%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV409^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:38:35 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV409^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.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
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 15:48:21 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.23/0.29 % (768737)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (768746)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3442246780:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (768746) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-768737-768746"...
% 0.23/0.29 % (768746)...printing done.
% 0.23/0.29 % (768746)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% 0.23/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.29 thf(func_def_3, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.23/0.29 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.23/0.29 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i)).
% 0.23/0.29 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.23/0.29 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.29 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.29 thf(f1,conjecture,(
% 0.23/0.29 ? [X0 : (($i > $o) > ($i > $o) > $o)] : ! [X2 : ($i > $o),X1 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X1)) => ! [X3 : $i] : ((X1 @ X3) <=> (X2 @ X3)))),
% 0.23/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_BUG_pme)).
% 0.23/0.29 thf(f2,negated_conjecture,(
% 0.23/0.29 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : ! [X2 : ($i > $o),X1 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X1)) => ! [X3 : $i] : ((X1 @ X3) <=> (X2 @ X3)))),
% 0.23/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.29 thf(f3,plain,(
% 0.23/0.29 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : ! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3 : $i] : ((X2 @ X3) <=> (X1 @ X3)))),
% 0.23/0.29 inference(rectify,[],[f2])).
% 0.23/0.29 thf(f4,plain,(
% 0.23/0.29 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : ! [X2 : ($i > $o),X1 : ($i > $o)] : (((((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) => ! [X3 : $i] : (((X1 @ X3)) = ((X2 @ X3))))),
% 0.23/0.29 inference(fool_elimination,[],[f3])).
% 0.23/0.29 thf(f5,plain,(
% 0.23/0.29 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ? [X2 : ($i > $o),X1 : ($i > $o)] : (? [X3 : $i] : (((X1 @ X3)) != ((X2 @ X3))) & ((((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)))),
% 0.23/0.29 inference(ennf_transformation,[],[f4])).
% 0.23/0.29 thf(f6,plain,(
% 0.23/0.29 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ? [X1 : ($i > $o),X2 : ($i > $o)] : ((((X0 @ X1 @ X2)) = $true) & ? [X3 : $i] : (((X1 @ X3)) != ((X2 @ X3))) & (((X0 @ X2 @ X1)) = $true))),
% 0.23/0.29 inference(flattening,[],[f5])).
% 0.23/0.29 thf(f7,plain,(
% 0.23/0.29 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) & (((sK1 @ X0 @ (sK2 @ X0))) != ((sK0 @ X0 @ (sK2 @ X0)))) & ($true = ((X0 @ (sK1 @ X0) @ (sK0 @ X0)))))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK2 @ X0),skolemize(X3,sK2 @ X0),skolemize(X3,sK2 @ X0)],[f6])).
% 0.23/0.29 thf(f8,plain,(
% 0.23/0.29 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK1 @ X0) @ (sK0 @ X0))))) )),
% 0.23/0.29 inference(cnf_transformation,[],[f7])).
% 0.23/0.29 thf(f17,plain,(
% 0.23/0.29 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false))))))))),
% 0.23/0.29 inference(primitive_instantiation,[],[f8])).
% 0.23/0.29 thf(f22,plain,(
% 0.23/0.29 ($true = $false)),
% 0.23/0.29 inference(beta-eta_normalization,[],[f17])).
% 0.23/0.29 thf(f23,plain,(
% 0.23/0.29 $false),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f22])).
% 0.23/0.29 % SZS output end Proof for theBenchmark
% 0.23/0.29 % (768746)------------------------------
% 0.23/0.29 % (768746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (768746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (768746)CaDiCaL version: 2.1.3
% 0.23/0.29 % (768746)Termination reason: Refutation
% 0.23/0.29 % (768746)Time elapsed: 0.001 s
% 0.23/0.29 % (768746)Peak memory usage: 12 MB
% 0.23/0.29 % (768746)Instructions burned: 1 (million)
% 0.23/0.29 % (768737)Success in time 0.029 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------