%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU524^2 : 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 : n016.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 08:29:55 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU524^2 : 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 : n016.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 13:53:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.28 % (383261)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (383270)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3191993147:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (383270) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-383261-383270"...
% 0.22/0.28 % (383270)...printing done.
% 0.22/0.28 % (383272)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (383272)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (383270)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.28 thf(func_def_1, type, powerset: ($i > $i)).
% 0.22/0.28 thf(func_def_2, type, setunion: ($i > $i)).
% 0.22/0.28 thf(func_def_3, type, powersetI: $o).
% 0.22/0.28 thf(func_def_5, type, setunionI: $o).
% 0.22/0.28 thf(func_def_10, type, sK2: ($i > $i > $i)).
% 0.22/0.28 thf(f1,axiom,(
% 0.22/0.28 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)).
% 0.22/0.28 thf(f2,axiom,(
% 0.22/0.28 (setunionI = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI)).
% 0.22/0.28 thf(f3,conjecture,(
% 0.22/0.28 powersetI => (setunionI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0)))))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU)).
% 0.22/0.28 thf(f4,negated_conjecture,(
% 0.22/0.28 ~(powersetI => (setunionI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0))))))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 (setunionI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ((in @ X2 @ X1) => (in @ X0 @ (setunion @ X1)))))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 (setunionI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X0 @ X2))) => ((((in @ X2 @ X1)) = $true) => ($true = ((in @ X0 @ (setunion @ X1))))))),
% 0.22/0.28 inference(fool_elimination,[],[f5])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.22/0.28 inference(rectify,[],[f1])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((in @ X1 @ (powerset @ X0))) = $true))),
% 0.22/0.28 inference(fool_elimination,[],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ~(powersetI => (setunionI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0))))))),
% 0.22/0.28 inference(rectify,[],[f4])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ~((powersetI = $true) => ((setunionI = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X1 @ X0)) = $true) => (((in @ X1 @ (powerset @ (setunion @ X0)))) = $true))))),
% 0.22/0.28 inference(fool_elimination,[],[f9])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 (setunionI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((($true = ((in @ X0 @ (setunion @ X1)))) | (((in @ X2 @ X1)) != $true)) | ($true != ((in @ X0 @ X2))))),
% 0.22/0.28 inference(ennf_transformation,[],[f6])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 (setunionI = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setunion @ X1)))) | (((in @ X2 @ X1)) != $true) | ($true != ((in @ X0 @ X2))))),
% 0.22/0.28 inference(flattening,[],[f11])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 (? [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ (setunion @ X0)))) != $true) & (((in @ X1 @ X0)) = $true)) & (setunionI = $true)) & (powersetI = $true)),
% 0.22/0.28 inference(ennf_transformation,[],[f10])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 ? [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ (setunion @ X0)))) != $true) & (((in @ X1 @ X0)) = $true)) & (powersetI = $true) & (setunionI = $true)),
% 0.22/0.28 inference(flattening,[],[f13])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 (powersetI = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((in @ X1 @ (powerset @ X0))) = $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f8])).
% 0.22/0.28 thf(f16,plain,(
% 0.22/0.28 ((powersetI = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & (((in @ X1 @ (powerset @ X0))) != $true))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((in @ X1 @ (powerset @ X0))) = $true)) | (powersetI != $true))),
% 0.22/0.28 inference(nnf_transformation,[],[f15])).
% 0.22/0.28 thf(f17,plain,(
% 0.22/0.28 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & ($true != ((in @ X0 @ (powerset @ X1)))))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true != ((in @ X5 @ X4))) & ($true = ((in @ X5 @ X3)))) | ($true = ((in @ X3 @ (powerset @ X4))))) | (powersetI != $true))),
% 0.22/0.28 inference(rectify,[],[f16])).
% 0.22/0.28 thf(f18,plain,(
% 0.22/0.28 ((powersetI = $true) | (! [X2 : $i] : (($true = ((in @ X2 @ sK1))) | ($true != ((in @ X2 @ sK0)))) & ($true != ((in @ sK0 @ (powerset @ sK1)))))) & (! [X3 : $i,X4 : $i] : ((($true != ((in @ (sK2 @ X4 @ X3) @ X4))) & (((in @ (sK2 @ X4 @ X3) @ X3)) = $true)) | ($true = ((in @ X3 @ (powerset @ X4))))) | (powersetI != $true))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2 @ X4 @ X3)],[f17])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 ((setunionI = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) & (((in @ X2 @ X1)) = $true) & ($true = ((in @ X0 @ X2))))) & (! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setunion @ X1)))) | (((in @ X2 @ X1)) != $true) | ($true != ((in @ X0 @ X2)))) | (setunionI != $true))),
% 0.22/0.28 inference(nnf_transformation,[],[f12])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 ((setunionI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X1 @ (setunion @ X2)))) & ($true = ((in @ X0 @ X2))) & (((in @ X1 @ X0)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ (setunion @ X5)))) | ($true != ((in @ X3 @ X5))) | ($true != ((in @ X4 @ X3)))) | (setunionI != $true))),
% 0.22/0.28 inference(rectify,[],[f19])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ((setunionI = $true) | (($true != ((in @ sK4 @ (setunion @ sK5)))) & ($true = ((in @ sK3 @ sK5))) & (((in @ sK4 @ sK3)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ (setunion @ X5)))) | ($true != ((in @ X3 @ X5))) | ($true != ((in @ X4 @ X3)))) | (setunionI != $true))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f20])).
% 0.22/0.28 thf(f22,plain,(
% 0.22/0.28 ? [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ (setunion @ X1))))) & ($true = ((in @ X0 @ X1)))) & (powersetI = $true) & (setunionI = $true)),
% 0.22/0.28 inference(rectify,[],[f14])).
% 0.22/0.28 thf(f23,plain,(
% 0.22/0.28 ((((in @ sK6 @ (powerset @ (setunion @ sK7)))) != $true) & (((in @ sK6 @ sK7)) = $true)) & (powersetI = $true) & (setunionI = $true)),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f22])).
% 0.22/0.28 thf(f24,plain,(
% 0.22/0.28 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X3)) = $true) | (powersetI != $true) | ($true = ((in @ X3 @ (powerset @ X4))))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f18])).
% 0.22/0.28 thf(f25,plain,(
% 0.22/0.28 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ X3 @ (powerset @ X4)))) | (powersetI != $true) | ($true != ((in @ (sK2 @ X4 @ X3) @ X4)))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f18])).
% 0.22/0.28 thf(f28,plain,(
% 0.22/0.28 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((setunionI != $true) | ($true != ((in @ X3 @ X5))) | ($true = ((in @ X4 @ (setunion @ X5)))) | ($true != ((in @ X4 @ X3)))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f21])).
% 0.22/0.28 thf(f32,plain,(
% 0.22/0.28 (setunionI = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f23])).
% 0.22/0.28 thf(f33,plain,(
% 0.22/0.28 (powersetI = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f23])).
% 0.22/0.28 thf(f34,plain,(
% 0.22/0.28 (((in @ sK6 @ sK7)) = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f23])).
% 0.22/0.28 thf(f35,plain,(
% 0.22/0.28 (((in @ sK6 @ (powerset @ (setunion @ sK7)))) != $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f23])).
% 0.22/0.28 thf(f39,plain,(
% 0.22/0.28 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X3)) = $true) | ($true = ((in @ X3 @ (powerset @ X4))))) )),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f24,f33])).
% 0.22/0.28 thf(f40,plain,(
% 0.22/0.28 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK2 @ X4 @ X3) @ X4))) | ($true = ((in @ X3 @ (powerset @ X4))))) )),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f25,f33])).
% 0.22/0.28 thf(f44,plain,(
% 0.22/0.28 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ X5))) | ($true = ((in @ X4 @ (setunion @ X5)))) | ($true != ((in @ X4 @ X3)))) )),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f28,f32])).
% 0.22/0.28 thf(f45,plain,(
% 0.22/0.28 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ X0 @ (setunion @ sK7)))) | ($true != ((in @ X0 @ sK6)))) )),
% 0.22/0.28 inference(superposition,[],[f44,f34])).
% 0.22/0.28 thf(f49,plain,(
% 0.22/0.28 ( ! [X0 : $i] : (($true = ((in @ X0 @ (setunion @ sK7)))) | ($true != ((in @ X0 @ sK6)))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f45])).
% 0.22/0.28 thf(f51,plain,(
% 0.22/0.28 ( ! [X0 : $i] : (($true = ((in @ X0 @ (powerset @ (setunion @ sK7))))) | ($true != ((in @ (sK2 @ (setunion @ sK7) @ X0) @ sK6))) | ($true != $true)) )),
% 0.22/0.28 inference(superposition,[],[f40,f49])).
% 0.22/0.28 thf(f54,plain,(
% 0.22/0.28 ( ! [X0 : $i] : (($true != ((in @ (sK2 @ (setunion @ sK7) @ X0) @ sK6))) | ($true = ((in @ X0 @ (powerset @ (setunion @ sK7)))))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f51])).
% 0.22/0.28 thf(f77,plain,(
% 0.22/0.28 (((in @ sK6 @ (powerset @ (setunion @ sK7)))) = $true) | ($true != $true) | (((in @ sK6 @ (powerset @ (setunion @ sK7)))) = $true)),
% 0.22/0.28 inference(superposition,[],[f54,f39])).
% 0.22/0.28 thf(f78,plain,(
% 0.22/0.28 (((in @ sK6 @ (powerset @ (setunion @ sK7)))) = $true) | ($true != $true)),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f77])).
% 0.22/0.28 thf(f79,plain,(
% 0.22/0.28 (((in @ sK6 @ (powerset @ (setunion @ sK7)))) = $true)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f78])).
% 0.22/0.28 thf(f80,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f79,f35])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (383270)------------------------------
% 0.22/0.28 % (383270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (383270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (383270)CaDiCaL version: 2.1.3
% 0.22/0.28 % (383270)Termination reason: Refutation
% 0.22/0.28 % (383270)Time elapsed: 0.003 s
% 0.22/0.28 % (383270)Peak memory usage: 12 MB
% 0.22/0.28 % (383270)Instructions burned: 8 (million)
% 0.22/0.28 % (383261)Success in time 0.027 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------