%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO079^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO079^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:32:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (2336991)Detected formulas, will run a generic FOF schedule.
% 0.20/0.28 % (2336998)lrs+10_1_sp=unary_first:urr=on:s2agt=32:random_seed=4059382364:s2a=on:i=272356:sd=1:bd=all:ss=included_2999 on theBenchmark for (2999ds/272356Mi)
% 0.20/0.28 % (2336998) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2336991-2336998"...
% 0.20/0.28 % (2336998)...printing done.
% 0.20/0.28 % (2336998)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 tff(func_def_0, type, cR: $o).
% 0.20/0.28 tff(func_def_1, type, cQ: $o).
% 0.20/0.28 tff(func_def_2, type, cP: $o).
% 0.20/0.28 tff(f1,conjecture,(
% 0.20/0.28 ((cP <=> cQ) <=> cR) => (cP <=> (cQ <=> cR))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM50_A)).
% 0.20/0.28 tff(f2,negated_conjecture,(
% 0.20/0.28 ~(((cP <=> cQ) <=> cR) => (cP <=> (cQ <=> cR)))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.28 tff(f3,plain,(
% 0.20/0.28 ~(((cP <=> cQ) <=> cR) => (cP <=> (cQ <=> cR)))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 tff(f4,plain,(
% 0.20/0.28 ~(((cP = cQ) <=> (cR = $true)) => ((cP = $true) <=> (cQ = cR)))),
% 0.20/0.28 inference(fool_elimination,[],[f3])).
% 0.20/0.28 tff(f5,plain,(
% 0.20/0.28 ((cP = $true) <~> (cQ = cR)) & ((cP = cQ) <=> (cR = $true))),
% 0.20/0.28 inference(ennf_transformation,[],[f4])).
% 0.20/0.28 tff(f6,plain,(
% 0.20/0.28 (((cQ != cR) | (cP != $true)) & ((cQ = cR) | (cP = $true))) & (((cP = cQ) | (cR != $true)) & ((cR = $true) | (cP != cQ)))),
% 0.20/0.28 inference(nnf_transformation,[],[f5])).
% 0.20/0.28 tff(f7,plain,(
% 0.20/0.28 ((cQ != cR) | (cP != $true)) & ((cQ = cR) | (cP = $true)) & ((cP = cQ) | (cR != $true)) & ((cR = $true) | (cP != cQ))),
% 0.20/0.28 inference(flattening,[],[f6])).
% 0.20/0.28 tff(f8,plain,(
% 0.20/0.28 (cR = $true) | (cP != cQ)),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 tff(f9,plain,(
% 0.20/0.28 (cP = cQ) | (cR != $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 tff(f10,plain,(
% 0.20/0.28 (cQ = cR) | (cP = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 tff(f11,plain,(
% 0.20/0.28 (cQ != cR) | (cP != $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 tff(f13,definition,(
% 0.20/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.28 tff(f15,definition,(
% 0.20/0.28 spl0_1 <=> (cP = cQ)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.20/0.28 tff(f16,plain,(
% 0.20/0.28 (cP = cQ) | ~spl0_1),
% 0.20/0.28 inference(avatar_component_clause,[],[f15])).
% 0.20/0.28 tff(f17,plain,(
% 0.20/0.28 (cP != cQ) | spl0_1),
% 0.20/0.28 inference(avatar_component_clause,[],[f15])).
% 0.20/0.28 tff(f19,definition,(
% 0.20/0.28 spl0_2 <=> (cR = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.20/0.28 tff(f20,plain,(
% 0.20/0.28 (cR != $true) | spl0_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f19])).
% 0.20/0.28 tff(f21,plain,(
% 0.20/0.28 (cR = $true) | ~spl0_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f19])).
% 0.20/0.28 tff(f22,plain,(
% 0.20/0.28 ~spl0_1 | spl0_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f8,f19,f15])).
% 0.20/0.28 tff(f23,plain,(
% 0.20/0.28 ~spl0_2 | spl0_1),
% 0.20/0.28 inference(avatar_split_clause,[],[f9,f15,f19])).
% 0.20/0.28 tff(f25,definition,(
% 0.20/0.28 spl0_3 <=> (cP = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.20/0.28 tff(f26,plain,(
% 0.20/0.28 (cP != $true) | spl0_3),
% 0.20/0.28 inference(avatar_component_clause,[],[f25])).
% 0.20/0.28 tff(f27,plain,(
% 0.20/0.28 (cP = $true) | ~spl0_3),
% 0.20/0.28 inference(avatar_component_clause,[],[f25])).
% 0.20/0.28 tff(f29,definition,(
% 0.20/0.28 spl0_4 <=> (cQ = cR)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.20/0.28 tff(f30,plain,(
% 0.20/0.28 (cQ != cR) | spl0_4),
% 0.20/0.28 inference(avatar_component_clause,[],[f29])).
% 0.20/0.28 tff(f31,plain,(
% 0.20/0.28 (cQ = cR) | ~spl0_4),
% 0.20/0.28 inference(avatar_component_clause,[],[f29])).
% 0.20/0.28 tff(f32,plain,(
% 0.20/0.28 spl0_3 | spl0_4),
% 0.20/0.28 inference(avatar_split_clause,[],[f10,f29,f25])).
% 0.20/0.28 tff(f33,plain,(
% 0.20/0.28 ~spl0_3 | ~spl0_4),
% 0.20/0.28 inference(avatar_split_clause,[],[f11,f29,f25])).
% 0.20/0.28 tff(f34,plain,(
% 0.20/0.28 (cQ != $true) | (spl0_1 | ~spl0_3)),
% 0.20/0.28 inference(backward_demodulation,[],[f17,f27])).
% 0.20/0.28 tff(f41,plain,(
% 0.20/0.28 ($true != $true) | (cR = $false) | spl0_2),
% 0.20/0.28 inference(superposition,[],[f20,f13])).
% 0.20/0.28 tff(f42,plain,(
% 0.20/0.28 ($true != $true) | (cQ = $false) | (spl0_1 | ~spl0_3)),
% 0.20/0.28 inference(superposition,[],[f34,f13])).
% 0.20/0.28 tff(f43,plain,(
% 0.20/0.28 (cR != $true) | (cQ = $false) | spl0_4),
% 0.20/0.28 inference(superposition,[],[f30,f13])).
% 0.20/0.28 tff(f45,plain,(
% 0.20/0.28 (cQ = $false) | (spl0_1 | ~spl0_3)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f42])).
% 0.20/0.28 tff(f46,plain,(
% 0.20/0.28 (cR = $false) | spl0_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f41])).
% 0.20/0.28 tff(f48,plain,(
% 0.20/0.28 (cR != $false) | (spl0_1 | ~spl0_3 | spl0_4)),
% 0.20/0.28 inference(backward_demodulation,[],[f30,f45])).
% 0.20/0.28 tff(f50,plain,(
% 0.20/0.28 $false | (spl0_1 | spl0_2 | ~spl0_3 | spl0_4)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f48,f46])).
% 0.20/0.28 tff(f51,plain,(
% 0.20/0.28 spl0_1 | spl0_2 | ~spl0_3 | spl0_4),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f50])).
% 0.20/0.28 tff(f52,plain,(
% 0.20/0.28 (cQ = $true) | (~spl0_1 | ~spl0_3)),
% 0.20/0.28 inference(forward_demodulation,[],[f16,f27])).
% 0.20/0.28 tff(f53,plain,(
% 0.20/0.28 (cQ = $false) | (~spl0_2 | spl0_4)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f43,f21])).
% 0.20/0.28 tff(f55,plain,(
% 0.20/0.28 ($true = $false) | (~spl0_1 | ~spl0_2 | ~spl0_3 | spl0_4)),
% 0.20/0.28 inference(backward_demodulation,[],[f52,f53])).
% 0.20/0.28 tff(f56,plain,(
% 0.20/0.28 $false | (~spl0_1 | ~spl0_2 | ~spl0_3 | spl0_4)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f55])).
% 0.20/0.28 tff(f57,plain,(
% 0.20/0.28 ~spl0_1 | ~spl0_2 | ~spl0_3 | spl0_4),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f56])).
% 0.20/0.28 tff(f59,plain,(
% 0.20/0.28 (cQ = $true) | (~spl0_2 | ~spl0_4)),
% 0.20/0.28 inference(forward_demodulation,[],[f31,f21])).
% 0.20/0.28 tff(f61,plain,(
% 0.20/0.28 (cP = $true) | (~spl0_1 | ~spl0_2 | ~spl0_4)),
% 0.20/0.28 inference(backward_demodulation,[],[f16,f59])).
% 0.20/0.28 tff(f64,plain,(
% 0.20/0.28 spl0_3 | ~spl0_1 | ~spl0_2 | ~spl0_4),
% 0.20/0.28 inference(avatar_split_clause,[],[f61,f29,f19,f15,f25])).
% 0.20/0.28 tff(f66,plain,(
% 0.20/0.28 (cQ = $false) | (spl0_2 | ~spl0_4)),
% 0.20/0.28 inference(forward_demodulation,[],[f31,f46])).
% 0.20/0.28 tff(f67,plain,(
% 0.20/0.28 (cP != $false) | (spl0_1 | spl0_2 | ~spl0_4)),
% 0.20/0.28 inference(backward_demodulation,[],[f17,f66])).
% 0.20/0.28 tff(f68,plain,(
% 0.20/0.28 (cP = $false) | spl0_3),
% 0.20/0.28 inference(unit_resulting_resolution,[],[f13,f26])).
% 0.20/0.28 tff(f73,plain,(
% 0.20/0.28 $false | (spl0_1 | spl0_2 | spl0_3 | ~spl0_4)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f68,f67])).
% 0.20/0.28 tff(f74,plain,(
% 0.20/0.28 spl0_1 | spl0_2 | spl0_3 | ~spl0_4),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f73])).
% 0.20/0.28 cnf(s1, plain, ~spl0_1 | spl0_2, inference(sat_conversion,[],[f22])).
% 0.20/0.28 cnf(s2, plain, spl0_1 | ~spl0_2, inference(sat_conversion,[],[f23])).
% 0.20/0.28 cnf(s3, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f32])).
% 0.20/0.28 cnf(s4, plain, ~spl0_3 | ~spl0_4, inference(sat_conversion,[],[f33])).
% 0.20/0.28 cnf(s5, plain, spl0_1 | spl0_2 | ~spl0_3 | spl0_4, inference(sat_conversion,[],[f51])).
% 0.20/0.28 cnf(s6, plain, ~spl0_1 | ~spl0_2 | ~spl0_3 | spl0_4, inference(sat_conversion,[],[f57])).
% 0.20/0.28 cnf(s8, plain, ~spl0_1 | ~spl0_2 | spl0_3 | ~spl0_4, inference(sat_conversion,[],[f64])).
% 0.20/0.28 cnf(s10, plain, spl0_1 | spl0_2 | spl0_3 | ~spl0_4, inference(sat_conversion,[],[f74])).
% 0.20/0.28 cnf(s11, plain, spl0_3 | spl0_1, inference(rat,[],[s10,s3,s2])).
% 0.20/0.28 cnf(s12, plain, spl0_1, inference(rat,[],[s5,s4,s11,s2])).
% 0.20/0.28 cnf(s13, plain, spl0_2, inference(rat,[],[s1,s12])).
% 0.20/0.28 cnf(s14, plain, spl0_3, inference(rat,[],[s8,s3,s13,s12])).
% 0.20/0.28 cnf(s15, plain, ~spl0_4, inference(rat,[],[s4,s14])).
% 0.20/0.28 cnf(s16, plain, $false, inference(rat,[],[s6,s13,s12,s15,s14])).
% 0.20/0.28 tff(f75,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(avatar_sat_refutation,[],[s16])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (2336998)------------------------------
% 0.20/0.28 % (2336998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2336998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2336998)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2336998)Termination reason: Refutation
% 0.20/0.28 % (2336998)Time elapsed: 0.002 s
% 0.20/0.28 % (2336998)Peak memory usage: 12 MB
% 0.20/0.28 % (2336998)Instructions burned: 2 (million)
% 0.20/0.28 % (2336991)Success in time 0.034 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------