%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU563^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:30:05 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU563^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n007.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 13:48:26 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.11/0.25 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
% 0.23/0.28 % (3393339)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.28 % (3393348)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1796941916:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.28 % (3393348) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3393339-3393348"...
% 0.23/0.28 % (3393348)...printing done.
% 0.23/0.28 % (3393348)Refutation found. Thanks to Tanya!
% 0.23/0.28 % SZS status Theorem for theBenchmark
% 0.23/0.28 % SZS output start Proof for theBenchmark
% 0.23/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.28 thf(func_def_2, type, emptysetimpfalse: $o).
% 0.23/0.28 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.23/0.28 thf(func_def_5, type, subsetI2: $o).
% 0.23/0.28 thf(func_def_8, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.28 thf(func_def_9, type, vIMP: ($o > $o > $o)).
% 0.23/0.28 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.28 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.28 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.28 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.28 thf(func_def_17, type, sK3: ($i > $i > $i)).
% 0.23/0.28 thf(f1,axiom,(
% 0.23/0.28 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 0.23/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse)).
% 0.23/0.28 thf(f3,axiom,(
% 0.23/0.28 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.23/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.23/0.28 thf(f4,conjecture,(
% 0.23/0.28 emptysetimpfalse => (subsetI2 => ! [X0 : $i] : (subset @ emptyset @ X0))),
% 0.23/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset)).
% 0.23/0.28 thf(f5,negated_conjecture,(
% 0.23/0.28 ~(emptysetimpfalse => (subsetI2 => ! [X0 : $i] : (subset @ emptyset @ X0)))),
% 0.23/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.23/0.28 thf(f6,plain,(
% 0.23/0.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
% 0.23/0.28 inference(rectify,[],[f3])).
% 0.23/0.28 thf(f7,plain,(
% 0.23/0.28 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => ($true = ((subset @ X1 @ X0)))) <=> (subsetI2 = $true)),
% 0.23/0.28 inference(fool_elimination,[],[f6])).
% 0.23/0.28 thf(f10,plain,(
% 0.23/0.28 ~(emptysetimpfalse => (subsetI2 => ! [X0 : $i] : (subset @ emptyset @ X0)))),
% 0.23/0.28 inference(rectify,[],[f5])).
% 0.23/0.28 thf(f11,plain,(
% 0.23/0.28 ~((emptysetimpfalse = $true) => ((subsetI2 = $true) => ! [X0 : $i] : (((subset @ emptyset @ X0)) = $true)))),
% 0.23/0.28 inference(fool_elimination,[],[f10])).
% 0.23/0.28 thf(f12,plain,(
% 0.23/0.28 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 0.23/0.28 inference(rectify,[],[f1])).
% 0.23/0.28 thf(f13,plain,(
% 0.23/0.28 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => $false)),
% 0.23/0.28 inference(fool_elimination,[],[f12])).
% 0.23/0.28 thf(f14,plain,(
% 0.23/0.28 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ~ (((in @ X0 @ emptyset)) = $true)),
% 0.23/0.28 inference(true_and_false_elimination,[],[f13])).
% 0.23/0.28 thf(f15,plain,(
% 0.23/0.28 ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) <=> (emptysetimpfalse = $true)),
% 0.23/0.28 inference(flattening,[],[f14])).
% 0.23/0.28 thf(f16,plain,(
% 0.23/0.28 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)))),
% 0.23/0.28 inference(ennf_transformation,[],[f7])).
% 0.23/0.28 thf(f17,plain,(
% 0.23/0.28 (? [X0 : $i] : (((subset @ emptyset @ X0)) != $true) & (subsetI2 = $true)) & (emptysetimpfalse = $true)),
% 0.23/0.28 inference(ennf_transformation,[],[f11])).
% 0.23/0.28 thf(f18,plain,(
% 0.23/0.28 ? [X0 : $i] : (((subset @ emptyset @ X0)) != $true) & (emptysetimpfalse = $true) & (subsetI2 = $true)),
% 0.23/0.28 inference(flattening,[],[f17])).
% 0.23/0.28 thf(f19,plain,(
% 0.23/0.28 (((subset @ emptyset @ sK0)) != $true) & (emptysetimpfalse = $true) & (subsetI2 = $true)),
% 0.23/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f18])).
% 0.23/0.28 thf(f20,plain,(
% 0.23/0.28 ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (($true != ((subset @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)))) & (! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) | (subsetI2 != $true))),
% 0.23/0.28 inference(nnf_transformation,[],[f16])).
% 0.23/0.28 thf(f21,plain,(
% 0.23/0.28 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | ? [X5 : $i] : (($true != ((in @ X5 @ X4))) & (((in @ X5 @ X3)) = $true))) | (subsetI2 != $true))),
% 0.23/0.28 inference(rectify,[],[f20])).
% 0.23/0.28 thf(f22,plain,(
% 0.23/0.28 ((subsetI2 = $true) | (($true != ((subset @ sK1 @ sK2))) & ! [X2 : $i] : (($true = ((in @ X2 @ sK2))) | ($true != ((in @ X2 @ sK1)))))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | (($true != ((in @ (sK3 @ X4 @ X3) @ X4))) & ($true = ((in @ (sK3 @ X4 @ X3) @ X3))))) | (subsetI2 != $true))),
% 0.23/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,vAPP]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X5,sK3 @ X4 @ X3)],[f21])).
% 0.23/0.28 thf(f23,plain,(
% 0.23/0.28 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (emptysetimpfalse != $true)) & ((emptysetimpfalse = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true))),
% 0.23/0.28 inference(nnf_transformation,[],[f15])).
% 0.23/0.28 thf(f24,plain,(
% 0.23/0.28 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (emptysetimpfalse != $true)) & ((emptysetimpfalse = $true) | ? [X1 : $i] : ($true = ((in @ X1 @ emptyset))))),
% 0.23/0.28 inference(rectify,[],[f23])).
% 0.23/0.28 thf(f25,plain,(
% 0.23/0.28 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (emptysetimpfalse != $true)) & ((emptysetimpfalse = $true) | ($true = ((in @ sK4 @ emptyset))))),
% 0.23/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4)],[f24])).
% 0.23/0.28 thf(f26,plain,(
% 0.23/0.28 (subsetI2 = $true)),
% 0.23/0.28 inference(cnf_transformation,[],[f19])).
% 0.23/0.28 thf(f27,plain,(
% 0.23/0.28 (emptysetimpfalse = $true)),
% 0.23/0.28 inference(cnf_transformation,[],[f19])).
% 0.23/0.28 thf(f28,plain,(
% 0.23/0.28 (((subset @ emptyset @ sK0)) != $true)),
% 0.23/0.28 inference(cnf_transformation,[],[f19])).
% 0.23/0.28 thf(f30,plain,(
% 0.23/0.28 ( ! [X3 : $i,X4 : $i] : ((subsetI2 != $true) | ($true = ((in @ (sK3 @ X4 @ X3) @ X3))) | ($true = ((subset @ X3 @ X4)))) )),
% 0.23/0.28 inference(cnf_transformation,[],[f22])).
% 0.23/0.28 thf(f35,plain,(
% 0.23/0.28 ( ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | (emptysetimpfalse != $true)) )),
% 0.23/0.28 inference(cnf_transformation,[],[f25])).
% 0.23/0.28 thf(f39,plain,(
% 0.23/0.28 ( ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true)) )),
% 0.23/0.28 inference(forward_subsumption_resolution,[],[f35,f27])).
% 0.23/0.28 thf(f40,plain,(
% 0.23/0.28 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK3 @ X4 @ X3) @ X3))) | ($true = ((subset @ X3 @ X4)))) )),
% 0.23/0.28 inference(forward_subsumption_resolution,[],[f30,f26])).
% 0.23/0.28 thf(f41,plain,(
% 0.23/0.28 ( ! [X0 : $i] : (($true != $true) | (((subset @ emptyset @ X0)) = $true)) )),
% 0.23/0.28 inference(superposition,[],[f39,f40])).
% 0.23/0.28 thf(f42,plain,(
% 0.23/0.28 ( ! [X0 : $i] : ((((subset @ emptyset @ X0)) = $true)) )),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f41])).
% 0.23/0.28 thf(f44,plain,(
% 0.23/0.28 ($true != $true)),
% 0.23/0.28 inference(superposition,[],[f28,f42])).
% 0.23/0.28 thf(f45,plain,(
% 0.23/0.28 $false),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f44])).
% 0.23/0.28 % SZS output end Proof for theBenchmark
% 0.23/0.28 % (3393348)------------------------------
% 0.23/0.28 % (3393348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (3393348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (3393348)CaDiCaL version: 2.1.3
% 0.23/0.28 % (3393348)Termination reason: Refutation
% 0.23/0.28 % (3393348)Time elapsed: 0.001 s
% 0.23/0.28 % (3393348)Peak memory usage: 12 MB
% 0.23/0.28 % (3393348)Instructions burned: 3 (million)
% 0.23/0.28 % (3393339)Success in time 0.016 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------