%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN382^5 : 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 : n007.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 08:41:41 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN382^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:13:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.27 % (3567920)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (3567931)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (3567931)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.27 % (3567931)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1323741967:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.27 % (3567931) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3567920-3567931"...
% 0.21/0.27 % (3567931)...printing done.
% 0.21/0.27 % (3567931)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% 0.21/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.27 thf(func_def_0, type, cQ: ($i > $i > $o)).
% 0.21/0.27 thf(func_def_1, type, cP: ($i > $i > $o)).
% 0.21/0.27 thf(func_def_6, type, sK1: ($i > $i)).
% 0.21/0.27 thf(func_def_7, type, sF2: ($i > $o)).
% 0.21/0.27 thf(func_def_8, type, sF3: ($i > $o)).
% 0.21/0.27 thf(func_def_9, type, sF4: ($i > $i)).
% 0.21/0.27 thf(func_def_10, type, sF5: ($i > $o)).
% 0.21/0.27 thf(func_def_11, type, sF6: ($i > $i > $o)).
% 0.21/0.27 thf(f1,conjecture,(
% 0.21/0.27 ! [X0 : $i] : ? [X1 : $i] : (! [X2 : $i] : (cP @ X1 @ X2) | (cQ @ X1 @ X0)) => ! [X2 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X2) | (cP @ X1 @ X2))),
% 0.21/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2134)).
% 0.21/0.27 thf(f2,negated_conjecture,(
% 0.21/0.27 ~(! [X0 : $i] : ? [X1 : $i] : (! [X2 : $i] : (cP @ X1 @ X2) | (cQ @ X1 @ X0)) => ! [X2 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X2) | (cP @ X1 @ X2)))),
% 0.21/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.27 thf(f3,plain,(
% 0.21/0.27 ~(! [X0 : $i] : ? [X1 : $i] : (! [X2 : $i] : (cP @ X1 @ X2) | (cQ @ X1 @ X0)) => ! [X3 : $i] : ? [X4 : $i] : ((cQ @ X4 @ X3) | (cP @ X4 @ X3)))),
% 0.21/0.27 inference(rectify,[],[f2])).
% 0.21/0.27 thf(f4,plain,(
% 0.21/0.27 ~(! [X0 : $i] : ? [X1 : $i] : ((((cQ @ X1 @ X0)) = $true) | ! [X2 : $i] : (((cP @ X1 @ X2)) = $true)) => ! [X3 : $i] : ? [X4 : $i] : (($true = ((cP @ X4 @ X3))) | ($true = ((cQ @ X4 @ X3)))))),
% 0.21/0.27 inference(fool_elimination,[],[f3])).
% 0.21/0.27 thf(f5,plain,(
% 0.21/0.27 ? [X3 : $i] : ! [X4 : $i] : (($true != ((cQ @ X4 @ X3))) & ($true != ((cP @ X4 @ X3)))) & ! [X0 : $i] : ? [X1 : $i] : ((((cQ @ X1 @ X0)) = $true) | ! [X2 : $i] : (((cP @ X1 @ X2)) = $true))),
% 0.21/0.27 inference(ennf_transformation,[],[f4])).
% 0.21/0.27 thf(f6,plain,(
% 0.21/0.27 ? [X0 : $i] : ! [X1 : $i] : ((((cQ @ X1 @ X0)) != $true) & ($true != ((cP @ X1 @ X0)))) & ! [X2 : $i] : ? [X3 : $i] : (($true = ((cQ @ X3 @ X2))) | ! [X4 : $i] : (((cP @ X3 @ X4)) = $true))),
% 0.21/0.27 inference(rectify,[],[f5])).
% 0.21/0.27 thf(f7,plain,(
% 0.21/0.27 ! [X1 : $i] : ((((cQ @ X1 @ sK0)) != $true) & ($true != ((cP @ X1 @ sK0)))) & ! [X2 : $i] : ((((cQ @ (sK1 @ X2) @ X2)) = $true) | ! [X4 : $i] : ($true = ((cP @ (sK1 @ X2) @ X4))))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X3,sK1 @ X2)],[f6])).
% 0.21/0.27 thf(f8,plain,(
% 0.21/0.27 ( ! [X2 : $i,X4 : $i] : ((((cQ @ (sK1 @ X2) @ X2)) = $true) | ($true = ((cP @ (sK1 @ X2) @ X4)))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f7])).
% 0.21/0.27 thf(f9,plain,(
% 0.21/0.27 ( ! [X1 : $i] : (($true != ((cP @ X1 @ sK0)))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f7])).
% 0.21/0.27 thf(f10,plain,(
% 0.21/0.27 ( ! [X1 : $i] : ((((cQ @ X1 @ sK0)) != $true)) )),
% 0.21/0.27 inference(cnf_transformation,[],[f7])).
% 0.21/0.27 thf(f13,definition,(
% 0.21/0.27 ( ! [X1 : $i] : ((((sF2 @ X1)) = ((cQ @ X1 @ sK0)))) )),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.21/0.27 thf(f14,plain,(
% 0.21/0.27 ( ! [X1 : $i] : ((((sF2 @ X1)) != $true)) )),
% 0.21/0.27 inference(definition_folding,[],[f10,f13])).
% 0.21/0.27 thf(f15,definition,(
% 0.21/0.27 ( ! [X1 : $i] : ((((sF3 @ X1)) = ((cP @ X1 @ sK0)))) )),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.21/0.27 thf(f16,plain,(
% 0.21/0.27 ( ! [X1 : $i] : ((((sF3 @ X1)) != $true)) )),
% 0.21/0.27 inference(definition_folding,[],[f9,f15])).
% 0.21/0.27 thf(f17,definition,(
% 0.21/0.27 ( ! [X2 : $i] : ((((sF4 @ X2)) = ((sK1 @ X2)))) )),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.21/0.27 thf(f18,plain,(
% 0.21/0.27 ( ! [X2 : $i] : ((((sK1 @ X2)) = ((sF4 @ X2)))) )),
% 0.21/0.27 inference(reorient_equations,[],[f17])).
% 0.21/0.27 thf(f19,definition,(
% 0.21/0.27 ( ! [X2 : $i] : ((((sF5 @ X2)) = ((cQ @ (sF4 @ X2) @ X2)))) )),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.21/0.27 thf(f20,definition,(
% 0.21/0.27 ( ! [X2 : $i,X4 : $i] : ((((sF6 @ X4 @ X2)) = ((cP @ (sF4 @ X2) @ X4)))) )),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 0.21/0.27 thf(f21,plain,(
% 0.21/0.27 ( ! [X2 : $i,X4 : $i] : (($true = ((sF6 @ X4 @ X2))) | ($true = ((sF5 @ X2)))) )),
% 0.21/0.27 inference(definition_folding,[],[f8,f20,f18,f19,f18])).
% 0.21/0.27 thf(f23,plain,(
% 0.21/0.27 ( ! [X2 : $i] : (($true = ((cQ @ (sF4 @ X2) @ X2))) | ($false = ((sF5 @ X2)))) )),
% 0.21/0.27 inference(iff_proxy_clausification,[],[f19])).
% 0.21/0.27 thf(f24,plain,(
% 0.21/0.27 ( ! [X1 : $i] : (($false = ((cQ @ X1 @ sK0))) | (((sF2 @ X1)) = $true)) )),
% 0.21/0.27 inference(iff_proxy_clausification,[],[f13])).
% 0.21/0.27 thf(f27,plain,(
% 0.21/0.27 ( ! [X2 : $i,X4 : $i] : (($true = ((cP @ (sF4 @ X2) @ X4))) | ($false = ((sF6 @ X4 @ X2)))) )),
% 0.21/0.27 inference(iff_proxy_clausification,[],[f20])).
% 0.21/0.27 thf(f28,plain,(
% 0.21/0.27 ( ! [X1 : $i] : (($false = ((cP @ X1 @ sK0))) | (((sF3 @ X1)) = $true)) )),
% 0.21/0.27 inference(iff_proxy_clausification,[],[f15])).
% 0.21/0.27 thf(f47,plain,(
% 0.21/0.27 ( ! [X1 : $i] : (($false = ((cQ @ X1 @ sK0)))) )),
% 0.21/0.27 inference(forward_subsumption_resolution,[],[f24,f14])).
% 0.21/0.27 thf(f50,plain,(
% 0.21/0.27 ( ! [X1 : $i] : (($false = ((cP @ X1 @ sK0)))) )),
% 0.21/0.27 inference(forward_subsumption_resolution,[],[f28,f16])).
% 0.21/0.27 thf(f58,plain,(
% 0.21/0.27 (((sF5 @ sK0)) = $false) | ($false = $true)),
% 0.21/0.27 inference(constrained_superposition,[],[f47,f23])).
% 0.21/0.27 thf(f60,plain,(
% 0.21/0.27 (((sF5 @ sK0)) = $false)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f58])).
% 0.21/0.27 thf(f68,plain,(
% 0.21/0.27 ( ! [X0 : $i] : (($false = $true) | ($false = ((sF6 @ sK0 @ X0)))) )),
% 0.21/0.27 inference(constrained_superposition,[],[f27,f50])).
% 0.21/0.27 thf(f73,plain,(
% 0.21/0.27 ( ! [X0 : $i] : (($false = ((sF6 @ sK0 @ X0)))) )),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f68])).
% 0.21/0.27 thf(f77,plain,(
% 0.21/0.27 ( ! [X0 : $i] : (($true = ((sF5 @ X0))) | ($false = $true)) )),
% 0.21/0.27 inference(constrained_superposition,[],[f21,f73])).
% 0.21/0.27 thf(f78,plain,(
% 0.21/0.27 ( ! [X0 : $i] : (($true = ((sF5 @ X0)))) )),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f77])).
% 0.21/0.27 thf(f81,plain,(
% 0.21/0.27 ($false = $true)),
% 0.21/0.27 inference(constrained_superposition,[],[f78,f60])).
% 0.21/0.27 thf(f83,plain,(
% 0.21/0.27 $false),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f81])).
% 0.21/0.27 % SZS output end Proof for theBenchmark
% 0.21/0.27 % (3567931)------------------------------
% 0.21/0.27 % (3567931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (3567931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (3567931)CaDiCaL version: 2.1.3
% 0.21/0.27 % (3567931)Termination reason: Refutation
% 0.21/0.27 % (3567931)Time elapsed: 0.002 s
% 0.21/0.27 % (3567931)Peak memory usage: 12 MB
% 0.21/0.27 % (3567931)Instructions burned: 5 (million)
% 0.21/0.27 % (3567920)Success in time 0.033 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------