%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU523^2 : 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 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU523^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:53:04 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.28 % (381615)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (381631)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2682305366:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (381631) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-381615-381631"...
% 0.21/0.28 % (381631)...printing done.
% 0.21/0.28 % (381631)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_1, type, setunion: ($i > $i)).
% 0.21/0.28 thf(func_def_2, type, setunionAx: $o).
% 0.21/0.28 thf(func_def_9, type, sK3: ($i > $i > $i)).
% 0.21/0.28 thf(func_def_12, type, sK6: $o).
% 0.21/0.28 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0))) = setunionAx)),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx)).
% 0.21/0.28 thf(f2,conjecture,(
% 0.21/0.28 setunionAx => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE)).
% 0.21/0.28 thf(f3,negated_conjecture,(
% 0.21/0.28 ~(setunionAx => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~(setunionAx => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))),
% 0.21/0.28 inference(rectify,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~((setunionAx = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) => ! [X2 : $o] : (! [X3 : $i] : ((((in @ X1 @ X3)) = $true) => ((((in @ X3 @ X0)) = $true) => ($true = X2))) => ($true = X2))))),
% 0.21/0.28 inference(fool_elimination,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) <=> ? [X2 : $i] : ((in @ X0 @ X2) & (in @ X2 @ X1))) = setunionAx)),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 (setunionAx = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X0 @ X2)) = $true)) <=> (((in @ X0 @ (setunion @ X1))) = $true))),
% 0.21/0.28 inference(fool_elimination,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ? [X1 : $i,X0 : $i] : (? [X2 : $o] : (($true != X2) & ! [X3 : $i] : ((($true = X2) | (((in @ X3 @ X0)) != $true)) | (((in @ X1 @ X3)) != $true))) & (((in @ X1 @ (setunion @ X0))) = $true)) & (setunionAx = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f5])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ? [X1 : $i,X0 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) & ? [X2 : $o] : (! [X3 : $i] : ((((in @ X1 @ X3)) != $true) | (((in @ X3 @ X0)) != $true) | ($true = X2)) & ($true != X2))) & (setunionAx = $true)),
% 0.21/0.28 inference(flattening,[],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ((setunionAx = $true) | ? [X1 : $i,X0 : $i] : (((((in @ X0 @ (setunion @ X1))) != $true) | ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X0 @ X2)) != $true))) & ((((in @ X0 @ (setunion @ X1))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X0 @ X2)) = $true))))) & (! [X1 : $i,X0 : $i] : ((? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X0 @ X2)) = $true)) | (((in @ X0 @ (setunion @ X1))) != $true)) & ((((in @ X0 @ (setunion @ X1))) = $true) | ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X0 @ X2)) != $true)))) | (setunionAx != $true))),
% 0.21/0.28 inference(nnf_transformation,[],[f7])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ((setunionAx = $true) | ? [X0 : $i,X1 : $i] : (((((in @ X1 @ (setunion @ X0))) != $true) | ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X1 @ X2)) != $true))) & ((((in @ X1 @ (setunion @ X0))) = $true) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X1 @ X3)) = $true))))) & (! [X4 : $i,X5 : $i] : ((? [X6 : $i] : ((((in @ X6 @ X4)) = $true) & (((in @ X5 @ X6)) = $true)) | (((in @ X5 @ (setunion @ X4))) != $true)) & ((((in @ X5 @ (setunion @ X4))) = $true) | ! [X7 : $i] : ((((in @ X7 @ X4)) != $true) | (((in @ X5 @ X7)) != $true)))) | (setunionAx != $true))),
% 0.21/0.28 inference(rectify,[],[f10])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ((setunionAx = $true) | (((((in @ sK1 @ (setunion @ sK0))) != $true) | ! [X2 : $i] : ((((in @ X2 @ sK0)) != $true) | ($true != ((in @ sK1 @ X2))))) & ((((in @ sK1 @ (setunion @ sK0))) = $true) | ((((in @ sK2 @ sK0)) = $true) & (((in @ sK1 @ sK2)) = $true))))) & (! [X4 : $i,X5 : $i] : ((((((in @ (sK3 @ X5 @ X4) @ X4)) = $true) & (((in @ X5 @ (sK3 @ X5 @ X4))) = $true)) | (((in @ X5 @ (setunion @ X4))) != $true)) & ((((in @ X5 @ (setunion @ X4))) = $true) | ! [X7 : $i] : ((((in @ X7 @ X4)) != $true) | (((in @ X5 @ X7)) != $true)))) | (setunionAx != $true))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2),skolemize(X6,sK3 @ X5 @ X4)],[f11])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (setunion @ X1))) = $true) & ? [X2 : $o] : (! [X3 : $i] : ((((in @ X0 @ X3)) != $true) | (((in @ X3 @ X1)) != $true) | ($true = X2)) & ($true != X2))) & (setunionAx = $true)),
% 0.21/0.28 inference(rectify,[],[f9])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ((((in @ sK4 @ (setunion @ sK5))) = $true) & (! [X3 : $i] : ((((in @ sK4 @ X3)) != $true) | (((in @ X3 @ sK5)) != $true) | (sK6 = $true)) & (sK6 != $true))) & (setunionAx = $true)),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f13])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ( ! [X4 : $i,X5 : $i] : ((((in @ X5 @ (sK3 @ X5 @ X4))) = $true) | (((in @ X5 @ (setunion @ X4))) != $true) | (setunionAx != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f12])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | (((in @ X5 @ (setunion @ X4))) != $true) | (setunionAx != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f12])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 (setunionAx = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f14])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 (sK6 != $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f14])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 ( ! [X3 : $i] : ((((in @ sK4 @ X3)) != $true) | (sK6 = $true) | (((in @ X3 @ sK5)) != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f14])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 (((in @ sK4 @ (setunion @ sK5))) = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f14])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 ( ! [X4 : $i,X5 : $i] : (($true != $true) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | (((in @ X5 @ (setunion @ X4))) != $true)) )),
% 0.21/0.28 inference(definition_unfolding,[],[f17,f21])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 ( ! [X4 : $i,X5 : $i] : ((((in @ X5 @ (setunion @ X4))) != $true) | ($true != $true) | (((in @ X5 @ (sK3 @ X5 @ X4))) = $true)) )),
% 0.21/0.28 inference(definition_unfolding,[],[f16,f21])).
% 0.21/0.28 thf(f33,plain,(
% 0.21/0.28 ( ! [X4 : $i,X5 : $i] : ((((in @ X5 @ (setunion @ X4))) != $true) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f30])).
% 0.21/0.28 thf(f35,plain,(
% 0.21/0.28 ( ! [X4 : $i,X5 : $i] : ((((in @ X5 @ (setunion @ X4))) != $true) | (((in @ X5 @ (sK3 @ X5 @ X4))) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f31])).
% 0.21/0.28 thf(f36,plain,(
% 0.21/0.28 ( ! [X3 : $i] : ((((in @ sK4 @ X3)) != $true) | (((in @ X3 @ sK5)) != $true)) )),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f23,f22])).
% 0.21/0.28 thf(f39,plain,(
% 0.21/0.28 ($true != $true) | (((in @ (sK3 @ sK4 @ sK5) @ sK5)) = $true)),
% 0.21/0.28 inference(constrained_superposition,[],[f33,f24])).
% 0.21/0.28 thf(f40,plain,(
% 0.21/0.28 (((in @ (sK3 @ sK4 @ sK5) @ sK5)) = $true)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f39])).
% 0.21/0.28 thf(f41,plain,(
% 0.21/0.28 (((in @ sK4 @ (sK3 @ sK4 @ sK5))) = $true) | ($true != $true)),
% 0.21/0.28 inference(constrained_superposition,[],[f35,f24])).
% 0.21/0.28 thf(f42,plain,(
% 0.21/0.28 (((in @ sK4 @ (sK3 @ sK4 @ sK5))) = $true)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f41])).
% 0.21/0.28 thf(f43,plain,(
% 0.21/0.28 ($true != $true) | (((in @ (sK3 @ sK4 @ sK5) @ sK5)) != $true)),
% 0.21/0.28 inference(constrained_superposition,[],[f36,f42])).
% 0.21/0.28 thf(f44,plain,(
% 0.21/0.28 (((in @ (sK3 @ sK4 @ sK5) @ sK5)) != $true)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f43])).
% 0.21/0.28 thf(f45,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f44,f40])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (381631)------------------------------
% 0.21/0.28 % (381631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (381631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (381631)CaDiCaL version: 2.1.3
% 0.21/0.28 % (381631)Termination reason: Refutation
% 0.21/0.28 % (381631)Time elapsed: 0.002 s
% 0.21/0.28 % (381631)Peak memory usage: 12 MB
% 0.21/0.28 % (381631)Instructions burned: 4 (million)
% 0.21/0.28 % (381615)Success in time 0.034 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------