%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO078^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:46:34 AM UTC 2026
% Result : Theorem 0.17s 0.26s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO078^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n026.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 16:35:43 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.26 % (821304)Detected formulas, will run a generic FOF schedule.
% 0.17/0.26 % (821312)lrs+1011_32_sil=2000:tgt=full:alpa=true:random_seed=1329373907:st=5:i=107:sd=1:ss=included:er=filter_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/0.26 % (821312) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-821304-821312"...
% 0.17/0.26 % (821312)...printing done.
% 0.17/0.26 % (821312)Refutation found. Thanks to Tanya!
% 0.17/0.26 % SZS status Theorem for theBenchmark
% 0.17/0.26 % SZS output start Proof for theBenchmark
% 0.17/0.26 tff(func_def_0, type, cR: $o).
% 0.17/0.26 tff(func_def_1, type, cP: $o).
% 0.17/0.26 tff(func_def_2, type, cQ: $o).
% 0.17/0.26 tff(f1,conjecture,(
% 0.17/0.26 (cP <=> cR) | (cQ <=> cR) | (cP <=> cQ)),
% 0.17/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM49)).
% 0.17/0.26 tff(f2,negated_conjecture,(
% 0.17/0.26 ~((cP <=> cR) | (cQ <=> cR) | (cP <=> cQ))),
% 0.17/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.17/0.26 tff(f3,plain,(
% 0.17/0.26 ~((cP <=> cR) | (cQ <=> cR) | (cP <=> cQ))),
% 0.17/0.26 inference(rectify,[],[f2])).
% 0.17/0.26 tff(f4,plain,(
% 0.17/0.26 ~((cP = cR) | (cQ = cR) | (cP = cQ))),
% 0.17/0.26 inference(fool_elimination,[],[f3])).
% 0.17/0.26 tff(f5,plain,(
% 0.17/0.26 (cP != cR) & (cQ != cR) & (cP != cQ)),
% 0.17/0.26 inference(ennf_transformation,[],[f4])).
% 0.17/0.26 tff(f6,plain,(
% 0.17/0.26 (cP != cQ)),
% 0.17/0.26 inference(cnf_transformation,[],[f5])).
% 0.17/0.26 tff(f7,plain,(
% 0.17/0.26 (cQ != cR)),
% 0.17/0.26 inference(cnf_transformation,[],[f5])).
% 0.17/0.26 tff(f8,plain,(
% 0.17/0.26 (cP != cR)),
% 0.17/0.26 inference(cnf_transformation,[],[f5])).
% 0.17/0.26 tff(f10,definition,(
% 0.17/0.26 ( ! [X0 : $o] : (($false = X0) | ($true = X0)) )),
% 0.17/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.17/0.26 tff(f12,plain,(
% 0.17/0.26 (cR != $false) | (cP = $true)),
% 0.17/0.26 inference(superposition,[],[f8,f10])).
% 0.17/0.26 tff(f13,plain,(
% 0.17/0.26 (cR != $false) | (cQ = $true)),
% 0.17/0.26 inference(superposition,[],[f7,f10])).
% 0.17/0.26 tff(f14,plain,(
% 0.17/0.26 (cP != $false) | (cQ = $true)),
% 0.17/0.26 inference(superposition,[],[f6,f10])).
% 0.17/0.26 tff(f17,definition,(
% 0.17/0.26 spl0_1 <=> (cQ = $true)),
% 0.17/0.26 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.17/0.26 tff(f19,plain,(
% 0.17/0.26 (cQ = $true) | ~spl0_1),
% 0.17/0.26 inference(avatar_component_clause,[],[f17])).
% 0.17/0.26 tff(f21,definition,(
% 0.17/0.26 spl0_2 <=> (cP = $false)),
% 0.17/0.26 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.17/0.26 tff(f23,plain,(
% 0.17/0.26 (cP != $false) | spl0_2),
% 0.17/0.26 inference(avatar_component_clause,[],[f21])).
% 0.17/0.26 tff(f24,plain,(
% 0.17/0.26 spl0_1 | ~spl0_2),
% 0.17/0.26 inference(avatar_split_clause,[],[f14,f21,f17])).
% 0.17/0.26 tff(f26,definition,(
% 0.17/0.26 spl0_3 <=> (cR = $false)),
% 0.17/0.26 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.17/0.26 tff(f28,plain,(
% 0.17/0.26 (cR != $false) | spl0_3),
% 0.17/0.26 inference(avatar_component_clause,[],[f26])).
% 0.17/0.26 tff(f29,plain,(
% 0.17/0.26 spl0_1 | ~spl0_3),
% 0.17/0.26 inference(avatar_split_clause,[],[f13,f26,f17])).
% 0.17/0.26 tff(f31,definition,(
% 0.17/0.26 spl0_4 <=> (cP = $true)),
% 0.17/0.26 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.17/0.26 tff(f32,plain,(
% 0.17/0.26 (cP != $true) | spl0_4),
% 0.17/0.26 inference(avatar_component_clause,[],[f31])).
% 0.17/0.26 tff(f33,plain,(
% 0.17/0.26 (cP = $true) | ~spl0_4),
% 0.17/0.26 inference(avatar_component_clause,[],[f31])).
% 0.17/0.26 tff(f34,plain,(
% 0.17/0.26 spl0_4 | ~spl0_3),
% 0.17/0.26 inference(avatar_split_clause,[],[f12,f26,f31])).
% 0.17/0.26 tff(f36,plain,(
% 0.17/0.26 (cR != $true) | ~spl0_1),
% 0.17/0.26 inference(superposition,[],[f7,f19])).
% 0.17/0.26 tff(f37,plain,(
% 0.17/0.26 (cP != $true) | ~spl0_1),
% 0.17/0.26 inference(superposition,[],[f6,f19])).
% 0.17/0.26 tff(f39,plain,(
% 0.17/0.26 ~spl0_4 | ~spl0_1),
% 0.17/0.26 inference(avatar_split_clause,[],[f37,f17,f31])).
% 0.17/0.26 tff(f40,plain,(
% 0.17/0.26 ($false != $false) | (cR = $true) | spl0_3),
% 0.17/0.26 inference(superposition,[],[f28,f10])).
% 0.17/0.26 tff(f41,plain,(
% 0.17/0.26 (cR = $true) | spl0_3),
% 0.17/0.26 inference(trivial_inequality_removal,[],[f40])).
% 0.17/0.26 tff(f42,plain,(
% 0.17/0.26 $false | (~spl0_1 | spl0_3)),
% 0.17/0.26 inference(forward_subsumption_resolution,[],[f41,f36])).
% 0.17/0.26 tff(f43,plain,(
% 0.17/0.26 ~spl0_1 | spl0_3),
% 0.17/0.26 inference(avatar_contradiction_clause,[],[f42])).
% 0.17/0.26 tff(f45,plain,(
% 0.17/0.26 ($false != $false) | (cP = $true) | spl0_2),
% 0.17/0.26 inference(superposition,[],[f23,f10])).
% 0.17/0.26 tff(f46,plain,(
% 0.17/0.26 (cP = $true) | spl0_2),
% 0.17/0.26 inference(trivial_inequality_removal,[],[f45])).
% 0.17/0.26 tff(f47,plain,(
% 0.17/0.26 $false | (spl0_2 | spl0_4)),
% 0.17/0.26 inference(forward_subsumption_resolution,[],[f46,f32])).
% 0.17/0.26 tff(f48,plain,(
% 0.17/0.26 spl0_2 | spl0_4),
% 0.17/0.26 inference(avatar_contradiction_clause,[],[f47])).
% 0.17/0.26 tff(f51,plain,(
% 0.17/0.26 (cR != $true) | ~spl0_4),
% 0.17/0.26 inference(superposition,[],[f8,f33])).
% 0.17/0.26 tff(f53,plain,(
% 0.17/0.26 $false | (spl0_3 | ~spl0_4)),
% 0.17/0.26 inference(forward_subsumption_resolution,[],[f51,f41])).
% 0.17/0.26 tff(f54,plain,(
% 0.17/0.26 spl0_3 | ~spl0_4),
% 0.17/0.26 inference(avatar_contradiction_clause,[],[f53])).
% 0.17/0.26 cnf(s1, plain, spl0_1 | ~spl0_2, inference(sat_conversion,[],[f24])).
% 0.17/0.26 cnf(s2, plain, spl0_1 | ~spl0_3, inference(sat_conversion,[],[f29])).
% 0.17/0.26 cnf(s3, plain, ~spl0_3 | spl0_4, inference(sat_conversion,[],[f34])).
% 0.17/0.26 cnf(s4, plain, ~spl0_1 | ~spl0_4, inference(sat_conversion,[],[f39])).
% 0.17/0.26 cnf(s5, plain, ~spl0_1 | spl0_3, inference(sat_conversion,[],[f43])).
% 0.17/0.26 cnf(s6, plain, spl0_2 | spl0_4, inference(sat_conversion,[],[f48])).
% 0.17/0.26 cnf(s7, plain, spl0_3 | ~spl0_4, inference(sat_conversion,[],[f54])).
% 0.17/0.26 cnf(s8, plain, spl0_1, inference(rat,[],[s6,s7,s1,s2])).
% 0.17/0.26 cnf(s9, plain, spl0_3, inference(rat,[],[s5,s8])).
% 0.17/0.26 cnf(s10, plain, ~spl0_4, inference(rat,[],[s4,s8])).
% 0.17/0.26 cnf(s11, plain, $false, inference(rat,[],[s3,s10,s9])).
% 0.17/0.26 tff(f55,plain,(
% 0.17/0.26 $false),
% 0.17/0.26 inference(avatar_sat_refutation,[],[s11])).
% 0.17/0.26 % SZS output end Proof for theBenchmark
% 0.17/0.26 % (821312)------------------------------
% 0.17/0.26 % (821312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.26 % (821312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.26 % (821312)CaDiCaL version: 2.1.3
% 0.17/0.26 % (821312)Termination reason: Refutation
% 0.17/0.26 % (821312)Time elapsed: 0.001 s
% 0.17/0.26 % (821312)Peak memory usage: 12 MB
% 0.17/0.26 % (821312)Instructions burned: 1 (million)
% 0.17/0.26 % (821304)Success in time 0.03 s
% 0.17/0.26 % Vampire exiting
%------------------------------------------------------------------------------