%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO382^5 : 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 : 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 08:47:34 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO382^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n014.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:49:45 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.19/0.26 % (2917472)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (2917477)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=855093066:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.26 % (2917477) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2917472-2917477"...
% 0.19/0.26 % (2917477)...printing done.
% 0.19/0.26 % (2917477)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% 0.19/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.26 thf(func_def_0, type, cS: ($i > $o)).
% 0.19/0.26 thf(func_def_1, type, cQ: ($i > $i > $o)).
% 0.19/0.26 thf(func_def_2, type, cP: ($i > $i > $o)).
% 0.19/0.26 thf(func_def_7, type, sK1: ($i > $i)).
% 0.19/0.26 thf(func_def_12, type, sK6: ($i > $i)).
% 0.19/0.26 thf(f1,conjecture,(
% 0.19/0.26 ((! [X2 : $i,X1 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2)) & ! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0)) => ? [X3 : $i] : ~(cS @ X3)) => ((! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0) & ! [X1 : $i,X2 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2))) => ? [X3 : $i] : ~(cS @ X3))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM407)).
% 0.19/0.26 thf(f2,negated_conjecture,(
% 0.19/0.26 ~(((! [X2 : $i,X1 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2)) & ! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0)) => ? [X3 : $i] : ~(cS @ X3)) => ((! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0) & ! [X1 : $i,X2 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2))) => ? [X3 : $i] : ~(cS @ X3)))),
% 0.19/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.26 thf(f3,plain,(
% 0.19/0.26 ~(((! [X0 : $i,X1 : $i] : ((cP @ X1 @ X0) => ~(cQ @ X1 @ X0)) & ! [X2 : $i] : ((cS @ X2) => ? [X3 : $i] : (cQ @ X3 @ X2)) & ? [X4 : $i] : ! [X5 : $i] : (cP @ X5 @ X4)) => ? [X6 : $i] : ~(cS @ X6)) => ((! [X7 : $i] : ((cS @ X7) => ? [X8 : $i] : (cQ @ X8 @ X7)) & ? [X9 : $i] : ! [X10 : $i] : (cP @ X10 @ X9) & ! [X11 : $i,X12 : $i] : ((cP @ X11 @ X12) => ~(cQ @ X11 @ X12))) => ? [X13 : $i] : ~(cS @ X13)))),
% 0.19/0.26 inference(rectify,[],[f2])).
% 0.19/0.26 thf(f4,plain,(
% 0.19/0.26 ~(((! [X0 : $i,X1 : $i] : ((((cP @ X1 @ X0)) = $true) => ~ ($true = ((cQ @ X1 @ X0)))) & ! [X2 : $i] : (($true = ((cS @ X2))) => ? [X3 : $i] : ($true = ((cQ @ X3 @ X2)))) & ? [X4 : $i] : ! [X5 : $i] : ($true = ((cP @ X5 @ X4)))) => ? [X6 : $i] : ~ (((cS @ X6)) = $true)) => ((! [X7 : $i] : (($true = ((cS @ X7))) => ? [X8 : $i] : ($true = ((cQ @ X8 @ X7)))) & ? [X9 : $i] : ! [X10 : $i] : (((cP @ X10 @ X9)) = $true) & ! [X11 : $i,X12 : $i] : (($true = ((cP @ X11 @ X12))) => ~ (((cQ @ X11 @ X12)) = $true))) => ? [X13 : $i] : ~ (((cS @ X13)) = $true)))),
% 0.19/0.26 inference(fool_elimination,[],[f3])).
% 0.19/0.26 thf(f5,plain,(
% 0.19/0.26 ~(((? [X4 : $i] : ! [X5 : $i] : ($true = ((cP @ X5 @ X4))) & ! [X0 : $i,X1 : $i] : ((((cP @ X1 @ X0)) = $true) => ($true != ((cQ @ X1 @ X0)))) & ! [X2 : $i] : (($true = ((cS @ X2))) => ? [X3 : $i] : ($true = ((cQ @ X3 @ X2))))) => ? [X6 : $i] : (((cS @ X6)) != $true)) => ((? [X9 : $i] : ! [X10 : $i] : (((cP @ X10 @ X9)) = $true) & ! [X7 : $i] : (($true = ((cS @ X7))) => ? [X8 : $i] : ($true = ((cQ @ X8 @ X7)))) & ! [X12 : $i,X11 : $i] : (($true = ((cP @ X11 @ X12))) => (((cQ @ X11 @ X12)) != $true))) => ? [X13 : $i] : (((cS @ X13)) != $true)))),
% 0.19/0.26 inference(flattening,[],[f4])).
% 0.19/0.26 thf(f6,plain,(
% 0.19/0.26 (! [X13 : $i] : (((cS @ X13)) = $true) & (? [X9 : $i] : ! [X10 : $i] : (((cP @ X10 @ X9)) = $true) & ! [X7 : $i] : (? [X8 : $i] : ($true = ((cQ @ X8 @ X7))) | ($true != ((cS @ X7)))) & ! [X12 : $i,X11 : $i] : (($true != ((cP @ X11 @ X12))) | (((cQ @ X11 @ X12)) != $true)))) & (? [X6 : $i] : (((cS @ X6)) != $true) | (! [X4 : $i] : ? [X5 : $i] : ($true != ((cP @ X5 @ X4))) | ? [X0 : $i,X1 : $i] : ((((cP @ X1 @ X0)) = $true) & ($true = ((cQ @ X1 @ X0)))) | ? [X2 : $i] : (! [X3 : $i] : ($true != ((cQ @ X3 @ X2))) & ($true = ((cS @ X2))))))),
% 0.19/0.26 inference(ennf_transformation,[],[f5])).
% 0.19/0.26 thf(f7,plain,(
% 0.19/0.26 ! [X12 : $i,X11 : $i] : (($true != ((cP @ X11 @ X12))) | (((cQ @ X11 @ X12)) != $true)) & ! [X13 : $i] : (((cS @ X13)) = $true) & ? [X9 : $i] : ! [X10 : $i] : (((cP @ X10 @ X9)) = $true) & (! [X4 : $i] : ? [X5 : $i] : ($true != ((cP @ X5 @ X4))) | ? [X2 : $i] : (! [X3 : $i] : ($true != ((cQ @ X3 @ X2))) & ($true = ((cS @ X2)))) | ? [X0 : $i,X1 : $i] : ((((cP @ X1 @ X0)) = $true) & ($true = ((cQ @ X1 @ X0)))) | ? [X6 : $i] : (((cS @ X6)) != $true)) & ! [X7 : $i] : (? [X8 : $i] : ($true = ((cQ @ X8 @ X7))) | ($true != ((cS @ X7))))),
% 0.19/0.26 inference(flattening,[],[f6])).
% 0.19/0.26 thf(f8,plain,(
% 0.19/0.26 ! [X0 : $i,X1 : $i] : ((((cP @ X1 @ X0)) != $true) | ($true != ((cQ @ X1 @ X0)))) & ! [X2 : $i] : ($true = ((cS @ X2))) & ? [X3 : $i] : ! [X4 : $i] : (((cP @ X4 @ X3)) = $true) & (! [X5 : $i] : ? [X6 : $i] : ($true != ((cP @ X6 @ X5))) | ? [X7 : $i] : (! [X8 : $i] : ($true != ((cQ @ X8 @ X7))) & ($true = ((cS @ X7)))) | ? [X9 : $i,X10 : $i] : ((((cP @ X10 @ X9)) = $true) & (((cQ @ X10 @ X9)) = $true)) | ? [X11 : $i] : ($true != ((cS @ X11)))) & ! [X12 : $i] : (? [X13 : $i] : ($true = ((cQ @ X13 @ X12))) | ($true != ((cS @ X12))))),
% 0.19/0.26 inference(rectify,[],[f7])).
% 0.19/0.26 thf(f9,plain,(
% 0.19/0.26 ! [X0 : $i,X1 : $i] : ((((cP @ X1 @ X0)) != $true) | ($true != ((cQ @ X1 @ X0)))) & ! [X2 : $i] : ($true = ((cS @ X2))) & ! [X4 : $i] : (((cP @ X4 @ sK0)) = $true) & (! [X5 : $i] : ($true != ((cP @ (sK1 @ X5) @ X5))) | (! [X8 : $i] : (((cQ @ X8 @ sK2)) != $true) & (((cS @ sK2)) = $true)) | (($true = ((cP @ sK4 @ sK3))) & (((cQ @ sK4 @ sK3)) = $true)) | (((cS @ sK5)) != $true)) & ! [X12 : $i] : ((((cQ @ (sK6 @ X12) @ X12)) = $true) | ($true != ((cS @ X12))))),
% 0.19/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,sK2,sK3,sK4,sK5,vAPP]),skolemize(X3,sK0),skolemize(X13,sK6 @ X12),skolemize(X7,sK2),skolemize(X9,sK3),skolemize(X10,sK4),skolemize(X11,sK5),skolemize(X13,sK6 @ X12)],[f8])).
% 0.19/0.26 thf(f10,plain,(
% 0.19/0.26 ( ! [X12 : $i] : (($true != ((cS @ X12))) | (((cQ @ (sK6 @ X12) @ X12)) = $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f9])).
% 0.19/0.26 thf(f13,plain,(
% 0.19/0.26 ( ! [X8 : $i,X5 : $i] : (($true != ((cP @ (sK1 @ X5) @ X5))) | (((cQ @ sK4 @ sK3)) = $true) | (((cQ @ X8 @ sK2)) != $true) | (((cS @ sK5)) != $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f9])).
% 0.19/0.26 thf(f14,plain,(
% 0.19/0.26 ( ! [X8 : $i,X5 : $i] : (($true = ((cP @ sK4 @ sK3))) | ($true != ((cP @ (sK1 @ X5) @ X5))) | (((cQ @ X8 @ sK2)) != $true) | (((cS @ sK5)) != $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f9])).
% 0.19/0.26 thf(f15,plain,(
% 0.19/0.26 ( ! [X4 : $i] : ((((cP @ X4 @ sK0)) = $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f9])).
% 0.19/0.26 thf(f16,plain,(
% 0.19/0.26 ( ! [X2 : $i] : (($true = ((cS @ X2)))) )),
% 0.19/0.26 inference(cnf_transformation,[],[f9])).
% 0.19/0.26 thf(f17,plain,(
% 0.19/0.26 ( ! [X0 : $i,X1 : $i] : (($true != ((cQ @ X1 @ X0))) | (((cP @ X1 @ X0)) != $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f9])).
% 0.19/0.26 thf(f21,definition,(
% 0.19/0.26 spl7_1 <=> (((cS @ sK5)) = $true)),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.19/0.26 thf(f23,plain,(
% 0.19/0.26 (((cS @ sK5)) != $true) | spl7_1),
% 0.19/0.26 inference(avatar_component_clause,[],[f21])).
% 0.19/0.26 thf(f25,definition,(
% 0.19/0.26 spl7_2 <=> ! [X5 : $i] : ($true != ((cP @ (sK1 @ X5) @ X5)))),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.19/0.26 thf(f26,plain,(
% 0.19/0.26 ( ! [X5 : $i] : (($true != ((cP @ (sK1 @ X5) @ X5)))) ) | ~spl7_2),
% 0.19/0.26 inference(avatar_component_clause,[],[f25])).
% 0.19/0.26 thf(f28,definition,(
% 0.19/0.26 spl7_3 <=> ($true = ((cP @ sK4 @ sK3)))),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.19/0.26 thf(f30,plain,(
% 0.19/0.26 ($true = ((cP @ sK4 @ sK3))) | ~spl7_3),
% 0.19/0.26 inference(avatar_component_clause,[],[f28])).
% 0.19/0.26 thf(f32,definition,(
% 0.19/0.26 spl7_4 <=> ! [X8 : $i] : (((cQ @ X8 @ sK2)) != $true)),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
% 0.19/0.26 thf(f33,plain,(
% 0.19/0.26 ( ! [X8 : $i] : ((((cQ @ X8 @ sK2)) != $true)) ) | ~spl7_4),
% 0.19/0.26 inference(avatar_component_clause,[],[f32])).
% 0.19/0.26 thf(f34,plain,(
% 0.19/0.26 ~spl7_1 | spl7_2 | spl7_3 | spl7_4),
% 0.19/0.26 inference(avatar_split_clause,[],[f14,f32,f28,f25,f21])).
% 0.19/0.26 thf(f41,definition,(
% 0.19/0.26 spl7_6 <=> (((cQ @ sK4 @ sK3)) = $true)),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.19/0.26 thf(f43,plain,(
% 0.19/0.26 (((cQ @ sK4 @ sK3)) = $true) | ~spl7_6),
% 0.19/0.27 inference(avatar_component_clause,[],[f41])).
% 0.19/0.27 thf(f44,plain,(
% 0.19/0.27 spl7_2 | spl7_6 | ~spl7_1 | spl7_4),
% 0.19/0.27 inference(avatar_split_clause,[],[f13,f32,f21,f41,f25])).
% 0.19/0.27 thf(f46,plain,(
% 0.19/0.27 $false | spl7_1),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f23,f16])).
% 0.19/0.27 thf(f47,plain,(
% 0.19/0.27 spl7_1),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f46])).
% 0.19/0.27 thf(f48,plain,(
% 0.19/0.27 ( ! [X0 : $i] : (($true != $true) | ($true = ((cQ @ (sK6 @ X0) @ X0)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f10,f16])).
% 0.19/0.27 thf(f49,plain,(
% 0.19/0.27 ( ! [X0 : $i] : (($true = ((cQ @ (sK6 @ X0) @ X0)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f48])).
% 0.19/0.27 thf(f50,plain,(
% 0.19/0.27 ($true != $true) | ~spl7_4),
% 0.19/0.27 inference(constrained_superposition,[],[f33,f49])).
% 0.19/0.27 thf(f51,plain,(
% 0.19/0.27 $false | ~spl7_4),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f50])).
% 0.19/0.27 thf(f52,plain,(
% 0.19/0.27 ~spl7_4),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f51])).
% 0.19/0.27 thf(f53,plain,(
% 0.19/0.27 ($true != $true) | ~spl7_2),
% 0.19/0.27 inference(constrained_superposition,[],[f26,f15])).
% 0.19/0.27 thf(f54,plain,(
% 0.19/0.27 $false | ~spl7_2),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f53])).
% 0.19/0.27 thf(f55,plain,(
% 0.19/0.27 ~spl7_2),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f54])).
% 0.19/0.27 thf(f57,plain,(
% 0.19/0.27 ($true != ((cP @ sK4 @ sK3))) | ($true != $true) | ~spl7_6),
% 0.19/0.27 inference(constrained_superposition,[],[f17,f43])).
% 0.19/0.27 thf(f58,plain,(
% 0.19/0.27 ($true != ((cP @ sK4 @ sK3))) | ~spl7_6),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f57])).
% 0.19/0.27 thf(f60,plain,(
% 0.19/0.27 $false | (~spl7_3 | ~spl7_6)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f58,f30])).
% 0.19/0.27 thf(f61,plain,(
% 0.19/0.27 ~spl7_3 | ~spl7_6),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f60])).
% 0.19/0.27 cnf(s1, plain, ~spl7_1 | spl7_2 | spl7_3 | spl7_4, inference(sat_conversion,[],[f34])).
% 0.19/0.27 cnf(s3, plain, ~spl7_1 | spl7_2 | spl7_4 | spl7_6, inference(sat_conversion,[],[f44])).
% 0.19/0.27 cnf(s5, plain, spl7_1, inference(sat_conversion,[],[f47])).
% 0.19/0.27 cnf(s6, plain, ~spl7_4, inference(sat_conversion,[],[f52])).
% 0.19/0.27 cnf(s7, plain, ~spl7_2, inference(sat_conversion,[],[f55])).
% 0.19/0.27 cnf(s8, plain, ~spl7_3 | ~spl7_6, inference(sat_conversion,[],[f61])).
% 0.19/0.27 cnf(s10, plain, spl7_6, inference(rat,[],[s3,s6,s7,s5])).
% 0.19/0.27 cnf(s11, plain, ~spl7_3, inference(rat,[],[s8,s10])).
% 0.19/0.27 cnf(s13, plain, $false, inference(rat,[],[s1,s6,s11,s7,s5])).
% 0.19/0.27 thf(f62,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s13])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (2917477)------------------------------
% 0.19/0.27 % (2917477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2917477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2917477)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2917477)Termination reason: Refutation
% 0.19/0.27 % (2917477)Time elapsed: 0.002 s
% 0.19/0.27 % (2917477)Peak memory usage: 13 MB
% 0.19/0.27 % (2917477)Instructions burned: 5 (million)
% 0.19/0.27 % (2917472)Success in time 0.034 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------