%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO105^5 : 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 : n013.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 08:46:37 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO105^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:33:26 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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
% 0.08/0.25 % (2338852)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.25 % (2338857)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3677775861:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.25 % (2338857) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2338852-2338857"...
% 0.08/0.25 % (2338857)...printing done.
% 0.08/0.25 % (2338857)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% 0.08/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.25 thf(func_def_0, type, cR: ($i > $o)).
% 0.08/0.25 thf(func_def_2, type, cP: ($i > $i > $i > $o)).
% 0.08/0.25 thf(func_def_3, type, cQ: ($i > $i > $o)).
% 0.08/0.25 thf(func_def_7, type, sK0: ($i > $i)).
% 0.08/0.25 thf(func_def_8, type, sK1: ($i > $i > $i)).
% 0.08/0.25 thf(func_def_12, type, sK5: ($i > $i)).
% 0.08/0.25 thf(func_def_14, type, sK7: ($i > $i)).
% 0.08/0.25 thf(f1,conjecture,(
% 0.08/0.25 ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((cQ @ X0 @ y) => ~((cP @ X2 @ y @ X1) => ~(cR @ X3))) <=> ~(? [X0 : $i] : (cQ @ X0 @ y) => ~ ! [X1 : $i] : (! [X2 : $i] : (cP @ X2 @ y @ X1) => ~ ? [X3 : $i] : (cR @ X3)))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2201TEST)).
% 0.08/0.25 thf(f2,negated_conjecture,(
% 0.08/0.25 ~(? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((cQ @ X0 @ y) => ~((cP @ X2 @ y @ X1) => ~(cR @ X3))) <=> ~(? [X0 : $i] : (cQ @ X0 @ y) => ~ ! [X1 : $i] : (! [X2 : $i] : (cP @ X2 @ y @ X1) => ~ ? [X3 : $i] : (cR @ X3))))),
% 0.08/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.25 thf(f3,plain,(
% 0.08/0.25 ~(? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((cQ @ X0 @ y) => ~((cP @ X2 @ y @ X1) => ~(cR @ X3))) <=> ~(? [X4 : $i] : (cQ @ X4 @ y) => ~ ! [X5 : $i] : (! [X6 : $i] : (cP @ X6 @ y @ X5) => ~ ? [X7 : $i] : (cR @ X7))))),
% 0.08/0.25 inference(rectify,[],[f2])).
% 0.08/0.25 thf(f4,plain,(
% 0.08/0.25 ~(? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((((cQ @ X0 @ y)) = $true) => ~((((cP @ X2 @ y @ X1)) = $true) => ~ (((cR @ X3)) = $true))) <=> ~(? [X4 : $i] : (((cQ @ X4 @ y)) = $true) => ~ ! [X5 : $i] : (! [X6 : $i] : (((cP @ X6 @ y @ X5)) = $true) => ~ ? [X7 : $i] : ($true = ((cR @ X7))))))),
% 0.08/0.25 inference(fool_elimination,[],[f3])).
% 0.08/0.25 thf(f5,plain,(
% 0.08/0.25 ~(? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((((cQ @ X0 @ y)) = $true) => ~((((cP @ X2 @ y @ X1)) = $true) => (((cR @ X3)) != $true))) <=> ~(? [X4 : $i] : (((cQ @ X4 @ y)) = $true) => ~ ! [X5 : $i] : (! [X6 : $i] : (((cP @ X6 @ y @ X5)) = $true) => ~ ? [X7 : $i] : ($true = ((cR @ X7))))))),
% 0.08/0.25 inference(flattening,[],[f4])).
% 0.08/0.25 thf(f6,plain,(
% 0.08/0.25 (? [X4 : $i] : (((cQ @ X4 @ y)) = $true) & ! [X5 : $i] : (? [X6 : $i] : (((cP @ X6 @ y @ X5)) != $true) | ! [X7 : $i] : ($true != ((cR @ X7))))) <~> ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ((((cQ @ X0 @ y)) = $true) & ((((cP @ X2 @ y @ X1)) != $true) | (((cR @ X3)) != $true)))),
% 0.08/0.25 inference(ennf_transformation,[],[f5])).
% 0.08/0.25 thf(f7,plain,(
% 0.08/0.25 (! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ? [X3 : $i] : ((((cQ @ X0 @ y)) != $true) | ((((cP @ X2 @ y @ X1)) = $true) & (((cR @ X3)) = $true))) | (! [X4 : $i] : (((cQ @ X4 @ y)) != $true) | ? [X5 : $i] : (! [X6 : $i] : (((cP @ X6 @ y @ X5)) = $true) & ? [X7 : $i] : ($true = ((cR @ X7)))))) & (? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ((((cQ @ X0 @ y)) = $true) & ((((cP @ X2 @ y @ X1)) != $true) | (((cR @ X3)) != $true))) | (? [X4 : $i] : (((cQ @ X4 @ y)) = $true) & ! [X5 : $i] : (? [X6 : $i] : (((cP @ X6 @ y @ X5)) != $true) | ! [X7 : $i] : ($true != ((cR @ X7))))))),
% 0.08/0.25 inference(nnf_transformation,[],[f6])).
% 0.08/0.25 thf(f8,plain,(
% 0.08/0.25 (! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ? [X3 : $i] : ((((cQ @ X0 @ y)) != $true) | ((((cP @ X2 @ y @ X1)) = $true) & (((cR @ X3)) = $true))) | ! [X4 : $i] : (((cQ @ X4 @ y)) != $true) | ? [X5 : $i] : (! [X6 : $i] : (((cP @ X6 @ y @ X5)) = $true) & ? [X7 : $i] : ($true = ((cR @ X7))))) & (? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ((((cQ @ X0 @ y)) = $true) & ((((cP @ X2 @ y @ X1)) != $true) | (((cR @ X3)) != $true))) | (? [X4 : $i] : (((cQ @ X4 @ y)) = $true) & ! [X5 : $i] : (? [X6 : $i] : (((cP @ X6 @ y @ X5)) != $true) | ! [X7 : $i] : ($true != ((cR @ X7))))))),
% 0.08/0.25 inference(flattening,[],[f7])).
% 0.08/0.25 thf(f9,plain,(
% 0.08/0.25 (! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ? [X3 : $i] : ((((cQ @ X0 @ y)) != $true) | ((((cP @ X2 @ y @ X1)) = $true) & (((cR @ X3)) = $true))) | ! [X4 : $i] : (((cQ @ X4 @ y)) != $true) | ? [X5 : $i] : (! [X6 : $i] : (((cP @ X6 @ y @ X5)) = $true) & ? [X7 : $i] : ($true = ((cR @ X7))))) & (? [X8 : $i] : ! [X9 : $i] : ? [X10 : $i] : ! [X11 : $i] : ((((cQ @ X8 @ y)) = $true) & ((((cP @ X10 @ y @ X9)) != $true) | (((cR @ X11)) != $true))) | (? [X12 : $i] : (((cQ @ X12 @ y)) = $true) & ! [X13 : $i] : (? [X14 : $i] : (((cP @ X14 @ y @ X13)) != $true) | ! [X15 : $i] : (((cR @ X15)) != $true))))),
% 0.08/0.25 inference(rectify,[],[f8])).
% 0.08/0.25 thf(f10,plain,(
% 0.08/0.25 (! [X0 : $i] : ! [X2 : $i] : ((((cQ @ X0 @ y)) != $true) | ((((cP @ X2 @ y @ (sK0 @ X0))) = $true) & (((cR @ (sK1 @ X2 @ X0))) = $true))) | ! [X4 : $i] : (((cQ @ X4 @ y)) != $true) | (! [X6 : $i] : (((cP @ X6 @ y @ sK2)) = $true) & (((cR @ sK3)) = $true))) & (! [X9 : $i] : ! [X11 : $i] : (($true = ((cQ @ sK4 @ y))) & ((((cP @ (sK5 @ X9) @ y @ X9)) != $true) | (((cR @ X11)) != $true))) | ((((cQ @ sK6 @ y)) = $true) & ! [X13 : $i] : (($true != ((cP @ (sK7 @ X13) @ y @ X13))) | ! [X15 : $i] : (((cR @ X15)) != $true))))),
% 0.08/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,sK4,vAPP,sK6,vAPP]),skolemize(X14,sK7 @ X13),skolemize(X14,sK7 @ X13),skolemize(X5,sK2),skolemize(X7,sK3),skolemize(X8,sK4),skolemize(X14,sK7 @ X13),skolemize(X12,sK6),skolemize(X14,sK7 @ X13)],[f9])).
% 0.08/0.25 thf(f11,plain,(
% 0.08/0.25 ( ! [X11 : $i,X9 : $i,X15 : $i,X13 : $i] : ((((cR @ X11)) != $true) | (((cR @ X15)) != $true) | (((cP @ (sK5 @ X9) @ y @ X9)) != $true) | ($true != ((cP @ (sK7 @ X13) @ y @ X13)))) )),
% 0.08/0.25 inference(cnf_transformation,[],[f10])).
% 0.08/0.25 thf(f12,plain,(
% 0.08/0.25 ( ! [X11 : $i,X9 : $i] : ((((cP @ (sK5 @ X9) @ y @ X9)) != $true) | (((cR @ X11)) != $true) | (((cQ @ sK6 @ y)) = $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f10])).
% 0.08/0.25 thf(f14,plain,(
% 0.08/0.25 ($true = ((cQ @ sK4 @ y))) | (((cQ @ sK6 @ y)) = $true)),
% 0.08/0.25 inference(cnf_transformation,[],[f10])).
% 0.08/0.25 thf(f15,plain,(
% 0.08/0.25 ( ! [X2 : $i,X0 : $i,X4 : $i] : ((((cQ @ X4 @ y)) != $true) | (((cQ @ X0 @ y)) != $true) | (((cR @ sK3)) = $true) | (((cR @ (sK1 @ X2 @ X0))) = $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f10])).
% 0.08/0.25 thf(f17,plain,(
% 0.08/0.25 ( ! [X2 : $i,X0 : $i,X4 : $i] : ((((cR @ sK3)) = $true) | (((cQ @ X4 @ y)) != $true) | (((cP @ X2 @ y @ (sK0 @ X0))) = $true) | (((cQ @ X0 @ y)) != $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f10])).
% 0.08/0.25 thf(f18,plain,(
% 0.08/0.25 ( ! [X2 : $i,X0 : $i,X6 : $i,X4 : $i] : ((((cQ @ X4 @ y)) != $true) | (((cP @ X2 @ y @ (sK0 @ X0))) = $true) | (((cP @ X6 @ y @ sK2)) = $true) | (((cQ @ X0 @ y)) != $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f10])).
% 0.08/0.25 thf(f22,definition,(
% 0.08/0.25 spl8_1 <=> (((cR @ sK3)) = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.08/0.25 thf(f24,plain,(
% 0.08/0.25 (((cR @ sK3)) = $true) | ~spl8_1),
% 0.08/0.25 inference(avatar_component_clause,[],[f22])).
% 0.08/0.25 thf(f26,definition,(
% 0.08/0.25 spl8_2 <=> ! [X2 : $i,X0 : $i] : ((((cQ @ X0 @ y)) != $true) | (((cR @ (sK1 @ X2 @ X0))) = $true))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.08/0.25 thf(f27,plain,(
% 0.08/0.25 ( ! [X2 : $i,X0 : $i] : ((((cQ @ X0 @ y)) != $true) | (((cR @ (sK1 @ X2 @ X0))) = $true)) ) | ~spl8_2),
% 0.08/0.25 inference(avatar_component_clause,[],[f26])).
% 0.08/0.25 thf(f29,definition,(
% 0.08/0.25 spl8_3 <=> ! [X4 : $i] : (((cQ @ X4 @ y)) != $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.08/0.25 thf(f30,plain,(
% 0.08/0.25 ( ! [X4 : $i] : ((((cQ @ X4 @ y)) != $true)) ) | ~spl8_3),
% 0.08/0.25 inference(avatar_component_clause,[],[f29])).
% 0.08/0.25 thf(f31,plain,(
% 0.08/0.25 spl8_1 | spl8_2 | spl8_3),
% 0.08/0.25 inference(avatar_split_clause,[],[f15,f29,f26,f22])).
% 0.08/0.25 thf(f33,definition,(
% 0.08/0.25 spl8_4 <=> ! [X9 : $i] : (((cP @ (sK5 @ X9) @ y @ X9)) != $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
% 0.08/0.25 thf(f34,plain,(
% 0.08/0.25 ( ! [X9 : $i] : ((((cP @ (sK5 @ X9) @ y @ X9)) != $true)) ) | ~spl8_4),
% 0.08/0.25 inference(avatar_component_clause,[],[f33])).
% 0.08/0.25 thf(f36,definition,(
% 0.08/0.25 spl8_5 <=> (((cQ @ sK6 @ y)) = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.08/0.25 thf(f38,plain,(
% 0.08/0.25 (((cQ @ sK6 @ y)) = $true) | ~spl8_5),
% 0.08/0.25 inference(avatar_component_clause,[],[f36])).
% 0.08/0.25 thf(f40,definition,(
% 0.08/0.25 spl8_6 <=> ! [X11 : $i] : (((cR @ X11)) != $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 0.08/0.25 thf(f41,plain,(
% 0.08/0.25 ( ! [X11 : $i] : ((((cR @ X11)) != $true)) ) | ~spl8_6),
% 0.08/0.25 inference(avatar_component_clause,[],[f40])).
% 0.08/0.25 thf(f42,plain,(
% 0.08/0.25 spl8_4 | spl8_5 | spl8_6),
% 0.08/0.25 inference(avatar_split_clause,[],[f12,f40,f36,f33])).
% 0.08/0.25 thf(f44,definition,(
% 0.08/0.25 spl8_7 <=> ! [X13 : $i] : ($true != ((cP @ (sK7 @ X13) @ y @ X13)))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition])).
% 0.08/0.25 thf(f45,plain,(
% 0.08/0.25 ( ! [X13 : $i] : (($true != ((cP @ (sK7 @ X13) @ y @ X13)))) ) | ~spl8_7),
% 0.08/0.25 inference(avatar_component_clause,[],[f44])).
% 0.08/0.25 thf(f47,definition,(
% 0.08/0.25 spl8_8 <=> ($true = ((cQ @ sK4 @ y)))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition])).
% 0.08/0.25 thf(f49,plain,(
% 0.08/0.25 ($true = ((cQ @ sK4 @ y))) | ~spl8_8),
% 0.08/0.25 inference(avatar_component_clause,[],[f47])).
% 0.08/0.25 thf(f52,definition,(
% 0.08/0.25 spl8_9 <=> ! [X6 : $i] : (((cP @ X6 @ y @ sK2)) = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition])).
% 0.08/0.25 thf(f53,plain,(
% 0.08/0.25 ( ! [X6 : $i] : ((((cP @ X6 @ y @ sK2)) = $true)) ) | ~spl8_9),
% 0.08/0.25 inference(avatar_component_clause,[],[f52])).
% 0.08/0.25 thf(f55,plain,(
% 0.08/0.25 spl8_4 | spl8_6 | spl8_6 | spl8_7),
% 0.08/0.25 inference(avatar_split_clause,[],[f11,f44,f40,f40,f33])).
% 0.08/0.25 thf(f57,definition,(
% 0.08/0.25 spl8_10 <=> ! [X2 : $i,X0 : $i] : ((((cP @ X2 @ y @ (sK0 @ X0))) = $true) | (((cQ @ X0 @ y)) != $true))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition])).
% 0.08/0.25 thf(f58,plain,(
% 0.08/0.25 ( ! [X2 : $i,X0 : $i] : ((((cQ @ X0 @ y)) != $true) | (((cP @ X2 @ y @ (sK0 @ X0))) = $true)) ) | ~spl8_10),
% 0.08/0.25 inference(avatar_component_clause,[],[f57])).
% 0.08/0.25 thf(f59,plain,(
% 0.08/0.25 spl8_10 | spl8_3 | spl8_9),
% 0.08/0.25 inference(avatar_split_clause,[],[f18,f52,f29,f57])).
% 0.08/0.25 thf(f60,plain,(
% 0.08/0.25 spl8_8 | spl8_5),
% 0.08/0.25 inference(avatar_split_clause,[],[f14,f36,f47])).
% 0.08/0.25 thf(f61,plain,(
% 0.08/0.25 spl8_10 | spl8_3 | spl8_1),
% 0.08/0.25 inference(avatar_split_clause,[],[f17,f22,f29,f57])).
% 0.08/0.25 thf(f62,plain,(
% 0.08/0.25 ($true != $true) | (~spl8_3 | ~spl8_5)),
% 0.08/0.25 inference(constrained_superposition,[],[f30,f38])).
% 0.08/0.25 thf(f63,plain,(
% 0.08/0.25 $false | (~spl8_3 | ~spl8_5)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f62])).
% 0.08/0.25 thf(f64,plain,(
% 0.08/0.25 ~spl8_3 | ~spl8_5),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f63])).
% 0.08/0.25 thf(f65,plain,(
% 0.08/0.25 $false | (~spl8_3 | ~spl8_8)),
% 0.08/0.25 inference(forward_subsumption_resolution,[],[f49,f30])).
% 0.08/0.25 thf(f66,plain,(
% 0.08/0.25 ~spl8_3 | ~spl8_8),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f65])).
% 0.08/0.25 thf(f67,plain,(
% 0.08/0.25 ( ! [X0 : $i] : ((((cQ @ X0 @ y)) != $true)) ) | (~spl8_2 | ~spl8_6)),
% 0.08/0.25 inference(forward_subsumption_resolution,[],[f27,f41])).
% 0.08/0.25 thf(f68,plain,(
% 0.08/0.25 spl8_3 | ~spl8_2 | ~spl8_6),
% 0.08/0.25 inference(avatar_split_clause,[],[f67,f40,f26,f29])).
% 0.08/0.25 thf(f69,plain,(
% 0.08/0.25 $false | (~spl8_1 | ~spl8_6)),
% 0.08/0.25 inference(forward_subsumption_resolution,[],[f24,f41])).
% 0.08/0.25 thf(f70,plain,(
% 0.08/0.25 ~spl8_1 | ~spl8_6),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f69])).
% 0.08/0.25 thf(f71,plain,(
% 0.08/0.25 ($true != $true) | (~spl8_4 | ~spl8_9)),
% 0.08/0.25 inference(constrained_superposition,[],[f34,f53])).
% 0.08/0.25 thf(f72,plain,(
% 0.08/0.25 $false | (~spl8_4 | ~spl8_9)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f71])).
% 0.08/0.25 thf(f73,plain,(
% 0.08/0.25 ~spl8_4 | ~spl8_9),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f72])).
% 0.08/0.25 thf(f76,plain,(
% 0.08/0.25 ( ! [X0 : $i] : ((((cP @ X0 @ y @ (sK0 @ sK4))) = $true) | ($true != $true)) ) | (~spl8_8 | ~spl8_10)),
% 0.08/0.25 inference(constrained_superposition,[],[f58,f49])).
% 0.08/0.25 thf(f77,plain,(
% 0.08/0.25 ( ! [X0 : $i] : ((((cP @ X0 @ y @ (sK0 @ sK4))) = $true)) ) | (~spl8_8 | ~spl8_10)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f76])).
% 0.08/0.25 thf(f78,plain,(
% 0.08/0.25 ($true != $true) | (~spl8_4 | ~spl8_8 | ~spl8_10)),
% 0.08/0.25 inference(constrained_superposition,[],[f34,f77])).
% 0.08/0.25 thf(f79,plain,(
% 0.08/0.25 $false | (~spl8_4 | ~spl8_8 | ~spl8_10)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f78])).
% 0.08/0.25 thf(f80,plain,(
% 0.08/0.25 ~spl8_4 | ~spl8_8 | ~spl8_10),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f79])).
% 0.08/0.25 thf(f81,plain,(
% 0.08/0.25 ( ! [X0 : $i] : ((((cP @ X0 @ y @ (sK0 @ sK6))) = $true) | ($true != $true)) ) | (~spl8_5 | ~spl8_10)),
% 0.08/0.25 inference(constrained_superposition,[],[f58,f38])).
% 0.08/0.25 thf(f83,plain,(
% 0.08/0.25 ( ! [X0 : $i] : ((((cP @ X0 @ y @ (sK0 @ sK6))) = $true)) ) | (~spl8_5 | ~spl8_10)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f81])).
% 0.08/0.25 thf(f85,plain,(
% 0.08/0.25 ($true != $true) | (~spl8_4 | ~spl8_5 | ~spl8_10)),
% 0.08/0.25 inference(constrained_superposition,[],[f34,f83])).
% 0.08/0.25 thf(f86,plain,(
% 0.08/0.25 ($true != $true) | (~spl8_5 | ~spl8_7 | ~spl8_10)),
% 0.08/0.25 inference(constrained_superposition,[],[f45,f83])).
% 0.08/0.25 thf(f87,plain,(
% 0.08/0.25 $false | (~spl8_5 | ~spl8_7 | ~spl8_10)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f86])).
% 0.08/0.25 thf(f88,plain,(
% 0.08/0.25 ~spl8_5 | ~spl8_7 | ~spl8_10),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f87])).
% 0.08/0.25 thf(f89,plain,(
% 0.08/0.25 $false | (~spl8_4 | ~spl8_5 | ~spl8_10)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f85])).
% 0.08/0.25 thf(f90,plain,(
% 0.08/0.25 ~spl8_4 | ~spl8_5 | ~spl8_10),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f89])).
% 0.08/0.25 thf(f91,plain,(
% 0.08/0.25 ($true != $true) | (~spl8_7 | ~spl8_9)),
% 0.08/0.25 inference(constrained_superposition,[],[f45,f53])).
% 0.08/0.25 thf(f92,plain,(
% 0.08/0.25 $false | (~spl8_7 | ~spl8_9)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f91])).
% 0.08/0.25 thf(f93,plain,(
% 0.08/0.25 ~spl8_7 | ~spl8_9),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f92])).
% 0.08/0.25 cnf(s1, plain, spl8_1 | spl8_2 | spl8_3, inference(sat_conversion,[],[f31])).
% 0.08/0.25 cnf(s2, plain, spl8_4 | spl8_5 | spl8_6, inference(sat_conversion,[],[f42])).
% 0.08/0.25 cnf(s5, plain, spl8_6 | spl8_4 | spl8_6 | spl8_7, inference(sat_conversion,[],[f55])).
% 0.08/0.25 cnf(s6, plain, spl8_4 | spl8_6 | spl8_7, inference(rat,[],[s5])).
% 0.08/0.25 cnf(s7, plain, spl8_3 | spl8_9 | spl8_10, inference(sat_conversion,[],[f59])).
% 0.08/0.25 cnf(s8, plain, spl8_5 | spl8_8, inference(sat_conversion,[],[f60])).
% 0.08/0.25 cnf(s9, plain, spl8_1 | spl8_3 | spl8_10, inference(sat_conversion,[],[f61])).
% 0.08/0.25 cnf(s10, plain, ~spl8_3 | ~spl8_5, inference(sat_conversion,[],[f64])).
% 0.08/0.25 cnf(s11, plain, ~spl8_3 | ~spl8_8, inference(sat_conversion,[],[f66])).
% 0.08/0.25 cnf(s12, plain, ~spl8_2 | spl8_3 | ~spl8_6, inference(sat_conversion,[],[f68])).
% 0.08/0.25 cnf(s13, plain, ~spl8_1 | ~spl8_6, inference(sat_conversion,[],[f70])).
% 0.08/0.25 cnf(s14, plain, ~spl8_4 | ~spl8_9, inference(sat_conversion,[],[f73])).
% 0.08/0.25 cnf(s15, plain, ~spl8_4 | ~spl8_8 | ~spl8_10, inference(sat_conversion,[],[f80])).
% 0.08/0.25 cnf(s16, plain, ~spl8_5 | ~spl8_7 | ~spl8_10, inference(sat_conversion,[],[f88])).
% 0.08/0.25 cnf(s17, plain, ~spl8_4 | ~spl8_5 | ~spl8_10, inference(sat_conversion,[],[f90])).
% 0.08/0.25 cnf(s18, plain, ~spl8_7 | ~spl8_9, inference(sat_conversion,[],[f93])).
% 0.08/0.25 cnf(s19, plain, ~spl8_3, inference(rat,[],[s8,s10,s11])).
% 0.08/0.25 cnf(s20, plain, spl8_4 | spl8_1, inference(rat,[],[s16,s2,s6,s9,s12,s1,s19])).
% 0.08/0.25 cnf(s21, plain, ~spl8_4 | ~spl8_10, inference(rat,[],[s8,s15,s17])).
% 0.08/0.25 cnf(s22, plain, spl8_1, inference(rat,[],[s21,s20,s9,s19])).
% 0.08/0.25 cnf(s23, plain, ~spl8_6, inference(rat,[],[s13,s22])).
% 0.08/0.25 cnf(s24, plain, spl8_4, inference(rat,[],[s7,s16,s18,s2,s6,s19,s23])).
% 0.08/0.25 cnf(s25, plain, ~spl8_10, inference(rat,[],[s21,s24])).
% 0.08/0.25 cnf(s26, plain, ~spl8_9, inference(rat,[],[s14,s24])).
% 0.08/0.25 cnf(s27, plain, $false, inference(rat,[],[s7,s19,s25,s26])).
% 0.08/0.25 thf(f94,plain,(
% 0.08/0.25 $false),
% 0.08/0.25 inference(avatar_sat_refutation,[],[s27])).
% 0.08/0.25 % SZS output end Proof for theBenchmark
% 0.08/0.25 % (2338857)------------------------------
% 0.08/0.25 % (2338857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (2338857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (2338857)CaDiCaL version: 2.1.3
% 0.08/0.25 % (2338857)Termination reason: Refutation
% 0.08/0.25 % (2338857)Time elapsed: 0.003 s
% 0.08/0.25 % (2338857)Peak memory usage: 13 MB
% 0.08/0.25 % (2338857)Instructions burned: 7 (million)
% 0.08/0.25 % (2338852)Success in time 0.028 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------