%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU580^2 : 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 : 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 08:30:10 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU580^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:52:15 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.08/0.26 % (4032650)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (4032660)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4128005699:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.26 % (4032660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4032650-4032660"...
% 0.08/0.26 % (4032660)...printing done.
% 0.08/0.26 % (4032660)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_1, type, powerset: ($i > $i)).
% 0.08/0.26 thf(func_def_2, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.08/0.26 thf(func_def_3, type, dsetconstrEL: $o).
% 0.08/0.26 thf(func_def_5, type, powersetI: $o).
% 0.08/0.26 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.26 thf(func_def_12, type, sK2: ($i > $i > $i)).
% 0.08/0.26 thf(func_def_15, type, sK5: ($i > $o)).
% 0.08/0.26 thf(func_def_17, type, sK7: ($i > $o)).
% 0.08/0.26 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.08/0.26 thf(f1,axiom,(
% 0.08/0.26 (dsetconstrEL = ! [X1 : ($i > $o),X2 : $i,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.08/0.26 thf(f2,axiom,(
% 0.08/0.26 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 0.08/0.26 thf(f3,conjecture,(
% 0.08/0.26 dsetconstrEL => (powersetI => ! [X1 : ($i > $o),X0 : $i] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ (powerset @ X0)))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset)).
% 0.08/0.26 thf(f4,negated_conjecture,(
% 0.08/0.26 ~(dsetconstrEL => (powersetI => ! [X1 : ($i > $o),X0 : $i] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ (powerset @ X0))))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f3])).
% 0.08/0.26 thf(f5,plain,(
% 0.08/0.26 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((in @ X1 @ (powerset @ X0))) = $true)) <=> (powersetI = $true)),
% 0.08/0.26 inference(fool_elimination,[],[f5])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 ~(dsetconstrEL => (powersetI => ! [X0 : ($i > $o),X1 : $i] : (in @ (dsetconstr @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) @ (powerset @ X1))))),
% 0.08/0.26 inference(rectify,[],[f4])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 ~((dsetconstrEL = $true) => ((powersetI = $true) => ! [X0 : ($i > $o),X1 : $i] : (((in @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (powerset @ X1))) = $true)))),
% 0.08/0.26 inference(fool_elimination,[],[f7])).
% 0.08/0.26 thf(f9,plain,(
% 0.08/0.26 (dsetconstrEL = ! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : ((X0 @ X3))))) => (in @ X1 @ X2)))),
% 0.08/0.26 inference(rectify,[],[f1])).
% 0.08/0.26 thf(f10,plain,(
% 0.08/0.26 ! [X2 : $i,X1 : $i,X0 : ($i > $o)] : ((((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) => (((in @ X1 @ X2)) = $true)) <=> (dsetconstrEL = $true)),
% 0.08/0.26 inference(fool_elimination,[],[f9])).
% 0.08/0.26 thf(f11,plain,(
% 0.08/0.26 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)))),
% 0.08/0.26 inference(ennf_transformation,[],[f6])).
% 0.08/0.26 thf(f12,plain,(
% 0.08/0.26 (? [X1 : $i,X0 : ($i > $o)] : (((in @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (powerset @ X1))) != $true) & (powersetI = $true)) & (dsetconstrEL = $true)),
% 0.08/0.26 inference(ennf_transformation,[],[f8])).
% 0.08/0.26 thf(f13,plain,(
% 0.08/0.26 (dsetconstrEL = $true) & (powersetI = $true) & ? [X1 : $i,X0 : ($i > $o)] : (((in @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (powerset @ X1))) != $true)),
% 0.08/0.26 inference(flattening,[],[f12])).
% 0.08/0.26 thf(f14,plain,(
% 0.08/0.26 (dsetconstrEL = $true) <=> ! [X1 : $i,X2 : $i,X0 : ($i > $o)] : ((((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) | (((in @ X1 @ X2)) = $true))),
% 0.08/0.26 inference(ennf_transformation,[],[f10])).
% 0.08/0.26 thf(f15,plain,(
% 0.08/0.26 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)))) & (! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) | (powersetI != $true))),
% 0.08/0.26 inference(nnf_transformation,[],[f11])).
% 0.08/0.26 thf(f16,plain,(
% 0.08/0.26 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)))) & (! [X3 : $i,X4 : $i] : ((((in @ X4 @ (powerset @ X3))) = $true) | ? [X5 : $i] : ((((in @ X5 @ X3)) != $true) & (((in @ X5 @ X4)) = $true))) | (powersetI != $true))),
% 0.08/0.26 inference(rectify,[],[f15])).
% 0.08/0.26 thf(f17,plain,(
% 0.08/0.26 ((powersetI = $true) | ((((in @ sK1 @ (powerset @ sK0))) != $true) & ! [X2 : $i] : ((((in @ X2 @ sK0)) = $true) | (((in @ X2 @ sK1)) != $true)))) & (! [X3 : $i,X4 : $i] : ((((in @ X4 @ (powerset @ X3))) = $true) | ((((in @ (sK2 @ X4 @ X3) @ X3)) != $true) & (((in @ (sK2 @ X4 @ X3) @ X4)) = $true))) | (powersetI != $true))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2 @ X4 @ X3)],[f16])).
% 0.08/0.26 thf(f18,plain,(
% 0.08/0.26 ((dsetconstrEL = $true) | ? [X1 : $i,X2 : $i,X0 : ($i > $o)] : ((((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) & (((in @ X1 @ X2)) != $true))) & (! [X1 : $i,X2 : $i,X0 : ($i > $o)] : ((((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) | (((in @ X1 @ X2)) = $true)) | (dsetconstrEL != $true))),
% 0.08/0.26 inference(nnf_transformation,[],[f14])).
% 0.08/0.26 thf(f19,plain,(
% 0.08/0.26 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true) & (((in @ X0 @ X1)) != $true))) & (! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) != $true) | (((in @ X3 @ X4)) = $true)) | (dsetconstrEL != $true))),
% 0.08/0.26 inference(rectify,[],[f18])).
% 0.08/0.26 thf(f20,plain,(
% 0.08/0.26 ((dsetconstrEL = $true) | ((((in @ sK3 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK5 @ Y0))))) = $true) & (((in @ sK3 @ sK4)) != $true))) & (! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) != $true) | (((in @ X3 @ X4)) = $true)) | (dsetconstrEL != $true))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f19])).
% 0.08/0.26 thf(f21,plain,(
% 0.08/0.26 (dsetconstrEL = $true) & (powersetI = $true) & ? [X0 : $i,X1 : ($i > $o)] : (((in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0))) != $true)),
% 0.08/0.26 inference(rectify,[],[f13])).
% 0.08/0.26 thf(f22,plain,(
% 0.08/0.26 (dsetconstrEL = $true) & (powersetI = $true) & (((in @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK7 @ Y0))) @ (powerset @ sK6))) != $true)),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f21])).
% 0.08/0.26 thf(f23,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i] : ((((in @ X4 @ (powerset @ X3))) = $true) | (((in @ (sK2 @ X4 @ X3) @ X4)) = $true) | (powersetI != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f17])).
% 0.08/0.26 thf(f24,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i] : ((((in @ X4 @ (powerset @ X3))) = $true) | (((in @ (sK2 @ X4 @ X3) @ X3)) != $true) | (powersetI != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f17])).
% 0.08/0.26 thf(f27,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) != $true) | (((in @ X3 @ X4)) = $true) | (dsetconstrEL != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f20])).
% 0.08/0.26 thf(f30,plain,(
% 0.08/0.26 (((in @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK7 @ Y0))) @ (powerset @ sK6))) != $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f22])).
% 0.08/0.26 thf(f31,plain,(
% 0.08/0.26 (powersetI = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f22])).
% 0.08/0.26 thf(f32,plain,(
% 0.08/0.26 (dsetconstrEL = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f22])).
% 0.08/0.26 thf(f34,definition,(
% 0.08/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.26 thf(f37,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i] : (($true != $true) | (((in @ X4 @ (powerset @ X3))) = $true) | (((in @ (sK2 @ X4 @ X3) @ X3)) != $true)) )),
% 0.08/0.26 inference(definition_unfolding,[],[f24,f31])).
% 0.08/0.26 thf(f38,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i] : ((((in @ X4 @ (powerset @ X3))) = $true) | (((in @ (sK2 @ X4 @ X3) @ X4)) = $true) | ($true != $true)) )),
% 0.08/0.26 inference(definition_unfolding,[],[f23,f31])).
% 0.08/0.26 thf(f41,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ X4)) = $true) | (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) != $true) | ($true != $true)) )),
% 0.08/0.26 inference(definition_unfolding,[],[f27,f32])).
% 0.08/0.26 thf(f42,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X4)) = $true) | (((in @ X4 @ (powerset @ X3))) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f38])).
% 0.08/0.26 thf(f43,plain,(
% 0.08/0.26 (((in @ (dsetconstr @ sK6 @ sK7) @ (powerset @ sK6))) != $true)),
% 0.08/0.26 inference(beta-eta_normalization,[],[f30])).
% 0.08/0.26 thf(f44,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X3)) != $true) | (((in @ X4 @ (powerset @ X3))) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f37])).
% 0.08/0.26 thf(f45,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ X4)) = $true) | (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) != $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f41])).
% 0.08/0.26 thf(f46,plain,(
% 0.08/0.26 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ (dsetconstr @ X4 @ X5))) != $true) | (((in @ X3 @ X4)) = $true)) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f45])).
% 0.08/0.26 thf(f50,plain,(
% 0.08/0.26 ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : ((((in @ (sK2 @ (dsetconstr @ X0 @ X1) @ X2) @ X0)) = $true) | ($true != $true) | (((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X2))) = $true)) )),
% 0.08/0.26 inference(constrained_superposition,[],[f46,f42])).
% 0.08/0.26 thf(f51,plain,(
% 0.08/0.26 ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : ((((in @ (sK2 @ (dsetconstr @ X0 @ X1) @ X2) @ X0)) = $true) | (((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X2))) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f50])).
% 0.08/0.26 thf(f54,plain,(
% 0.08/0.26 ($true != $true) | (((in @ (dsetconstr @ sK6 @ sK7) @ (powerset @ sK6))) = $false)),
% 0.08/0.26 inference(constrained_superposition,[],[f43,f34])).
% 0.32/0.26 thf(f58,plain,(
% 0.32/0.26 (((in @ (dsetconstr @ sK6 @ sK7) @ (powerset @ sK6))) = $false)),
% 0.32/0.26 inference(trivial_inequality_removal,[],[f54])).
% 0.32/0.26 thf(f66,plain,(
% 0.32/0.26 ( ! [X0 : $i,X1 : ($i > $o)] : ((((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0))) = $true) | ($true != $true) | (((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0))) = $true)) )),
% 0.32/0.26 inference(constrained_superposition,[],[f44,f51])).
% 0.32/0.26 thf(f68,plain,(
% 0.32/0.26 ( ! [X0 : $i,X1 : ($i > $o)] : (($true != $true) | (((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0))) = $true)) )),
% 0.32/0.26 inference(duplicate_literal_removal,[],[f66])).
% 0.32/0.26 thf(f69,plain,(
% 0.32/0.26 ( ! [X0 : $i,X1 : ($i > $o)] : ((((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0))) = $true)) )),
% 0.32/0.26 inference(trivial_inequality_removal,[],[f68])).
% 0.32/0.26 thf(f71,plain,(
% 0.32/0.26 ($true = $false)),
% 0.32/0.26 inference(backward_demodulation,[],[f58,f69])).
% 0.32/0.26 thf(f72,plain,(
% 0.32/0.26 $false),
% 0.32/0.26 inference(trivial_inequality_removal,[],[f71])).
% 0.32/0.26 % SZS output end Proof for theBenchmark
% 0.32/0.26 % (4032660)------------------------------
% 0.32/0.26 % (4032660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.26 % (4032660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.26 % (4032660)CaDiCaL version: 2.1.3
% 0.32/0.26 % (4032660)Termination reason: Refutation
% 0.32/0.26 % (4032660)Time elapsed: 0.003 s
% 0.32/0.26 % (4032660)Peak memory usage: 12 MB
% 0.32/0.26 % (4032660)Instructions burned: 7 (million)
% 0.32/0.26 % (4032650)Success in time 0.03 s
% 0.32/0.26 % Vampire exiting
%------------------------------------------------------------------------------