.22/0.29 $false | (~spl2_5 | ~spl2_7)),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f74,f70])).
% 0.22/0.29 tff(f77,plain,(
% 0.22/0.29 ~spl2_5 | ~spl2_7),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f76])).
% 0.22/0.29 tff(f78,plain,(
% 0.22/0.29 ($true = $false) | (~spl2_3 | ~spl2_7)),
% 0.22/0.29 inference(forward_demodulation,[],[f32,f65])).
% 0.22/0.29 tff(f79,plain,(
% 0.22/0.29 $false | (~spl2_3 | ~spl2_7)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f78])).
% 0.22/0.29 tff(f80,plain,(
% 0.22/0.29 ~spl2_3 | ~spl2_7),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f79])).
% 0.22/0.29 tff(f87,plain,(
% 0.22/0.29 ($true = $false) | (~spl2_4 | ~spl2_5)),
% 0.22/0.29 inference(forward_demodulation,[],[f39,f55])).
% 0.22/0.29 tff(f88,plain,(
% 0.22/0.29 $false | (~spl2_4 | ~spl2_5)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f87])).
% 0.22/0.29 tff(f89,plain,(
% 0.22/0.29 ~spl2_4 | ~spl2_5),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f88])).
% 0.22/0.29 cnf(s1, plain, ~spl2_1 | ~spl2_2 | spl2_3, inference(sat_conversion,[],[f33])).
% 0.22/0.29 cnf(s2, plain, spl2_1 | ~spl2_3, inference(sat_conversion,[],[f34])).
% 0.22/0.29 cnf(s3, plain, spl2_2 | ~spl2_3, inference(sat_conversion,[],[f35])).
% 0.22/0.29 cnf(s4, plain, ~spl2_1 | ~spl2_2 | spl2_4, inference(sat_conversion,[],[f40])).
% 0.22/0.29 cnf(s5, plain, spl2_2 | ~spl2_4, inference(sat_conversion,[],[f41])).
% 0.22/0.29 cnf(s6, plain, spl2_1 | ~spl2_4, inference(sat_conversion,[],[f42])).
% 0.22/0.29 cnf(s7, plain, spl2_5 | ~spl2_6, inference(sat_conversion,[],[f60])).
% 0.22/0.29 cnf(s8, plain, spl2_4 | spl2_5, inference(sat_conversion,[],[f61])).
% 0.22/0.29 cnf(s9, plain, spl2_6 | spl2_7, inference(sat_conversion,[],[f66])).
% 0.22/0.29 cnf(s10, plain, spl2_3 | spl2_7, inference(sat_conversion,[],[f67])).
% 0.22/0.29 cnf(s11, plain, ~spl2_5 | ~spl2_7, inference(sat_conversion,[],[f77])).
% 0.22/0.29 cnf(s12, plain, ~spl2_3 | ~spl2_7, inference(sat_conversion,[],[f80])).
% 0.22/0.29 cnf(s13, plain, ~spl2_4 | ~spl2_5, inference(sat_conversion,[],[f89])).
% 0.22/0.29 cnf(s14, plain, spl2_1, inference(rat,[],[s11,s10,s8,s2,s6])).
% 0.22/0.29 cnf(s15, plain, spl2_2, inference(rat,[],[s11,s10,s8,s3,s5])).
% 0.22/0.29 cnf(s16, plain, spl2_4, inference(rat,[],[s4,s14,s15])).
% 0.22/0.29 cnf(s17, plain, spl2_3, inference(rat,[],[s1,s14,s15])).
% 0.22/0.29 cnf(s18, plain, ~spl2_5, inference(rat,[],[s13,s16])).
% 0.22/0.29 cnf(s19, plain, ~spl2_7, inference(rat,[],[s12,s17])).
% 0.22/0.29 cnf(s20, plain, ~spl2_6, inference(rat,[],[s7,s18])).
% 0.22/0.29 cnf(s21, plain, $false, inference(rat,[],[s9,s19,s20])).
% 0.22/0.29 tff(f90,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(avatar_sat_refutation,[],[s21])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (2409020)------------------------------
% 0.22/0.29 % (2409020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2409020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2409020)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2409020)Termination reason: Refutation
% 0.22/0.29 % (2409020)Time elapsed: 0.003 s
% 0.22/0.29 % (2409020)Peak memory usage: 12 MB
% 0.22/0.29 % (2409020)Instructions burned: 2 (million)
% 0.22/0.29 % (2409012)Success in time 0.026 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------