%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU571^2 : 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 : n003.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 08:30:07 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU571^2 : 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 : n003.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
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:52:59 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
% 0.21/0.29 % (2537762)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2537771)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=514583689:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (2537771) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2537762-2537771"...
% 0.21/0.29 % (2537771)...printing done.
% 0.21/0.29 % (2537771)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_1, type, setadjoin: ($i > $i > $i)).
% 0.21/0.29 thf(func_def_2, type, setadjoinIR: $o).
% 0.21/0.29 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_5, type, subsetI1: $o).
% 0.21/0.29 thf(func_def_8, type, sK0: ($i > $i > $i)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 (setadjoinIR = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 0.21/0.29 thf(f3,conjecture,(
% 0.21/0.29 setadjoinIR => (subsetI1 => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub)).
% 0.21/0.29 thf(f4,negated_conjecture,(
% 0.21/0.29 ~(setadjoinIR => (subsetI1 => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.29 thf(f5,plain,(
% 0.21/0.29 ~(setadjoinIR => (subsetI1 => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1))))),
% 0.21/0.29 inference(rectify,[],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ~((setadjoinIR = $true) => ((subsetI1 = $true) => ! [X1 : $i,X0 : $i] : (((subset @ X1 @ (setadjoin @ X0 @ X1))) = $true)))),
% 0.21/0.29 inference(fool_elimination,[],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true)) <=> (subsetI1 = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f7])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 (setadjoinIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (in @ X0 @ (setadjoin @ X1 @ X2))))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) => (((in @ X0 @ (setadjoin @ X1 @ X2))) = $true)) <=> (setadjoinIR = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f9])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 (? [X0 : $i,X1 : $i] : (((subset @ X1 @ (setadjoin @ X0 @ X1))) != $true) & (subsetI1 = $true)) & (setadjoinIR = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f6])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 (subsetI1 = $true) & (setadjoinIR = $true) & ? [X0 : $i,X1 : $i] : (((subset @ X1 @ (setadjoin @ X0 @ X1))) != $true)),
% 0.21/0.29 inference(flattening,[],[f11])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 (setadjoinIR = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X2))) | (((in @ X0 @ (setadjoin @ X1 @ X2))) = $true))),
% 0.21/0.29 inference(ennf_transformation,[],[f10])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) <=> (subsetI1 = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f8])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 (! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true))))),
% 0.21/0.29 inference(nnf_transformation,[],[f14])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (($true != ((subset @ X4 @ X3))) & ! [X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ X5 @ X3))))))),
% 0.21/0.29 inference(rectify,[],[f15])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ((((in @ (sK0 @ X1 @ X0) @ X1)) = $true) & (((in @ (sK0 @ X1 @ X0) @ X0)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != ((subset @ sK2 @ sK1))) & ! [X5 : $i] : (($true != ((in @ X5 @ sK2))) | ($true = ((in @ X5 @ sK1))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X2,sK0 @ X1 @ X0),skolemize(X3,sK1),skolemize(X4,sK2)],[f16])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 (subsetI1 = $true) & (setadjoinIR = $true) & (((subset @ sK4 @ (setadjoin @ sK3 @ sK4))) != $true)),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f12])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 ((setadjoinIR = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) & (((in @ X0 @ (setadjoin @ X1 @ X2))) != $true))) & (! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X2))) | (((in @ X0 @ (setadjoin @ X1 @ X2))) = $true)) | (setadjoinIR != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f13])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 ((setadjoinIR = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ X0))) & (((in @ X1 @ (setadjoin @ X2 @ X0))) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) != $true) | ($true = ((in @ X4 @ (setadjoin @ X5 @ X3))))) | (setadjoinIR != $true))),
% 0.21/0.29 inference(rectify,[],[f19])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 ((setadjoinIR = $true) | (($true = ((in @ sK6 @ sK5))) & ($true != ((in @ sK6 @ (setadjoin @ sK7 @ sK5)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) != $true) | ($true = ((in @ X4 @ (setadjoin @ X5 @ X3))))) | (setadjoinIR != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f20])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) != $true) | (subsetI1 != $true) | ($true = ((subset @ X1 @ X0)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f17])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1)) = $true) | (subsetI1 != $true) | ($true = ((subset @ X1 @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f17])).
% 0.21/0.30 thf(f26,plain,(
% 0.21/0.30 (((subset @ sK4 @ (setadjoin @ sK3 @ sK4))) != $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f27,plain,(
% 0.21/0.30 (setadjoinIR = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f28,plain,(
% 0.21/0.30 (subsetI1 = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) != $true) | ($true = ((in @ X4 @ (setadjoin @ X5 @ X3)))) | (setadjoinIR != $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f21])).
% 0.21/0.30 thf(f35,plain,(
% 0.21/0.30 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) != $true) | ($true = ((subset @ X1 @ X0)))) )),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f24,f28])).
% 0.21/0.30 thf(f36,plain,(
% 0.21/0.30 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1)) = $true) | ($true = ((subset @ X1 @ X0)))) )),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f25,f28])).
% 0.21/0.30 thf(f40,plain,(
% 0.21/0.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ (setadjoin @ X5 @ X3)))) | (((in @ X4 @ X3)) != $true)) )),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f29,f27])).
% 0.21/0.30 thf(f41,plain,(
% 0.21/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((subset @ X0 @ (setadjoin @ X1 @ X2)))) | (((in @ (sK0 @ X0 @ (setadjoin @ X1 @ X2)) @ X2)) != $true) | ($true != $true)) )),
% 0.21/0.30 inference(superposition,[],[f35,f40])).
% 0.21/0.30 thf(f42,plain,(
% 0.21/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK0 @ X0 @ (setadjoin @ X1 @ X2)) @ X2)) != $true) | ($true = ((subset @ X0 @ (setadjoin @ X1 @ X2))))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f41])).
% 0.21/0.30 thf(f43,plain,(
% 0.21/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ X0 @ (setadjoin @ X1 @ X0)))) | ($true = ((subset @ X0 @ (setadjoin @ X1 @ X0)))) | ($true != $true)) )),
% 0.21/0.30 inference(superposition,[],[f42,f36])).
% 0.21/0.30 thf(f46,plain,(
% 0.21/0.30 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((subset @ X0 @ (setadjoin @ X1 @ X0))))) )),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f43])).
% 0.21/0.30 thf(f47,plain,(
% 0.21/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ X0 @ (setadjoin @ X1 @ X0))))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f46])).
% 0.21/0.30 thf(f48,plain,(
% 0.21/0.30 ($true != $true)),
% 0.21/0.30 inference(superposition,[],[f26,f47])).
% 0.21/0.30 thf(f49,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f48])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (2537771)------------------------------
% 0.21/0.30 % (2537771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2537771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2537771)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2537771)Termination reason: Refutation
% 0.21/0.30 % (2537771)Time elapsed: 0.002 s
% 0.21/0.30 % (2537771)Peak memory usage: 12 MB
% 0.21/0.30 % (2537771)Instructions burned: 5 (million)
% 0.21/0.30 % (2537762)Success in time 0.042 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------