%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU573^2 : 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 : n009.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 08:30:08 AM UTC 2026
% Result : Theorem 0.24s 0.29s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU573^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:51:30 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.25 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
% 0.24/0.29 % (4030084)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.29 % (4030096)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3845310745:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.29 % (4030096) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4030084-4030096"...
% 0.24/0.29 % (4030096)...printing done.
% 0.24/0.29 % (4030096)Refutation found. Thanks to Tanya!
% 0.24/0.29 % SZS status Theorem for theBenchmark
% 0.24/0.29 % SZS output start Proof for theBenchmark
% 0.24/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.24/0.29 thf(func_def_1, type, powerset: ($i > $i)).
% 0.24/0.29 thf(func_def_2, type, powersetI: $o).
% 0.24/0.29 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.24/0.29 thf(func_def_5, type, subsetE: $o).
% 0.24/0.29 thf(func_def_12, type, sK4: ($i > $i > $i)).
% 0.24/0.29 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.24/0.29 thf(f1,axiom,(
% 0.24/0.29 (powersetI = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.24/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)).
% 0.24/0.29 thf(f2,axiom,(
% 0.24/0.29 (subsetE = ! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.24/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 0.24/0.29 thf(f3,conjecture,(
% 0.24/0.29 powersetI => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 0.24/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset)).
% 0.24/0.29 thf(f4,negated_conjecture,(
% 0.24/0.29 ~(powersetI => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1)))))),
% 0.24/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.24/0.29 thf(f5,plain,(
% 0.24/0.29 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 0.24/0.29 inference(rectify,[],[f1])).
% 0.24/0.29 thf(f6,plain,(
% 0.24/0.29 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((in @ X0 @ (powerset @ X1))) = $true)) <=> (powersetI = $true)),
% 0.24/0.29 inference(fool_elimination,[],[f5])).
% 0.24/0.29 thf(f7,plain,(
% 0.24/0.29 ~(powersetI => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0)))))),
% 0.24/0.29 inference(rectify,[],[f4])).
% 0.24/0.29 thf(f8,plain,(
% 0.24/0.29 ~((powersetI = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) => (((in @ X1 @ (powerset @ X0))) = $true))))),
% 0.24/0.29 inference(fool_elimination,[],[f7])).
% 0.24/0.29 thf(f9,plain,(
% 0.24/0.29 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))))),
% 0.24/0.29 inference(rectify,[],[f2])).
% 0.24/0.29 thf(f10,plain,(
% 0.24/0.29 (subsetE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((subset @ X2 @ X1)) = $true) => ((((in @ X0 @ X2)) = $true) => (((in @ X0 @ X1)) = $true)))),
% 0.24/0.29 inference(fool_elimination,[],[f9])).
% 0.24/0.29 thf(f11,plain,(
% 0.24/0.29 (subsetE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (((((in @ X0 @ X1)) = $true) | (((in @ X0 @ X2)) != $true)) | (((subset @ X2 @ X1)) != $true))),
% 0.24/0.29 inference(ennf_transformation,[],[f10])).
% 0.24/0.29 thf(f12,plain,(
% 0.24/0.29 ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) | (((subset @ X2 @ X1)) != $true) | (((in @ X0 @ X2)) != $true)) <=> (subsetE = $true)),
% 0.24/0.29 inference(flattening,[],[f11])).
% 0.24/0.29 thf(f13,plain,(
% 0.24/0.29 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)))),
% 0.24/0.29 inference(ennf_transformation,[],[f6])).
% 0.24/0.29 thf(f14,plain,(
% 0.24/0.29 (? [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) & (((in @ X1 @ (powerset @ X0))) != $true)) & (subsetE = $true)) & (powersetI = $true)),
% 0.24/0.29 inference(ennf_transformation,[],[f8])).
% 0.24/0.29 thf(f15,plain,(
% 0.24/0.29 (subsetE = $true) & (powersetI = $true) & ? [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) & (((in @ X1 @ (powerset @ X0))) != $true))),
% 0.24/0.29 inference(flattening,[],[f14])).
% 0.24/0.29 thf(f16,plain,(
% 0.24/0.29 (subsetE = $true) & (powersetI = $true) & ((((subset @ sK1 @ sK0)) = $true) & (((in @ sK1 @ (powerset @ sK0))) != $true))),
% 0.24/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15])).
% 0.24/0.29 thf(f17,plain,(
% 0.24/0.29 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (powersetI != $true))),
% 0.24/0.29 inference(nnf_transformation,[],[f13])).
% 0.24/0.29 thf(f18,plain,(
% 0.24/0.29 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((in @ X3 @ (powerset @ X4)))) | ? [X5 : $i] : (($true != ((in @ X5 @ X4))) & ($true = ((in @ X5 @ X3))))) | (powersetI != $true))),
% 0.24/0.29 inference(rectify,[],[f17])).
% 0.24/0.29 thf(f19,plain,(
% 0.24/0.29 ((powersetI = $true) | ((((in @ sK2 @ (powerset @ sK3))) != $true) & ! [X2 : $i] : ((((in @ X2 @ sK3)) = $true) | (((in @ X2 @ sK2)) != $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((in @ X3 @ (powerset @ X4)))) | ((((in @ (sK4 @ X4 @ X3) @ X4)) != $true) & ($true = ((in @ (sK4 @ X4 @ X3) @ X3))))) | (powersetI != $true))),
% 0.24/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,vAPP]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X5,sK4 @ X4 @ X3)],[f18])).
% 0.24/0.29 thf(f20,plain,(
% 0.24/0.29 (! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) | (((subset @ X2 @ X1)) != $true) | (((in @ X0 @ X2)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) & (((subset @ X2 @ X1)) = $true) & (((in @ X0 @ X2)) = $true)))),
% 0.24/0.29 inference(nnf_transformation,[],[f12])).
% 0.24/0.29 thf(f21,plain,(
% 0.24/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X2)) = $true) | (((subset @ X1 @ X2)) != $true) | (((in @ X0 @ X1)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ X5))) & ($true = ((subset @ X4 @ X5))) & ($true = ((in @ X3 @ X4)))))),
% 0.24/0.29 inference(rectify,[],[f20])).
% 0.24/0.29 thf(f22,plain,(
% 0.24/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X2)) = $true) | (((subset @ X1 @ X2)) != $true) | (((in @ X0 @ X1)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ((((in @ sK5 @ sK7)) != $true) & ($true = ((subset @ sK6 @ sK7))) & ($true = ((in @ sK5 @ sK6)))))),
% 0.24/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,sK5),skolemize(X4,sK6),skolemize(X5,sK7)],[f21])).
% 0.24/0.29 thf(f23,plain,(
% 0.24/0.29 (((in @ sK1 @ (powerset @ sK0))) != $true)),
% 0.24/0.29 inference(cnf_transformation,[],[f16])).
% 0.24/0.29 thf(f24,plain,(
% 0.24/0.29 (((subset @ sK1 @ sK0)) = $true)),
% 0.24/0.29 inference(cnf_transformation,[],[f16])).
% 0.24/0.29 thf(f25,plain,(
% 0.24/0.29 (powersetI = $true)),
% 0.24/0.29 inference(cnf_transformation,[],[f16])).
% 0.24/0.29 thf(f26,plain,(
% 0.24/0.29 (subsetE = $true)),
% 0.24/0.29 inference(cnf_transformation,[],[f16])).
% 0.24/0.29 thf(f27,plain,(
% 0.24/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ X3 @ (powerset @ X4)))) | ($true = ((in @ (sK4 @ X4 @ X3) @ X3))) | (powersetI != $true)) )),
% 0.24/0.29 inference(cnf_transformation,[],[f19])).
% 0.24/0.29 thf(f28,plain,(
% 0.24/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ X3 @ (powerset @ X4)))) | (((in @ (sK4 @ X4 @ X3) @ X4)) != $true) | (powersetI != $true)) )),
% 0.24/0.29 inference(cnf_transformation,[],[f19])).
% 0.24/0.29 thf(f34,plain,(
% 0.24/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2)) = $true) | (((subset @ X1 @ X2)) != $true) | (((in @ X0 @ X1)) != $true) | (subsetE != $true)) )),
% 0.24/0.29 inference(cnf_transformation,[],[f22])).
% 0.24/0.29 thf(f39,plain,(
% 0.24/0.29 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ($true = ((in @ X3 @ (powerset @ X4)))) | (((in @ (sK4 @ X4 @ X3) @ X4)) != $true)) )),
% 0.24/0.29 inference(definition_unfolding,[],[f28,f25])).
% 0.24/0.29 thf(f40,plain,(
% 0.24/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ X3 @ (powerset @ X4)))) | ($true = ((in @ (sK4 @ X4 @ X3) @ X3))) | ($true != $true)) )),
% 0.24/0.29 inference(definition_unfolding,[],[f27,f25])).
% 0.24/0.29 thf(f41,plain,(
% 0.24/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((subset @ X1 @ X2)) != $true) | (((in @ X0 @ X2)) = $true) | (((in @ X0 @ X1)) != $true)) )),
% 0.24/0.29 inference(definition_unfolding,[],[f34,f26])).
% 0.24/0.29 thf(f45,plain,(
% 0.24/0.29 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK4 @ X4 @ X3) @ X4)) != $true) | ($true = ((in @ X3 @ (powerset @ X4))))) )),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f39])).
% 0.24/0.29 thf(f46,plain,(
% 0.24/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK4 @ X4 @ X3) @ X3))) | ($true = ((in @ X3 @ (powerset @ X4))))) )),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f40])).
% 0.24/0.29 thf(f47,plain,(
% 0.24/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X1 @ X2)) != $true) | (((in @ X0 @ X1)) != $true) | (((in @ X0 @ X2)) = $true)) )),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f41])).
% 0.24/0.29 thf(f48,plain,(
% 0.24/0.29 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK1))) | ($true != $true) | (((in @ X0 @ sK0)) = $true)) )),
% 0.24/0.29 inference(constrained_superposition,[],[f47,f24])).
% 0.24/0.29 thf(f49,plain,(
% 0.24/0.29 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK1))) | (((in @ X0 @ sK0)) = $true)) )),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f48])).
% 0.24/0.29 thf(f50,plain,(
% 0.24/0.29 ( ! [X0 : $i] : (($true != $true) | (((in @ sK1 @ (powerset @ X0))) = $true) | ($true = ((in @ (sK4 @ X0 @ sK1) @ sK0)))) )),
% 0.24/0.29 inference(constrained_superposition,[],[f49,f46])).
% 0.24/0.29 thf(f54,plain,(
% 0.24/0.29 ( ! [X0 : $i] : (($true = ((in @ (sK4 @ X0 @ sK1) @ sK0))) | (((in @ sK1 @ (powerset @ X0))) = $true)) )),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f50])).
% 0.24/0.29 thf(f55,plain,(
% 0.24/0.29 (((in @ sK1 @ (powerset @ sK0))) = $true) | ($true != $true) | (((in @ sK1 @ (powerset @ sK0))) = $true)),
% 0.24/0.29 inference(constrained_superposition,[],[f45,f54])).
% 0.24/0.29 thf(f56,plain,(
% 0.24/0.29 (((in @ sK1 @ (powerset @ sK0))) = $true) | ($true != $true)),
% 0.24/0.29 inference(duplicate_literal_removal,[],[f55])).
% 0.24/0.29 thf(f57,plain,(
% 0.24/0.29 (((in @ sK1 @ (powerset @ sK0))) = $true)),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f56])).
% 0.24/0.29 thf(f58,plain,(
% 0.24/0.29 $false),
% 0.24/0.29 inference(forward_subsumption_resolution,[],[f57,f23])).
% 0.24/0.29 % SZS output end Proof for theBenchmark
% 0.24/0.29 % (4030096)------------------------------
% 0.24/0.29 % (4030096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.29 % (4030096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.29 % (4030096)CaDiCaL version: 2.1.3
% 0.24/0.29 % (4030096)Termination reason: Refutation
% 0.24/0.29 % (4030096)Time elapsed: 0.002 s
% 0.24/0.29 % (4030096)Peak memory usage: 12 MB
% 0.24/0.29 % (4030096)Instructions burned: 5 (million)
% 0.24/0.29 % (4030084)Success in time 0.03 s
% 0.24/0.29 % Vampire exiting
%------------------------------------------------------------------------------