%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO382^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:49:50 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% 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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n009.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 16:50:01 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.24 % (58515)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (58521)% WARNING: option uhcvi not known.
% 0.07/0.24 % (58521)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3135397486:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.24 % (58521)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.24 % (58521)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.24 % (58521) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-58515-58521"...
% 0.07/0.24 % (58521)...printing done.
% 0.07/0.24 % (58521)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% 0.07/0.24 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.24 thf(func_def_0, type, cS: ($i > $o)).
% 0.07/0.24 thf(func_def_1, type, cQ: ($i > $i > $o)).
% 0.07/0.24 thf(func_def_2, type, cP: ($i > $i > $o)).
% 0.07/0.24 thf(func_def_6, type, sK0: ($i > $i)).
% 0.07/0.24 thf(func_def_12, type, sK6: ($i > $i)).
% 0.07/0.24 thf(f1,conjecture,(
% 0.07/0.24 ((! [X1 : $i,X2 : $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,X2 : $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))),
% 0.07/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM407)).
% 0.07/0.24 thf(f2,negated_conjecture,(
% 0.07/0.24 ~(((! [X1 : $i,X2 : $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,X2 : $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)))),
% 0.07/0.24 inference(negated_conjecture,[status(cth)],[f1])).
% 0.07/0.24 thf(f3,plain,(
% 0.07/0.24 ~(((! [X0 : $i,X1 : $i] : ((cP @ X0 @ X1) => ~(cQ @ X0 @ X1)) & ! [X2 : $i] : ((cS @ X2) => ? [X3 : $i] : (cQ @ X3 @ X2)) & ? [X4 : $i] : ! [X5 : $i] : (cP @ X5 @ X4)) => ? [X6 : $i] : ~(cS @ X6)) => ((! [X7 : $i,X8 : $i] : ((cP @ X7 @ X8) => ~(cQ @ X7 @ X8)) & ! [X9 : $i] : ((cS @ X9) => ? [X10 : $i] : (cQ @ X10 @ X9)) & ? [X11 : $i] : ! [X12 : $i] : (cP @ X12 @ X11)) => ? [X13 : $i] : ~(cS @ X13)))),
% 0.07/0.24 inference(rectify,[],[f2])).
% 0.07/0.24 thf(f4,plain,(
% 0.07/0.24 ~(((! [X0 : $i,X1 : $i] : ((((cP @ X0 @ X1)) = $true) => ~ (((cQ @ X0 @ X1)) = $true)) & ! [X2 : $i] : ((((cS @ X2)) = $true) => ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true)) & ? [X4 : $i] : ! [X5 : $i] : (((cP @ X5 @ X4)) = $true)) => ? [X6 : $i] : ~ (((cS @ X6)) = $true)) => ((! [X7 : $i,X8 : $i] : ((((cP @ X7 @ X8)) = $true) => ~ (((cQ @ X7 @ X8)) = $true)) & ! [X9 : $i] : ((((cS @ X9)) = $true) => ? [X10 : $i] : (((cQ @ X10 @ X9)) = $true)) & ? [X11 : $i] : ! [X12 : $i] : (((cP @ X12 @ X11)) = $true)) => ? [X13 : $i] : ~ (((cS @ X13)) = $true)))),
% 0.07/0.24 inference(fool_elimination,[],[f3])).
% 0.07/0.24 thf(f5,plain,(
% 0.07/0.24 ~(((! [X0 : $i,X1 : $i] : ((((cP @ X0 @ X1)) = $true) => (((cQ @ X0 @ X1)) != $true)) & ! [X2 : $i] : ((((cS @ X2)) = $true) => ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true)) & ? [X4 : $i] : ! [X5 : $i] : (((cP @ X5 @ X4)) = $true)) => ? [X6 : $i] : (((cS @ X6)) != $true)) => ((! [X7 : $i,X8 : $i] : ((((cP @ X7 @ X8)) = $true) => (((cQ @ X7 @ X8)) != $true)) & ! [X9 : $i] : ((((cS @ X9)) = $true) => ? [X10 : $i] : (((cQ @ X10 @ X9)) = $true)) & ? [X11 : $i] : ! [X12 : $i] : (((cP @ X12 @ X11)) = $true)) => ? [X13 : $i] : (((cS @ X13)) != $true)))),
% 0.07/0.24 inference(flattening,[],[f4])).
% 0.07/0.24 thf(f6,plain,(
% 0.07/0.24 (! [X13 : $i] : (((cS @ X13)) = $true) & (! [X7 : $i,X8 : $i] : ((((cQ @ X7 @ X8)) != $true) | (((cP @ X7 @ X8)) != $true)) & ! [X9 : $i] : (? [X10 : $i] : (((cQ @ X10 @ X9)) = $true) | (((cS @ X9)) != $true)) & ? [X11 : $i] : ! [X12 : $i] : (((cP @ X12 @ X11)) = $true))) & (? [X6 : $i] : (((cS @ X6)) != $true) | (? [X0 : $i,X1 : $i] : ((((cQ @ X0 @ X1)) = $true) & (((cP @ X0 @ X1)) = $true)) | ? [X2 : $i] : (! [X3 : $i] : (((cQ @ X3 @ X2)) != $true) & (((cS @ X2)) = $true)) | ! [X4 : $i] : ? [X5 : $i] : (((cP @ X5 @ X4)) != $true)))),
% 0.07/0.24 inference(ennf_transformation,[],[f5])).
% 0.07/0.24 thf(f7,plain,(
% 0.07/0.24 ! [X13 : $i] : (((cS @ X13)) = $true) & ! [X7 : $i,X8 : $i] : ((((cQ @ X7 @ X8)) != $true) | (((cP @ X7 @ X8)) != $true)) & ! [X9 : $i] : (? [X10 : $i] : (((cQ @ X10 @ X9)) = $true) | (((cS @ X9)) != $true)) & ? [X11 : $i] : ! [X12 : $i] : (((cP @ X12 @ X11)) = $true) & (? [X6 : $i] : (((cS @ X6)) != $true) | ? [X0 : $i,X1 : $i] : ((((cQ @ X0 @ X1)) = $true) & (((cP @ X0 @ X1)) = $true)) | ? [X2 : $i] : (! [X3 : $i] : (((cQ @ X3 @ X2)) != $true) & (((cS @ X2)) = $true)) | ! [X4 : $i] : ? [X5 : $i] : (((cP @ X5 @ X4)) != $true))),
% 0.07/0.24 inference(flattening,[],[f6])).
% 0.07/0.24 thf(f8,plain,(
% 0.07/0.24 ! [X0 : $i] : ($true = ((cS @ X0))) & ! [X1 : $i,X2 : $i] : ((((cQ @ X1 @ X2)) != $true) | (((cP @ X1 @ X2)) != $true)) & ! [X3 : $i] : (? [X4 : $i] : ($true = ((cQ @ X4 @ X3))) | (((cS @ X3)) != $true)) & ? [X5 : $i] : ! [X6 : $i] : ($true = ((cP @ X6 @ X5))) & (? [X7 : $i] : ($true != ((cS @ X7))) | ? [X8 : $i,X9 : $i] : (($true = ((cQ @ X8 @ X9))) & ($true = ((cP @ X8 @ X9)))) | ? [X10 : $i] : (! [X11 : $i] : ($true != ((cQ @ X11 @ X10))) & ($true = ((cS @ X10)))) | ! [X12 : $i] : ? [X13 : $i] : ($true != ((cP @ X13 @ X12))))),
% 0.07/0.24 inference(rectify,[],[f7])).
% 0.07/0.24 thf(f9,plain,(
% 0.07/0.24 ! [X0 : $i] : ($true = ((cS @ X0))) & ! [X1 : $i,X2 : $i] : ((((cQ @ X1 @ X2)) != $true) | (((cP @ X1 @ X2)) != $true)) & ! [X3 : $i] : (($true = ((cQ @ (sK0 @ X3) @ X3))) | (((cS @ X3)) != $true)) & ! [X6 : $i] : ($true = ((cP @ X6 @ sK1))) & (($true != ((cS @ sK2))) | (($true = ((cQ @ sK3 @ sK4))) & ($true = ((cP @ sK3 @ sK4)))) | (! [X11 : $i] : ($true != ((cQ @ X11 @ sK5))) & ($true = ((cS @ sK5)))) | ! [X12 : $i] : ($true != ((cP @ (sK6 @ X12) @ X12))))),
% 0.07/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2,sK3,sK4,sK5,vAPP]),skolemize(X13,sK6 @ X12),skolemize(X5,sK1),skolemize(X7,sK2),skolemize(X8,sK3),skolemize(X9,sK4),skolemize(X10,sK5),skolemize(X13,sK6 @ X12)],[f8])).
% 0.07/0.24 thf(f11,plain,(
% 0.07/0.24 ( ! [X11 : $i,X12 : $i] : (($true != ((cS @ sK2))) | ($true = ((cP @ sK3 @ sK4))) | ($true != ((cQ @ X11 @ sK5))) | ($true != ((cP @ (sK6 @ X12) @ X12)))) )),
% 0.07/0.24 inference(cnf_transformation,[],[f9])).
% 0.07/0.24 thf(f13,plain,(
% 0.07/0.24 ( ! [X11 : $i,X12 : $i] : (($true != ((cS @ sK2))) | ($true = ((cQ @ sK3 @ sK4))) | ($true != ((cQ @ X11 @ sK5))) | ($true != ((cP @ (sK6 @ X12) @ X12)))) )),
% 0.07/0.24 inference(cnf_transformation,[],[f9])).
% 0.07/0.24 thf(f14,plain,(
% 0.07/0.24 ( ! [X6 : $i] : (($true = ((cP @ X6 @ sK1)))) )),
% 0.07/0.24 inference(cnf_transformation,[],[f9])).
% 0.07/0.24 thf(f15,plain,(
% 0.07/0.24 ( ! [X3 : $i] : (($true = ((cQ @ (sK0 @ X3) @ X3))) | (((cS @ X3)) != $true)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f9])).
% 0.07/0.24 thf(f16,plain,(
% 0.07/0.24 ( ! [X2 : $i,X1 : $i] : ((((cP @ X1 @ X2)) != $true) | (((cQ @ X1 @ X2)) != $true)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f9])).
% 0.07/0.24 thf(f17,plain,(
% 0.07/0.24 ( ! [X0 : $i] : (($true = ((cS @ X0)))) )),
% 0.07/0.24 inference(cnf_transformation,[],[f9])).
% 0.07/0.24 thf(f21,definition,(
% 0.07/0.24 spl7_1 <=> ! [X12 : $i] : ($true != ((cP @ (sK6 @ X12) @ X12)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.07/0.24 thf(f22,plain,(
% 0.07/0.24 ( ! [X12 : $i] : (($true != ((cP @ (sK6 @ X12) @ X12)))) ) | ~spl7_1),
% 0.07/0.24 inference(avatar_component_clause,[],[f21])).
% 0.07/0.24 thf(f28,definition,(
% 0.07/0.24 spl7_3 <=> ($true = ((cP @ sK3 @ sK4)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.07/0.24 thf(f30,plain,(
% 0.07/0.24 ($true = ((cP @ sK3 @ sK4))) | ~spl7_3),
% 0.07/0.24 inference(avatar_component_clause,[],[f28])).
% 0.07/0.24 thf(f32,definition,(
% 0.07/0.24 spl7_4 <=> ($true = ((cS @ sK2)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
% 0.07/0.24 thf(f34,plain,(
% 0.07/0.24 ($true != ((cS @ sK2))) | spl7_4),
% 0.07/0.24 inference(avatar_component_clause,[],[f32])).
% 0.07/0.24 thf(f37,definition,(
% 0.07/0.24 spl7_5 <=> ! [X11 : $i] : ($true != ((cQ @ X11 @ sK5)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition])).
% 0.07/0.24 thf(f38,plain,(
% 0.07/0.24 ( ! [X11 : $i] : (($true != ((cQ @ X11 @ sK5)))) ) | ~spl7_5),
% 0.07/0.24 inference(avatar_component_clause,[],[f37])).
% 0.07/0.24 thf(f39,plain,(
% 0.07/0.24 spl7_1 | spl7_5 | spl7_3 | ~spl7_4),
% 0.07/0.24 inference(avatar_split_clause,[],[f11,f32,f28,f37,f21])).
% 0.07/0.24 thf(f41,definition,(
% 0.07/0.24 spl7_6 <=> ($true = ((cQ @ sK3 @ sK4)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.07/0.24 thf(f45,plain,(
% 0.07/0.24 spl7_1 | spl7_5 | spl7_6 | ~spl7_4),
% 0.07/0.24 inference(avatar_split_clause,[],[f13,f32,f41,f37,f21])).
% 0.07/0.24 thf(f46,plain,(
% 0.07/0.24 $false | spl7_4),
% 0.07/0.24 inference(forward_subsumption_resolution,[],[f34,f17])).
% 0.07/0.24 thf(f47,plain,(
% 0.07/0.24 spl7_4),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f46])).
% 0.07/0.24 thf(f48,plain,(
% 0.07/0.24 ( ! [X3 : $i] : (($true = ((cQ @ (sK0 @ X3) @ X3)))) )),
% 0.07/0.24 inference(forward_subsumption_resolution,[],[f15,f17])).
% 0.07/0.24 thf(f50,plain,(
% 0.07/0.24 ($true != $true) | ($true != ((cQ @ sK3 @ sK4))) | ~spl7_3),
% 0.07/0.24 inference(constrained_superposition,[],[f16,f30])).
% 0.07/0.24 thf(f51,plain,(
% 0.07/0.24 ($true != ((cQ @ sK3 @ sK4))) | ~spl7_3),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f50])).
% 0.07/0.24 thf(f55,plain,(
% 0.07/0.24 ~spl7_6 | ~spl7_3),
% 0.07/0.24 inference(avatar_split_clause,[],[f51,f28,f41])).
% 0.07/0.24 thf(f56,plain,(
% 0.07/0.24 ($true != $true) | ~spl7_1),
% 0.07/0.24 inference(constrained_superposition,[],[f22,f14])).
% 0.07/0.24 thf(f57,plain,(
% 0.07/0.24 $false | ~spl7_1),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f56])).
% 0.07/0.24 thf(f58,plain,(
% 0.07/0.24 ~spl7_1),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f57])).
% 0.07/0.24 thf(f59,plain,(
% 0.07/0.24 ($true != $true) | ~spl7_5),
% 0.07/0.24 inference(constrained_superposition,[],[f38,f48])).
% 0.07/0.24 thf(f60,plain,(
% 0.07/0.24 $false | ~spl7_5),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f59])).
% 0.07/0.24 thf(f61,plain,(
% 0.07/0.24 ~spl7_5),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f60])).
% 0.07/0.24 cnf(s2, plain, spl7_1 | spl7_3 | ~spl7_4 | spl7_5, inference(sat_conversion,[],[f39])).
% 0.07/0.24 cnf(s4, plain, spl7_1 | ~spl7_4 | spl7_5 | spl7_6, inference(sat_conversion,[],[f45])).
% 0.07/0.24 cnf(s5, plain, spl7_4, inference(sat_conversion,[],[f47])).
% 0.07/0.24 cnf(s7, plain, ~spl7_3 | ~spl7_6, inference(sat_conversion,[],[f55])).
% 0.07/0.24 cnf(s8, plain, ~spl7_1, inference(sat_conversion,[],[f58])).
% 0.07/0.24 cnf(s9, plain, ~spl7_5, inference(sat_conversion,[],[f61])).
% 0.07/0.24 cnf(s10, plain, spl7_6, inference(rat,[],[s4,s9,s5,s8])).
% 0.07/0.24 cnf(s11, plain, ~spl7_3, inference(rat,[],[s7,s10])).
% 0.07/0.24 cnf(s12, plain, $false, inference(rat,[],[s2,s9,s5,s11,s8])).
% 0.07/0.24 thf(f62,plain,(
% 0.07/0.24 $false),
% 0.07/0.24 inference(avatar_sat_refutation,[],[s12])).
% 0.07/0.24 % SZS output end Proof for theBenchmark
% 0.07/0.24 % (58521)------------------------------
% 0.07/0.24 % (58521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.24 % (58521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.24 % (58521)CaDiCaL version: 2.1.3
% 0.07/0.24 % (58521)Termination reason: Refutation
% 0.07/0.24 % (58521)Time elapsed: 0.002 s
% 0.07/0.24 % (58521)Peak memory usage: 12 MB
% 0.07/0.24 % (58521)Instructions burned: 5 (million)
% 0.07/0.24 % (58515)Success in time 0.027 s
% 0.07/0.24 % Vampire exiting
%------------------------------------------------------------------------------