%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO105^5 : 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 : n006.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 08:48:58 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO105^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:33:45 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.20/0.27 % (950119)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (950129)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4256930439:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (950129) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-950119-950129"...
% 0.20/0.27 % (950125)% WARNING: option uhcvi not known.
% 0.20/0.27 % (950129)...printing done.
% 0.20/0.27 % (950129)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_0, type, cR: ($i > $o)).
% 0.20/0.27 thf(func_def_2, type, cP: ($i > $i > $i > $o)).
% 0.20/0.27 thf(func_def_3, type, cQ: ($i > $i > $o)).
% 0.20/0.27 thf(func_def_7, type, sK0: ($i > $i)).
% 0.20/0.27 thf(func_def_8, type, sK1: ($i > $i > $i)).
% 0.20/0.27 thf(func_def_12, type, sK5: ($i > $i)).
% 0.20/0.27 thf(func_def_13, type, sK6: ($i > $i)).
% 0.20/0.27 thf(f1,conjecture,(
% 0.20/0.27 ~(? [X0 : $i] : (cQ @ X0 @ y) => ~ ! [X1 : $i] : (! [X2 : $i] : (cP @ X2 @ y @ X1) => ~ ? [X3 : $i] : (cR @ X3))) <=> ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((cQ @ X0 @ y) => ~((cP @ X2 @ y @ X1) => ~(cR @ X3)))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2201TEST)).
% 0.20/0.27 thf(f2,negated_conjecture,(
% 0.20/0.27 ~(~(? [X0 : $i] : (cQ @ X0 @ y) => ~ ! [X1 : $i] : (! [X2 : $i] : (cP @ X2 @ y @ X1) => ~ ? [X3 : $i] : (cR @ X3))) <=> ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((cQ @ X0 @ y) => ~((cP @ X2 @ y @ X1) => ~(cR @ X3))))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.27 thf(f3,plain,(
% 0.20/0.27 ~(~(? [X0 : $i] : (cQ @ X0 @ y) => ~ ! [X1 : $i] : (! [X2 : $i] : (cP @ X2 @ y @ X1) => ~ ? [X3 : $i] : (cR @ X3))) <=> ? [X4 : $i] : ! [X5 : $i] : ? [X6 : $i] : ! [X7 : $i] : ~((cQ @ X4 @ y) => ~((cP @ X6 @ y @ X5) => ~(cR @ X7))))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ~(~(? [X0 : $i] : (((cQ @ X0 @ y)) = $true) => ~ ! [X1 : $i] : (! [X2 : $i] : (((cP @ X2 @ y @ X1)) = $true) => ~ ? [X3 : $i] : (((cR @ X3)) = $true))) <=> ? [X4 : $i] : ! [X5 : $i] : ? [X6 : $i] : ! [X7 : $i] : ~((((cQ @ X4 @ y)) = $true) => ~((((cP @ X6 @ y @ X5)) = $true) => ~ (((cR @ X7)) = $true))))),
% 0.20/0.27 inference(fool_elimination,[],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ~(~(? [X0 : $i] : (((cQ @ X0 @ y)) = $true) => ~ ! [X1 : $i] : (! [X2 : $i] : (((cP @ X2 @ y @ X1)) = $true) => ~ ? [X3 : $i] : (((cR @ X3)) = $true))) <=> ? [X4 : $i] : ! [X5 : $i] : ? [X6 : $i] : ! [X7 : $i] : ~((((cQ @ X4 @ y)) = $true) => ~((((cP @ X6 @ y @ X5)) = $true) => (((cR @ X7)) != $true))))),
% 0.20/0.27 inference(flattening,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 (! [X1 : $i] : (! [X3 : $i] : (((cR @ X3)) != $true) | ? [X2 : $i] : (((cP @ X2 @ y @ X1)) != $true)) & ? [X0 : $i] : (((cQ @ X0 @ y)) = $true)) <~> ? [X4 : $i] : ! [X5 : $i] : ? [X6 : $i] : ! [X7 : $i] : (((((cR @ X7)) != $true) | (((cP @ X6 @ y @ X5)) != $true)) & (((cQ @ X4 @ y)) = $true))),
% 0.20/0.27 inference(ennf_transformation,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 (! [X4 : $i] : ? [X5 : $i] : ! [X6 : $i] : ? [X7 : $i] : (((((cR @ X7)) = $true) & (((cP @ X6 @ y @ X5)) = $true)) | (((cQ @ X4 @ y)) != $true)) | (? [X1 : $i] : (? [X3 : $i] : (((cR @ X3)) = $true) & ! [X2 : $i] : (((cP @ X2 @ y @ X1)) = $true)) | ! [X0 : $i] : (((cQ @ X0 @ y)) != $true))) & (? [X4 : $i] : ! [X5 : $i] : ? [X6 : $i] : ! [X7 : $i] : (((((cR @ X7)) != $true) | (((cP @ X6 @ y @ X5)) != $true)) & (((cQ @ X4 @ y)) = $true)) | (! [X1 : $i] : (! [X3 : $i] : (((cR @ X3)) != $true) | ? [X2 : $i] : (((cP @ X2 @ y @ X1)) != $true)) & ? [X0 : $i] : (((cQ @ X0 @ y)) = $true)))),
% 0.20/0.27 inference(nnf_transformation,[],[f6])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 (! [X4 : $i] : ? [X5 : $i] : ! [X6 : $i] : ? [X7 : $i] : (((((cR @ X7)) = $true) & (((cP @ X6 @ y @ X5)) = $true)) | (((cQ @ X4 @ y)) != $true)) | ? [X1 : $i] : (? [X3 : $i] : (((cR @ X3)) = $true) & ! [X2 : $i] : (((cP @ X2 @ y @ X1)) = $true)) | ! [X0 : $i] : (((cQ @ X0 @ y)) != $true)) & (? [X4 : $i] : ! [X5 : $i] : ? [X6 : $i] : ! [X7 : $i] : (((((cR @ X7)) != $true) | (((cP @ X6 @ y @ X5)) != $true)) & (((cQ @ X4 @ y)) = $true)) | (! [X1 : $i] : (! [X3 : $i] : (((cR @ X3)) != $true) | ? [X2 : $i] : (((cP @ X2 @ y @ X1)) != $true)) & ? [X0 : $i] : (((cQ @ X0 @ y)) = $true)))),
% 0.20/0.27 inference(flattening,[],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 (! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ? [X3 : $i] : (((((cR @ X3)) = $true) & (((cP @ X2 @ y @ X1)) = $true)) | (((cQ @ X0 @ y)) != $true)) | ? [X4 : $i] : (? [X5 : $i] : ($true = ((cR @ X5))) & ! [X6 : $i] : ($true = ((cP @ X6 @ y @ X4)))) | ! [X7 : $i] : ($true != ((cQ @ X7 @ y)))) & (? [X8 : $i] : ! [X9 : $i] : ? [X10 : $i] : ! [X11 : $i] : ((($true != ((cR @ X11))) | ($true != ((cP @ X10 @ y @ X9)))) & ($true = ((cQ @ X8 @ y)))) | (! [X12 : $i] : (! [X13 : $i] : ($true != ((cR @ X13))) | ? [X14 : $i] : ($true != ((cP @ X14 @ y @ X12)))) & ? [X15 : $i] : ($true = ((cQ @ X15 @ y)))))),
% 0.20/0.27 inference(rectify,[],[f8])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 (! [X0 : $i] : ! [X2 : $i] : ((($true = ((cR @ (sK1 @ X2 @ X0)))) & ($true = ((cP @ X2 @ y @ (sK0 @ X0))))) | (((cQ @ X0 @ y)) != $true)) | (($true = ((cR @ sK3))) & ! [X6 : $i] : ($true = ((cP @ X6 @ y @ sK2)))) | ! [X7 : $i] : ($true != ((cQ @ X7 @ y)))) & (! [X9 : $i] : ! [X11 : $i] : ((($true != ((cR @ X11))) | ($true != ((cP @ (sK5 @ X9) @ y @ X9)))) & ($true = ((cQ @ sK4 @ y)))) | (! [X12 : $i] : (! [X13 : $i] : ($true != ((cR @ X13))) | ($true != ((cP @ (sK6 @ X12) @ y @ X12)))) & ($true = ((cQ @ sK7 @ y)))))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,sK4,vAPP,vAPP,sK7]),skolemize(X14,sK6 @ X12),skolemize(X14,sK6 @ X12),skolemize(X4,sK2),skolemize(X5,sK3),skolemize(X8,sK4),skolemize(X14,sK6 @ X12),skolemize(X14,sK6 @ X12),skolemize(X15,sK7)],[f9])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 ($true = ((cQ @ sK4 @ y))) | ($true = ((cQ @ sK7 @ y)))),
% 0.20/0.27 inference(cnf_transformation,[],[f10])).
% 0.20/0.27 thf(f12,plain,(
% 0.20/0.27 ( ! [X12 : $i,X13 : $i] : (($true = ((cQ @ sK4 @ y))) | ($true != ((cR @ X13))) | ($true != ((cP @ (sK6 @ X12) @ y @ X12)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f10])).
% 0.20/0.27 thf(f13,plain,(
% 0.20/0.27 ( ! [X11 : $i,X9 : $i] : (($true != ((cR @ X11))) | ($true != ((cP @ (sK5 @ X9) @ y @ X9))) | ($true = ((cQ @ sK7 @ y)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f10])).
% 0.20/0.27 thf(f14,plain,(
% 0.20/0.27 ( ! [X11 : $i,X9 : $i,X12 : $i,X13 : $i] : (($true != ((cR @ X11))) | ($true != ((cP @ (sK5 @ X9) @ y @ X9))) | ($true != ((cR @ X13))) | ($true != ((cP @ (sK6 @ X12) @ y @ X12)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f10])).
% 0.20/0.27 thf(f15,plain,(
% 0.20/0.27 ( ! [X2 : $i,X0 : $i,X6 : $i,X7 : $i] : (($true = ((cP @ X2 @ y @ (sK0 @ X0)))) | (((cQ @ X0 @ y)) != $true) | ($true = ((cP @ X6 @ y @ sK2))) | ($true != ((cQ @ X7 @ y)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f10])).
% 0.20/0.27 thf(f18,plain,(
% 0.20/0.27 ( ! [X2 : $i,X0 : $i,X7 : $i] : (($true = ((cR @ (sK1 @ X2 @ X0)))) | (((cQ @ X0 @ y)) != $true) | ($true = ((cR @ sK3))) | ($true != ((cQ @ X7 @ y)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f10])).
% 0.20/0.27 thf(f22,definition,(
% 0.20/0.27 spl8_1 <=> ($true = ((cQ @ sK7 @ y)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.20/0.27 thf(f24,plain,(
% 0.20/0.27 ($true = ((cQ @ sK7 @ y))) | ~spl8_1),
% 0.20/0.27 inference(avatar_component_clause,[],[f22])).
% 0.20/0.27 thf(f26,definition,(
% 0.20/0.27 spl8_2 <=> ($true = ((cQ @ sK4 @ y)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.20/0.27 thf(f28,plain,(
% 0.20/0.27 ($true = ((cQ @ sK4 @ y))) | ~spl8_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f26])).
% 0.20/0.27 thf(f29,plain,(
% 0.20/0.27 spl8_1 | spl8_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f11,f26,f22])).
% 0.20/0.27 thf(f31,definition,(
% 0.20/0.27 spl8_3 <=> ! [X12 : $i] : ($true != ((cP @ (sK6 @ X12) @ y @ X12)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.20/0.27 thf(f32,plain,(
% 0.20/0.27 ( ! [X12 : $i] : (($true != ((cP @ (sK6 @ X12) @ y @ X12)))) ) | ~spl8_3),
% 0.20/0.27 inference(avatar_component_clause,[],[f31])).
% 0.20/0.27 thf(f34,definition,(
% 0.20/0.27 spl8_4 <=> ! [X13 : $i] : ($true != ((cR @ X13)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
% 0.20/0.27 thf(f35,plain,(
% 0.20/0.27 ( ! [X13 : $i] : (($true != ((cR @ X13)))) ) | ~spl8_4),
% 0.20/0.27 inference(avatar_component_clause,[],[f34])).
% 0.20/0.27 thf(f36,plain,(
% 0.20/0.27 spl8_3 | spl8_4 | spl8_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f12,f26,f34,f31])).
% 0.20/0.27 thf(f38,definition,(
% 0.20/0.27 spl8_5 <=> ! [X9 : $i] : ($true != ((cP @ (sK5 @ X9) @ y @ X9)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.20/0.27 thf(f39,plain,(
% 0.20/0.27 ( ! [X9 : $i] : (($true != ((cP @ (sK5 @ X9) @ y @ X9)))) ) | ~spl8_5),
% 0.20/0.27 inference(avatar_component_clause,[],[f38])).
% 0.20/0.27 thf(f40,plain,(
% 0.20/0.27 spl8_1 | spl8_5 | spl8_4),
% 0.20/0.27 inference(avatar_split_clause,[],[f13,f34,f38,f22])).
% 0.20/0.27 thf(f41,plain,(
% 0.20/0.27 spl8_3 | spl8_4 | spl8_5 | spl8_4),
% 0.20/0.27 inference(avatar_split_clause,[],[f14,f34,f38,f34,f31])).
% 0.20/0.27 thf(f43,definition,(
% 0.20/0.27 spl8_6 <=> ! [X7 : $i] : ($true != ((cQ @ X7 @ y)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 0.20/0.27 thf(f44,plain,(
% 0.20/0.27 ( ! [X7 : $i] : (($true != ((cQ @ X7 @ y)))) ) | ~spl8_6),
% 0.20/0.27 inference(avatar_component_clause,[],[f43])).
% 0.20/0.27 thf(f46,definition,(
% 0.20/0.27 spl8_7 <=> ! [X6 : $i] : ($true = ((cP @ X6 @ y @ sK2)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition])).
% 0.20/0.27 thf(f47,plain,(
% 0.20/0.27 ( ! [X6 : $i] : (($true = ((cP @ X6 @ y @ sK2)))) ) | ~spl8_7),
% 0.20/0.27 inference(avatar_component_clause,[],[f46])).
% 0.20/0.27 thf(f49,definition,(
% 0.20/0.27 spl8_8 <=> ! [X2 : $i,X0 : $i] : (($true = ((cP @ X2 @ y @ (sK0 @ X0)))) | (((cQ @ X0 @ y)) != $true))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition])).
% 0.20/0.27 thf(f50,plain,(
% 0.20/0.27 ( ! [X2 : $i,X0 : $i] : ((((cQ @ X0 @ y)) != $true) | ($true = ((cP @ X2 @ y @ (sK0 @ X0))))) ) | ~spl8_8),
% 0.20/0.27 inference(avatar_component_clause,[],[f49])).
% 0.20/0.27 thf(f51,plain,(
% 0.20/0.27 spl8_6 | spl8_7 | spl8_8),
% 0.20/0.27 inference(avatar_split_clause,[],[f15,f49,f46,f43])).
% 0.20/0.27 thf(f53,definition,(
% 0.20/0.27 spl8_9 <=> ($true = ((cR @ sK3)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition])).
% 0.20/0.27 thf(f55,plain,(
% 0.20/0.27 ($true = ((cR @ sK3))) | ~spl8_9),
% 0.20/0.27 inference(avatar_component_clause,[],[f53])).
% 0.20/0.27 thf(f58,definition,(
% 0.20/0.27 spl8_10 <=> ! [X2 : $i,X0 : $i] : (($true = ((cR @ (sK1 @ X2 @ X0)))) | (((cQ @ X0 @ y)) != $true))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition])).
% 0.20/0.27 thf(f59,plain,(
% 0.20/0.27 ( ! [X2 : $i,X0 : $i] : ((((cQ @ X0 @ y)) != $true) | ($true = ((cR @ (sK1 @ X2 @ X0))))) ) | ~spl8_10),
% 0.20/0.27 inference(avatar_component_clause,[],[f58])).
% 0.20/0.27 thf(f61,plain,(
% 0.20/0.27 spl8_6 | spl8_9 | spl8_10),
% 0.20/0.27 inference(avatar_split_clause,[],[f18,f58,f53,f43])).
% 0.20/0.27 thf(f62,plain,(
% 0.20/0.27 ($true != $true) | (~spl8_2 | ~spl8_6)),
% 0.20/0.27 inference(constrained_superposition,[],[f44,f28])).
% 0.20/0.27 thf(f63,plain,(
% 0.20/0.27 $false | (~spl8_2 | ~spl8_6)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f62])).
% 0.20/0.27 thf(f64,plain,(
% 0.20/0.27 ~spl8_2 | ~spl8_6),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f63])).
% 0.20/0.27 thf(f65,plain,(
% 0.20/0.27 $false | (~spl8_4 | ~spl8_9)),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f55,f35])).
% 0.20/0.27 thf(f66,plain,(
% 0.20/0.27 ~spl8_4 | ~spl8_9),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f65])).
% 0.20/0.27 thf(f67,plain,(
% 0.20/0.27 ( ! [X0 : $i] : ((((cQ @ X0 @ y)) != $true)) ) | (~spl8_4 | ~spl8_10)),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f59,f35])).
% 0.20/0.27 thf(f68,plain,(
% 0.20/0.27 spl8_6 | ~spl8_4 | ~spl8_10),
% 0.20/0.27 inference(avatar_split_clause,[],[f67,f58,f34,f43])).
% 0.20/0.27 thf(f69,plain,(
% 0.20/0.27 ($true != $true) | (~spl8_1 | ~spl8_6)),
% 0.20/0.27 inference(constrained_superposition,[],[f44,f24])).
% 0.20/0.27 thf(f70,plain,(
% 0.20/0.27 $false | (~spl8_1 | ~spl8_6)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f69])).
% 0.20/0.27 thf(f71,plain,(
% 0.20/0.27 ~spl8_1 | ~spl8_6),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f70])).
% 0.20/0.27 thf(f72,plain,(
% 0.20/0.27 ($true != $true) | (~spl8_5 | ~spl8_7)),
% 0.20/0.27 inference(constrained_superposition,[],[f39,f47])).
% 0.20/0.27 thf(f73,plain,(
% 0.20/0.27 $false | (~spl8_5 | ~spl8_7)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f72])).
% 0.20/0.27 thf(f74,plain,(
% 0.20/0.27 ~spl8_5 | ~spl8_7),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f73])).
% 0.20/0.27 thf(f77,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true != $true) | ($true = ((cP @ X0 @ y @ (sK0 @ sK4))))) ) | (~spl8_2 | ~spl8_8)),
% 0.20/0.27 inference(constrained_superposition,[],[f50,f28])).
% 0.20/0.27 thf(f78,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true = ((cP @ X0 @ y @ (sK0 @ sK4))))) ) | (~spl8_2 | ~spl8_8)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f77])).
% 0.20/0.27 thf(f79,plain,(
% 0.20/0.27 ($true != $true) | (~spl8_2 | ~spl8_5 | ~spl8_8)),
% 0.20/0.27 inference(constrained_superposition,[],[f39,f78])).
% 0.20/0.27 thf(f80,plain,(
% 0.20/0.27 $false | (~spl8_2 | ~spl8_5 | ~spl8_8)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f79])).
% 0.20/0.27 thf(f81,plain,(
% 0.20/0.27 ~spl8_2 | ~spl8_5 | ~spl8_8),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f80])).
% 0.20/0.27 thf(f84,plain,(
% 0.20/0.27 ($true != $true) | (~spl8_3 | ~spl8_7)),
% 0.20/0.27 inference(constrained_superposition,[],[f32,f47])).
% 0.20/0.27 thf(f85,plain,(
% 0.20/0.27 $false | (~spl8_3 | ~spl8_7)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f84])).
% 0.20/0.27 thf(f86,plain,(
% 0.20/0.27 ~spl8_3 | ~spl8_7),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f85])).
% 0.20/0.27 thf(f91,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true != $true) | ($true = ((cP @ X0 @ y @ (sK0 @ sK7))))) ) | (~spl8_1 | ~spl8_8)),
% 0.20/0.27 inference(constrained_superposition,[],[f50,f24])).
% 0.20/0.27 thf(f92,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true = ((cP @ X0 @ y @ (sK0 @ sK7))))) ) | (~spl8_1 | ~spl8_8)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f91])).
% 0.20/0.27 thf(f113,plain,(
% 0.20/0.27 ($true != $true) | (~spl8_1 | ~spl8_3 | ~spl8_8)),
% 0.20/0.27 inference(constrained_superposition,[],[f32,f92])).
% 0.20/0.27 thf(f114,plain,(
% 0.20/0.27 $false | (~spl8_1 | ~spl8_3 | ~spl8_8)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f113])).
% 0.20/0.27 thf(f115,plain,(
% 0.20/0.27 ~spl8_1 | ~spl8_3 | ~spl8_8),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f114])).
% 0.20/0.27 cnf(s1, plain, spl8_1 | spl8_2, inference(sat_conversion,[],[f29])).
% 0.20/0.27 cnf(s2, plain, spl8_2 | spl8_3 | spl8_4, inference(sat_conversion,[],[f36])).
% 0.20/0.27 cnf(s3, plain, spl8_1 | spl8_4 | spl8_5, inference(sat_conversion,[],[f40])).
% 0.20/0.27 cnf(s4, plain, spl8_4 | spl8_3 | spl8_4 | spl8_5, inference(sat_conversion,[],[f41])).
% 0.20/0.27 cnf(s5, plain, spl8_3 | spl8_4 | spl8_5, inference(rat,[],[s4])).
% 0.20/0.27 cnf(s6, plain, spl8_6 | spl8_7 | spl8_8, inference(sat_conversion,[],[f51])).
% 0.20/0.27 cnf(s9, plain, spl8_6 | spl8_9 | spl8_10, inference(sat_conversion,[],[f61])).
% 0.20/0.27 cnf(s10, plain, ~spl8_2 | ~spl8_6, inference(sat_conversion,[],[f64])).
% 0.20/0.27 cnf(s11, plain, ~spl8_4 | ~spl8_9, inference(sat_conversion,[],[f66])).
% 0.20/0.27 cnf(s12, plain, ~spl8_4 | spl8_6 | ~spl8_10, inference(sat_conversion,[],[f68])).
% 0.20/0.27 cnf(s13, plain, ~spl8_1 | ~spl8_6, inference(sat_conversion,[],[f71])).
% 0.20/0.27 cnf(s14, plain, ~spl8_5 | ~spl8_7, inference(sat_conversion,[],[f74])).
% 0.20/0.27 cnf(s15, plain, ~spl8_2 | ~spl8_5 | ~spl8_8, inference(sat_conversion,[],[f81])).
% 0.20/0.27 cnf(s16, plain, ~spl8_3 | ~spl8_7, inference(sat_conversion,[],[f86])).
% 0.20/0.27 cnf(s18, plain, ~spl8_1 | ~spl8_3 | ~spl8_8, inference(sat_conversion,[],[f115])).
% 0.20/0.27 cnf(s19, plain, ~spl8_5 | ~spl8_2, inference(rat,[],[s6,s14,s15,s10])).
% 0.20/0.27 cnf(s20, plain, ~spl8_4 | spl8_6, inference(rat,[],[s9,s12,s11])).
% 0.20/0.27 cnf(s21, plain, spl8_1, inference(rat,[],[s3,s20,s19,s10,s1])).
% 0.20/0.27 cnf(s22, plain, ~spl8_6, inference(rat,[],[s13,s21])).
% 0.20/0.27 cnf(s23, plain, ~spl8_4, inference(rat,[],[s20,s22])).
% 0.20/0.27 cnf(s24, plain, ~spl8_3, inference(rat,[],[s6,s16,s18,s22,s21])).
% 0.20/0.27 cnf(s25, plain, spl8_5, inference(rat,[],[s5,s23,s24])).
% 0.20/0.27 cnf(s26, plain, spl8_2, inference(rat,[],[s2,s23,s24])).
% 0.20/0.27 cnf(s29, plain, $false, inference(rat,[],[s19,s26,s25])).
% 0.20/0.27 thf(f116,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s29])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (950129)------------------------------
% 0.20/0.27 % (950129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (950129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (950129)CaDiCaL version: 2.1.3
% 0.20/0.27 % (950129)Termination reason: Refutation
% 0.20/0.27 % (950129)Time elapsed: 0.004 s
% 0.20/0.27 % (950129)Peak memory usage: 13 MB
% 0.20/0.27 % (950129)Instructions burned: 9 (million)
% 0.20/0.27 % (950119)Success in time 0.039 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------