%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO169^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:49:05 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO169^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 % Computer : n014.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 16:36:16 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 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
% 0.19/0.29 % (2898796)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (2898807)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1836814923:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (2898802)% WARNING: option uhcvi not known.
% 0.19/0.29 % (2898802)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4020216627:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (2898801)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=693766335_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (2898804)dis+10_1_sil=32000:sp=arity:random_seed=2749692998:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (2898803)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3296584927:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (2898802)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (2898805)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3142408895:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (2898802)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.29 % (2898806)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2276536577:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (2898805)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (2898807) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2898796-2898807"...
% 0.19/0.29 % (2898807)...printing done.
% 0.19/0.29 % (2898807)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% 0.19/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.29 thf(func_def_3, type, cP: ($i > $i > $i > $o)).
% 0.19/0.29 thf(func_def_4, type, cPx: ($i > $i > $o)).
% 0.19/0.29 thf(f1,conjecture,(
% 0.19/0.29 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (((cP @ X1 @ X2 @ X4) & (cP @ X0 @ X1 @ X3)) => ((cP @ X3 @ X2 @ X5) <=> (cPx @ X4 @ X5))) & ! [X2 : $i] : (cP @ X2 @ X2 @ e) & ! [X1 : $i] : (cP @ X1 @ e @ X1) & ! [X0 : $i] : (cP @ e @ X0 @ X0)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab))),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_COMM)).
% 0.19/0.29 thf(f2,negated_conjecture,(
% 0.19/0.29 ~((! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (((cP @ X1 @ X2 @ X4) & (cP @ X0 @ X1 @ X3)) => ((cP @ X3 @ X2 @ X5) <=> (cPx @ X4 @ X5))) & ! [X2 : $i] : (cP @ X2 @ X2 @ e) & ! [X1 : $i] : (cP @ X1 @ e @ X1) & ! [X0 : $i] : (cP @ e @ X0 @ X0)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab)))),
% 0.19/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.29 thf(f3,plain,(
% 0.19/0.29 ~((! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (((cP @ X1 @ X2 @ X4) & (cP @ X0 @ X1 @ X3)) => ((cP @ X3 @ X2 @ X5) <=> (cPx @ X4 @ X5))) & ! [X6 : $i] : (cP @ X6 @ X6 @ e) & ! [X7 : $i] : (cP @ X7 @ e @ X7) & ! [X8 : $i] : (cP @ e @ X8 @ X8)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab)))),
% 0.19/0.29 inference(rectify,[],[f2])).
% 0.19/0.29 thf(f4,plain,(
% 0.19/0.29 ~((! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (((((cP @ X1 @ X2 @ X4)) = $true) & (((cP @ X0 @ X1 @ X3)) = $true)) => (((cP @ X3 @ X2 @ X5)) = ((cPx @ X4 @ X5)))) & ! [X6 : $i] : (((cP @ X6 @ X6 @ e)) = $true) & ! [X7 : $i] : (((cP @ X7 @ e @ X7)) = $true) & ! [X8 : $i] : (((cP @ e @ X8 @ X8)) = $true)) => ((((cP @ a @ b @ ab)) = $true) => (((cP @ b @ a @ ab)) = $true)))),
% 0.19/0.29 inference(fool_elimination,[],[f3])).
% 0.19/0.29 thf(f5,plain,(
% 0.19/0.29 ((((cP @ b @ a @ ab)) != $true) & (((cP @ a @ b @ ab)) = $true)) & (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((((cP @ X3 @ X2 @ X5)) = ((cPx @ X4 @ X5))) | ((((cP @ X1 @ X2 @ X4)) != $true) | (((cP @ X0 @ X1 @ X3)) != $true))) & ! [X6 : $i] : (((cP @ X6 @ X6 @ e)) = $true) & ! [X7 : $i] : (((cP @ X7 @ e @ X7)) = $true) & ! [X8 : $i] : (((cP @ e @ X8 @ X8)) = $true))),
% 0.19/0.29 inference(ennf_transformation,[],[f4])).
% 0.19/0.29 thf(f6,plain,(
% 0.19/0.29 (((cP @ b @ a @ ab)) != $true) & (((cP @ a @ b @ ab)) = $true) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((((cP @ X3 @ X2 @ X5)) = ((cPx @ X4 @ X5))) | (((cP @ X1 @ X2 @ X4)) != $true) | (((cP @ X0 @ X1 @ X3)) != $true)) & ! [X6 : $i] : (((cP @ X6 @ X6 @ e)) = $true) & ! [X7 : $i] : (((cP @ X7 @ e @ X7)) = $true) & ! [X8 : $i] : (((cP @ e @ X8 @ X8)) = $true)),
% 0.19/0.29 inference(flattening,[],[f5])).
% 0.19/0.29 thf(f7,plain,(
% 0.19/0.29 ( ! [X8 : $i] : ((((cP @ e @ X8 @ X8)) = $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f6])).
% 0.19/0.29 thf(f9,plain,(
% 0.19/0.29 ( ! [X6 : $i] : ((((cP @ X6 @ X6 @ e)) = $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f6])).
% 0.19/0.29 thf(f10,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((cP @ X3 @ X2 @ X5)) = ((cPx @ X4 @ X5))) | (((cP @ X1 @ X2 @ X4)) != $true) | (((cP @ X0 @ X1 @ X3)) != $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f6])).
% 0.19/0.29 thf(f12,plain,(
% 0.19/0.29 (((cP @ b @ a @ ab)) != $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f6])).
% 0.19/0.29 thf(f14,definition,(
% 0.19/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.29 thf(f15,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((cP @ X1 @ X2 @ X4)) != $true) | (((cP @ X3 @ X2 @ X5)) = $true) | (((cP @ X0 @ X1 @ X3)) != $true) | (((cPx @ X4 @ X5)) = $false)) )),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f10])).
% 0.19/0.29 thf(f16,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((cP @ X1 @ X2 @ X4)) != $true) | (((cP @ X3 @ X2 @ X5)) = $false) | (((cP @ X0 @ X1 @ X3)) != $true) | (((cPx @ X4 @ X5)) = $true)) )),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f10])).
% 0.19/0.29 thf(f19,plain,(
% 0.19/0.29 ($true != $true) | (((cP @ b @ a @ ab)) = $false)),
% 0.19/0.29 inference(constrained_superposition,[],[f12,f14])).
% 0.19/0.29 thf(f21,plain,(
% 0.19/0.29 (((cP @ b @ a @ ab)) = $false)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f19])).
% 0.19/0.29 thf(f31,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cP @ X1 @ X0 @ X2))) | ($true != ((cP @ X3 @ X0 @ X1))) | ($false = ((cPx @ e @ X2)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f15,f9])).
% 0.19/0.29 thf(f37,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((cP @ X3 @ X0 @ X1))) | ($true = ((cP @ X1 @ X0 @ X2))) | ($false = ((cPx @ e @ X2)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f31])).
% 0.19/0.29 thf(f55,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cP @ e @ X0 @ X1))) | ($false = ((cPx @ e @ X1)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f37,f9])).
% 0.19/0.29 thf(f61,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((cP @ e @ X0 @ X1))) | ($false = ((cPx @ e @ X1)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f55])).
% 0.19/0.29 thf(f71,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cP @ X1 @ X0 @ X2))) | ($false = ((cPx @ e @ X2))) | ($false = ((cPx @ e @ X1)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f37,f61])).
% 0.19/0.29 thf(f74,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((cP @ X1 @ X0 @ X2))) | ($false = ((cPx @ e @ X2))) | ($false = ((cPx @ e @ X1)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f71])).
% 0.19/0.29 thf(f101,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($false = ((cP @ X1 @ X0 @ X2))) | ($true != ((cP @ X3 @ X0 @ X1))) | ($true = ((cPx @ e @ X2)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f16,f9])).
% 0.19/0.29 thf(f104,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((cP @ X3 @ X0 @ X1))) | ($false = ((cP @ X1 @ X0 @ X2))) | ($true = ((cPx @ e @ X2)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f101])).
% 0.19/0.29 thf(f121,plain,(
% 0.19/0.29 ($true = $false) | ($false = ((cPx @ e @ ab))) | ($false = ((cPx @ e @ b)))),
% 0.19/0.29 inference(constrained_superposition,[],[f74,f21])).
% 0.19/0.29 thf(f134,plain,(
% 0.19/0.29 ($false = ((cPx @ e @ ab))) | ($false = ((cPx @ e @ b)))),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f121])).
% 0.19/0.29 thf(f136,definition,(
% 0.19/0.29 spl0_1 <=> ($false = ((cPx @ e @ b)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.19/0.29 thf(f138,plain,(
% 0.19/0.29 ($false = ((cPx @ e @ b))) | ~spl0_1),
% 0.19/0.29 inference(avatar_component_clause,[],[f136])).
% 0.19/0.29 thf(f140,definition,(
% 0.19/0.29 spl0_2 <=> ($false = ((cPx @ e @ ab)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.19/0.29 thf(f142,plain,(
% 0.19/0.29 ($false = ((cPx @ e @ ab))) | ~spl0_2),
% 0.19/0.29 inference(avatar_component_clause,[],[f140])).
% 0.19/0.29 thf(f145,plain,(
% 0.19/0.29 spl0_1 | spl0_2),
% 0.19/0.29 inference(avatar_split_clause,[],[f134,f140,f136])).
% 0.19/0.29 thf(f357,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($false = ((cP @ e @ X0 @ X1))) | ($true = ((cPx @ e @ X1)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f104,f9])).
% 0.19/0.29 thf(f360,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($false = ((cP @ e @ X0 @ X1))) | ($true = ((cPx @ e @ X1)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f357])).
% 0.19/0.29 thf(f418,plain,(
% 0.19/0.29 ( ! [X0 : $i] : (($true = $false) | ($true = ((cPx @ e @ X0)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f7,f360])).
% 0.19/0.29 thf(f458,plain,(
% 0.19/0.29 ( ! [X0 : $i] : (($true = ((cPx @ e @ X0)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f418])).
% 0.19/0.29 thf(f479,plain,(
% 0.19/0.29 ($true = $false) | ~spl0_2),
% 0.19/0.29 inference(constrained_superposition,[],[f458,f142])).
% 0.19/0.29 thf(f484,plain,(
% 0.19/0.29 $false | ~spl0_2),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f479])).
% 0.19/0.29 thf(f485,plain,(
% 0.19/0.29 ~spl0_2),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f484])).
% 0.19/0.29 thf(f486,plain,(
% 0.19/0.29 ($true = $false) | ~spl0_1),
% 0.19/0.29 inference(constrained_superposition,[],[f138,f458])).
% 0.19/0.29 thf(f492,plain,(
% 0.19/0.29 $false | ~spl0_1),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f486])).
% 0.19/0.29 thf(f493,plain,(
% 0.19/0.29 ~spl0_1),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f492])).
% 0.19/0.29 cnf(s3, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f145])).
% 0.19/0.29 cnf(s26, plain, ~spl0_2, inference(sat_conversion,[],[f485])).
% 0.19/0.29 cnf(s28, plain, ~spl0_1, inference(sat_conversion,[],[f493])).
% 0.19/0.29 cnf(s29, plain, $false, inference(rat,[],[s3,s26,s28])).
% 0.19/0.29 thf(f494,plain,(
% 0.19/0.29 $false),
% 0.19/0.29 inference(avatar_sat_refutation,[],[s29])).
% 0.19/0.29 % SZS output end Proof for theBenchmark
% 0.19/0.29 % (2898807)------------------------------
% 0.19/0.29 % (2898807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2898807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2898807)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2898807)Termination reason: Refutation
% 0.19/0.29 % (2898807)Time elapsed: 0.011 s
% 0.19/0.29 % (2898807)Peak memory usage: 12 MB
% 0.19/0.29 % (2898807)Instructions burned: 39 (million)
% 0.19/0.29 % (2898796)Success in time 0.039 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------