%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU635^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:30:26 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU635^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:01:24 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.28 % (3203779)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3203784)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3761166983:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (3203785)lrs+10_16_si=on:nwc=1.5:random_seed=3747891123:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (3203786)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=799102160:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (3203786)Refutation not found, incomplete strategy
% 0.21/0.28 % (3203786)------------------------------
% 0.21/0.28 % (3203786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3203786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3203786)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3203786)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.28 % (3203786)Time elapsed: 0.001 s
% 0.21/0.28 % (3203786)Peak memory usage: 12 MB
% 0.21/0.28 % (3203786)Instructions burned: 2 (million)
% 0.21/0.28 % (3203786)------------------------------
% 0.21/0.28 % (3203786)------------------------------
% 0.21/0.28 % (3203784) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3203779-3203784"...
% 0.21/0.28 % (3203784)...printing done.
% 0.21/0.28 % (3203784)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.21/0.28 thf(func_def_3, type, setunion: ($i > $i)).
% 0.21/0.28 thf(func_def_4, type, setadjoinIL: $o).
% 0.21/0.28 thf(func_def_6, type, setunionI: $o).
% 0.21/0.28 thf(func_def_7, type, subset: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_8, type, subsetI2: $o).
% 0.21/0.28 thf(func_def_14, type, sK3: ($i > $i > $i)).
% 0.21/0.28 thf(func_def_20, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 (setadjoinIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL)).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))) = setunionI)),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI)).
% 0.21/0.28 thf(f3,axiom,(
% 0.21/0.28 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.21/0.28 thf(f4,conjecture,(
% 0.21/0.28 setadjoinIL => (setunionI => (subsetI2 => ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset)))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2)).
% 0.21/0.28 thf(f5,negated_conjecture,(
% 0.21/0.28 ~(setadjoinIL => (setunionI => (subsetI2 => ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 (setadjoinIL = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.21/0.28 inference(rectify,[],[f3])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => ($true = ((subset @ X1 @ X0))))),
% 0.21/0.28 inference(fool_elimination,[],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ~(setadjoinIL => (setunionI => (subsetI2 => ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))))),
% 0.21/0.28 inference(rectify,[],[f5])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ~((setadjoinIL = $true) => ((setunionI = $true) => ((subsetI2 = $true) => ! [X0 : $i] : (((subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset)))) = $true))))),
% 0.21/0.28 inference(fool_elimination,[],[f10])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ((in @ X1 @ X2) => (in @ X0 @ (setunion @ X2)))) = setunionI)),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 ! [X2 : $i,X1 : $i,X0 : $i] : (($true = ((in @ X0 @ X1))) => ((((in @ X1 @ X2)) = $true) => ($true = ((in @ X0 @ (setunion @ X2)))))) <=> (setunionI = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f12])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) <=> (subsetI2 = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f9])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ((? [X0 : $i] : (((subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset)))) != $true) & (subsetI2 = $true)) & (setunionI = $true)) & (setadjoinIL = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f11])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 (setadjoinIL = $true) & (subsetI2 = $true) & (setunionI = $true) & ? [X0 : $i] : (((subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset)))) != $true)),
% 0.21/0.28 inference(flattening,[],[f15])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ! [X2 : $i,X1 : $i,X0 : $i] : ((($true = ((in @ X0 @ (setunion @ X2)))) | (((in @ X1 @ X2)) != $true)) | ($true != ((in @ X0 @ X1)))) <=> (setunionI = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f13])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 (setunionI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | ($true = ((in @ X0 @ (setunion @ X2)))) | (((in @ X1 @ X2)) != $true))),
% 0.21/0.28 inference(flattening,[],[f17])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 (setadjoinIL = $true) & (subsetI2 = $true) & (setunionI = $true) & ($true != ((subset @ sK0 @ (setunion @ (setadjoin @ sK0 @ emptyset)))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 ((setadjoinIL = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) != $true)) & (! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) = $true) | (setadjoinIL != $true))),
% 0.21/0.28 inference(nnf_transformation,[],[f7])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1))) != $true)) & (! [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X2 @ X3))) = $true) | (setadjoinIL != $true))),
% 0.21/0.28 inference(rectify,[],[f20])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 ((setadjoinIL = $true) | ($true != ((in @ sK1 @ (setadjoin @ sK1 @ sK2))))) & (! [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X2 @ X3))) = $true) | (setadjoinIL != $true))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f21])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 (! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (($true != ((subset @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true))))),
% 0.21/0.28 inference(nnf_transformation,[],[f14])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (($true != ((subset @ X3 @ X4))) & ! [X5 : $i] : ((((in @ X5 @ X3)) != $true) | ($true = ((in @ X5 @ X4))))))),
% 0.21/0.28 inference(rectify,[],[f23])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (($true = ((in @ (sK3 @ X1 @ X0) @ X0))) & ($true != ((in @ (sK3 @ X1 @ X0) @ X1))))) | (subsetI2 != $true)) & ((subsetI2 = $true) | (($true != ((subset @ sK4 @ sK5))) & ! [X5 : $i] : (($true != ((in @ X5 @ sK4))) | (((in @ X5 @ sK5)) = $true))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK4,sK5]),skolemize(X2,sK3 @ X1 @ X0),skolemize(X3,sK4),skolemize(X4,sK5)],[f24])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 ((setunionI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X1))) & ($true != ((in @ X0 @ (setunion @ X2)))) & (((in @ X1 @ X2)) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | ($true = ((in @ X0 @ (setunion @ X2)))) | (((in @ X1 @ X2)) != $true)) | (setunionI != $true))),
% 0.21/0.28 inference(nnf_transformation,[],[f18])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ((setunionI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X1))) & ($true != ((in @ X0 @ (setunion @ X2)))) & (((in @ X1 @ X2)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ X4))) | ($true = ((in @ X3 @ (setunion @ X5)))) | ($true != ((in @ X4 @ X5)))) | (setunionI != $true))),
% 0.21/0.28 inference(rectify,[],[f26])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ((setunionI = $true) | (($true = ((in @ sK6 @ sK7))) & ($true != ((in @ sK6 @ (setunion @ sK8)))) & ($true = ((in @ sK7 @ sK8))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ X4))) | ($true = ((in @ X3 @ (setunion @ X5)))) | ($true != ((in @ X4 @ X5)))) | (setunionI != $true))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f27])).
% 0.21/0.28 thf(f29,plain,(
% 0.21/0.28 ($true != ((subset @ sK0 @ (setunion @ (setadjoin @ sK0 @ emptyset)))))),
% 0.21/0.28 inference(cnf_transformation,[],[f19])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 (setunionI = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f19])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 (subsetI2 = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f19])).
% 0.21/0.28 thf(f32,plain,(
% 0.21/0.28 (setadjoinIL = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f19])).
% 0.21/0.28 thf(f33,plain,(
% 0.21/0.28 ( ! [X2 : $i,X3 : $i] : ((((in @ X2 @ (setadjoin @ X2 @ X3))) = $true) | (setadjoinIL != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f22])).
% 0.21/0.28 thf(f37,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | (subsetI2 != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f25])).
% 0.21/0.28 thf(f38,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (subsetI2 != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f25])).
% 0.21/0.28 thf(f39,plain,(
% 0.21/0.28 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ X4))) | ($true = ((in @ X3 @ (setunion @ X5)))) | ($true != ((in @ X4 @ X5))) | (setunionI != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f28])).
% 0.21/0.28 thf(f46,plain,(
% 0.21/0.28 ( ! [X2 : $i,X3 : $i] : ((((in @ X2 @ (setadjoin @ X2 @ X3))) = $true) | ($true != $true)) )),
% 0.21/0.28 inference(definition_unfolding,[],[f33,f32])).
% 0.21/0.28 thf(f47,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((subset @ X0 @ X1)) = $true) | ($true = ((in @ (sK3 @ X1 @ X0) @ X0)))) )),
% 0.21/0.28 inference(definition_unfolding,[],[f38,f31])).
% 0.21/0.28 thf(f48,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.21/0.28 inference(definition_unfolding,[],[f37,f31])).
% 0.21/0.28 thf(f54,plain,(
% 0.21/0.28 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != ((in @ X3 @ X4))) | ($true = ((in @ X3 @ (setunion @ X5)))) | ($true != ((in @ X4 @ X5)))) )),
% 0.21/0.28 inference(definition_unfolding,[],[f39,f30])).
% 0.21/0.28 thf(f55,plain,(
% 0.21/0.28 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X5))) | ($true = ((in @ X3 @ (setunion @ X5)))) | ($true != ((in @ X3 @ X4)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f54])).
% 0.21/0.28 thf(f56,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f48])).
% 0.21/0.28 thf(f57,plain,(
% 0.21/0.28 ( ! [X2 : $i,X3 : $i] : ((((in @ X2 @ (setadjoin @ X2 @ X3))) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f46])).
% 0.21/0.28 thf(f58,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f47])).
% 0.21/0.28 thf(f62,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((in @ X2 @ X0)) != $true) | (((in @ X2 @ (setunion @ (setadjoin @ X0 @ X1)))) = $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f55,f57])).
% 0.21/0.28 thf(f64,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ (setunion @ (setadjoin @ X0 @ X1)))) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f62])).
% 0.21/0.28 thf(f67,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ($true = ((in @ (sK3 @ X0 @ X1) @ (setunion @ (setadjoin @ X1 @ X2))))) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f64,f58])).
% 0.21/0.28 thf(f69,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X0 @ X1) @ (setunion @ (setadjoin @ X1 @ X2))))) | ($true = ((subset @ X1 @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f67])).
% 0.21/0.28 thf(f76,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((subset @ X0 @ (setunion @ (setadjoin @ X0 @ X1))))) | ($true = ((subset @ X0 @ (setunion @ (setadjoin @ X0 @ X1)))))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f56,f69])).
% 0.21/0.28 thf(f79,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ X0 @ (setunion @ (setadjoin @ X0 @ X1))))) | ($true != $true)) )),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f76])).
% 0.21/0.28 thf(f80,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ X0 @ (setunion @ (setadjoin @ X0 @ X1)))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f79])).
% 0.21/0.28 thf(f81,plain,(
% 0.21/0.28 ($true != $true)),
% 0.21/0.28 inference(constrained_superposition,[],[f29,f80])).
% 0.21/0.28 thf(f82,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f81])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (3203784)------------------------------
% 0.21/0.28 % (3203784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3203784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3203784)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3203784)Termination reason: Refutation
% 0.21/0.28 % (3203784)Time elapsed: 0.005 s
% 0.21/0.28 % (3203784)Peak memory usage: 12 MB
% 0.21/0.28 % (3203784)Instructions burned: 7 (million)
% 0.21/0.28 % (3203779)Success in time 0.039 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------