%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET046^5 : 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 : n004.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 08:23:12 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET046^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:36:07 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.29 % (1287406)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1287413)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=166681191:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (1287413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1287406-1287413"...
% 0.21/0.29 % (1287413)...printing done.
% 0.21/0.29 % (1287413)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, cF: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_5, type, sK1: ($i > $i)).
% 0.21/0.29 thf(f1,conjecture,(
% 0.21/0.29 ~ ? [X0 : $i] : ! [X1 : $i] : ((~ ? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2)) => (cF @ X1 @ X0)) & ((cF @ X1 @ X0) => ~ ? [X2 : $i] : ((cF @ X1 @ X2) & (cF @ X2 @ X1))))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL42)).
% 0.21/0.29 thf(f2,negated_conjecture,(
% 0.21/0.29 ~ ~ ? [X0 : $i] : ! [X1 : $i] : ((~ ? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2)) => (cF @ X1 @ X0)) & ((cF @ X1 @ X0) => ~ ? [X2 : $i] : ((cF @ X1 @ X2) & (cF @ X2 @ X1))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.29 thf(f3,plain,(
% 0.21/0.29 ~ ~ ? [X0 : $i] : ! [X1 : $i] : ((~ ? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2)) => (cF @ X1 @ X0)) & ((cF @ X1 @ X0) => ~ ? [X3 : $i] : ((cF @ X1 @ X3) & (cF @ X3 @ X1))))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f4,plain,(
% 0.21/0.29 ~ ~ ? [X0 : $i] : ! [X1 : $i] : (((((cF @ X1 @ X0)) = $true) => ~ ? [X3 : $i] : (($true = ((cF @ X1 @ X3))) & ($true = ((cF @ X3 @ X1))))) & (~ ? [X2 : $i] : ((((cF @ X1 @ X2)) = $true) & (((cF @ X2 @ X1)) = $true)) => (((cF @ X1 @ X0)) = $true)))),
% 0.21/0.29 inference(fool_elimination,[],[f3])).
% 0.21/0.29 thf(f5,plain,(
% 0.21/0.29 ? [X0 : $i] : ! [X1 : $i] : (((((cF @ X1 @ X0)) = $true) => ~ ? [X3 : $i] : (($true = ((cF @ X1 @ X3))) & ($true = ((cF @ X3 @ X1))))) & (~ ? [X2 : $i] : ((((cF @ X1 @ X2)) = $true) & (((cF @ X2 @ X1)) = $true)) => (((cF @ X1 @ X0)) = $true)))),
% 0.21/0.29 inference(flattening,[],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ? [X0 : $i] : ! [X1 : $i] : ((! [X3 : $i] : (($true != ((cF @ X3 @ X1))) | ($true != ((cF @ X1 @ X3)))) | (((cF @ X1 @ X0)) != $true)) & ((((cF @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((cF @ X1 @ X2)) = $true) & (((cF @ X2 @ X1)) = $true))))),
% 0.21/0.29 inference(ennf_transformation,[],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ? [X0 : $i] : ! [X1 : $i] : ((! [X2 : $i] : ((((cF @ X2 @ X1)) != $true) | (((cF @ X1 @ X2)) != $true)) | (((cF @ X1 @ X0)) != $true)) & ((((cF @ X1 @ X0)) = $true) | ? [X3 : $i] : (($true = ((cF @ X1 @ X3))) & ($true = ((cF @ X3 @ X1))))))),
% 0.21/0.29 inference(rectify,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ! [X1 : $i] : ((! [X2 : $i] : ((((cF @ X2 @ X1)) != $true) | (((cF @ X1 @ X2)) != $true)) | ($true != ((cF @ X1 @ sK0)))) & (($true = ((cF @ X1 @ sK0))) | ((((cF @ X1 @ (sK1 @ X1))) = $true) & ($true = ((cF @ (sK1 @ X1) @ X1))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X3,sK1 @ X1)],[f7])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ( ! [X1 : $i] : (($true = ((cF @ (sK1 @ X1) @ X1))) | ($true = ((cF @ X1 @ sK0)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ( ! [X1 : $i] : ((((cF @ X1 @ (sK1 @ X1))) = $true) | ($true = ((cF @ X1 @ sK0)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ( ! [X2 : $i,X1 : $i] : (($true != ((cF @ X1 @ sK0))) | (((cF @ X1 @ X2)) != $true) | (((cF @ X2 @ X1)) != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((cF @ X0 @ (sK1 @ sK0)))) | ($true != $true) | ($true != ((cF @ (sK1 @ sK0) @ X0))) | ($true = ((cF @ sK0 @ sK0)))) )),
% 0.21/0.29 inference(constrained_superposition,[],[f11,f9])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((cF @ (sK1 @ sK0) @ X0))) | ($true = ((cF @ sK0 @ sK0))) | ($true != ((cF @ X0 @ (sK1 @ sK0))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f14])).
% 0.21/0.29 thf(f17,definition,(
% 0.21/0.29 spl2_1 <=> ! [X0 : $i] : (($true != ((cF @ (sK1 @ sK0) @ X0))) | ($true != ((cF @ X0 @ (sK1 @ sK0)))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((cF @ (sK1 @ sK0) @ X0))) | ($true != ((cF @ X0 @ (sK1 @ sK0))))) ) | ~spl2_1),
% 0.21/0.29 inference(avatar_component_clause,[],[f17])).
% 0.21/0.29 thf(f20,definition,(
% 0.21/0.29 spl2_2 <=> ($true = ((cF @ sK0 @ sK0)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 ($true != ((cF @ sK0 @ sK0))) | spl2_2),
% 0.21/0.29 inference(avatar_component_clause,[],[f20])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ($true = ((cF @ sK0 @ sK0))) | ~spl2_2),
% 0.21/0.29 inference(avatar_component_clause,[],[f20])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 spl2_1 | spl2_2),
% 0.21/0.29 inference(avatar_split_clause,[],[f15,f20,f17])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((cF @ X0 @ sK0)) != $true) | ($true != ((cF @ sK0 @ X0)))) ) | ~spl2_2),
% 0.21/0.29 inference(constrained_superposition,[],[f11,f22])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((cF @ sK0 @ X0))) | (((cF @ X0 @ sK0)) != $true)) ) | ~spl2_2),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f24])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 ($true != $true) | ($true != $true) | ~spl2_2),
% 0.21/0.29 inference(constrained_superposition,[],[f25,f22])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ($true != $true) | ~spl2_2),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f27])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 $false | ~spl2_2),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f29])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 ~spl2_2),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f30])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 ($true != ((cF @ sK0 @ (sK1 @ sK0)))) | ($true != $true) | ($true = ((cF @ sK0 @ sK0))) | ~spl2_1),
% 0.21/0.29 inference(constrained_superposition,[],[f18,f9])).
% 0.21/0.29 thf(f35,plain,(
% 0.21/0.29 ($true != ((cF @ sK0 @ (sK1 @ sK0)))) | ($true = ((cF @ sK0 @ sK0))) | ~spl2_1),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f32])).
% 0.21/0.29 thf(f37,plain,(
% 0.21/0.29 ($true = ((cF @ sK0 @ sK0))) | ~spl2_1),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f35,f10])).
% 0.21/0.29 thf(f38,plain,(
% 0.21/0.29 $false | (~spl2_1 | spl2_2)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f37,f21])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 ~spl2_1 | spl2_2),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f38])).
% 0.21/0.29 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f23])).
% 0.21/0.29 cnf(s2, plain, ~spl2_2, inference(sat_conversion,[],[f31])).
% 0.21/0.29 cnf(s3, plain, ~spl2_1 | spl2_2, inference(sat_conversion,[],[f39])).
% 0.21/0.29 cnf(s4, plain, ~spl2_1, inference(rat,[],[s3,s2])).
% 0.21/0.29 cnf(s5, plain, $false, inference(rat,[],[s1,s2,s4])).
% 0.21/0.29 thf(f40,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(avatar_sat_refutation,[],[s5])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (1287413)------------------------------
% 0.21/0.29 % (1287413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1287413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1287413)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1287413)Termination reason: Refutation
% 0.21/0.29 % (1287413)Time elapsed: 0.002 s
% 0.21/0.29 % (1287413)Peak memory usage: 13 MB
% 0.21/0.29 % (1287413)Instructions burned: 3 (million)
% 0.21/0.29 % (1287406)Success in time 0.03 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------