%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU926^5 : 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 : n011.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 08:31:57 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU926^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:46:16 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.26 % (180684)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (180693)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3662719617:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.26 % (180693) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-180684-180693"...
% 0.20/0.26 % (180693)...printing done.
% 0.20/0.26 % (180693)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.26 thf(func_def_5, type, sK0: ($i > $o)).
% 0.20/0.26 thf(func_def_6, type, sK1: ((($i > $i) > $o) > $i > $i)).
% 0.20/0.26 thf(func_def_7, type, sK2: ((($i > $i) > $o) > $i)).
% 0.20/0.26 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.20/0.26 thf(f1,conjecture,(
% 0.20/0.26 ! [X0 : ($i > $o)] : ? [X1 : (($i > $i) > $o)] : ! [X2 : ($i > $i)] : ((X1 @ X2) => ((X1 @ (^[X3 : $i] : ((X2 @ (X2 @ X3))))) & ! [X4 : $i] : ((X0 @ X4) => (X0 @ (X2 @ X4)))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM113)).
% 0.20/0.26 thf(f2,negated_conjecture,(
% 0.20/0.26 ~ ! [X0 : ($i > $o)] : ? [X1 : (($i > $i) > $o)] : ! [X2 : ($i > $i)] : ((X1 @ X2) => ((X1 @ (^[X3 : $i] : ((X2 @ (X2 @ X3))))) & ! [X4 : $i] : ((X0 @ X4) => (X0 @ (X2 @ X4)))))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.26 thf(f3,plain,(
% 0.20/0.26 ~ ! [X0 : ($i > $o)] : ? [X1 : (($i > $i) > $o)] : ! [X2 : ($i > $i)] : ((X1 @ X2) => ((X1 @ (^[X3 : $i] : ((X2 @ (X2 @ X3))))) & ! [X4 : $i] : ((X0 @ X4) => (X0 @ (X2 @ X4)))))),
% 0.20/0.26 inference(rectify,[],[f2])).
% 0.20/0.26 thf(f4,plain,(
% 0.20/0.26 ~ ! [X0 : ($i > $o)] : ? [X1 : (($i > $i) > $o)] : ! [X2 : ($i > $i)] : ((((X1 @ X2)) = $true) => ((((X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0))))) = $true) & ! [X4 : $i] : ((((X0 @ X4)) = $true) => (((X0 @ (X2 @ X4))) = $true))))),
% 0.20/0.26 inference(fool_elimination,[],[f3])).
% 0.20/0.26 thf(f5,plain,(
% 0.20/0.26 ~ ! [X0 : ($i > $o)] : ? [X1 : (($i > $i) > $o)] : ! [X2 : ($i > $i)] : ((((X1 @ X2)) = $true) => ((((X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0))))) = $true) & ! [X3 : $i] : ((((X0 @ X3)) = $true) => (((X0 @ (X2 @ X3))) = $true))))),
% 0.20/0.26 inference(rectify,[],[f4])).
% 0.20/0.26 thf(f6,plain,(
% 0.20/0.26 ? [X0 : ($i > $o)] : ! [X1 : (($i > $i) > $o)] : ? [X2 : ($i > $i)] : ((((X1 @ X2)) = $true) & (? [X3 : $i] : ((((X0 @ X3)) = $true) & (((X0 @ (X2 @ X3))) != $true)) | (((X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0))))) != $true)))),
% 0.20/0.26 inference(ennf_transformation,[],[f5])).
% 0.20/0.26 thf(f7,plain,(
% 0.20/0.26 ! [X1 : (($i > $i) > $o)] : ((((X1 @ (sK1 @ X1))) = $true) & (((((sK0 @ (sK2 @ X1))) = $true) & (((sK0 @ (sK1 @ X1 @ (sK2 @ X1)))) != $true)) | (((X1 @ (^[Y0 : $i]: (sK1 @ X1 @ (sK1 @ X1 @ Y0))))) != $true)))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X3,sK2 @ X1),skolemize(X3,sK2 @ X1)],[f6])).
% 0.20/0.26 thf(f10,plain,(
% 0.20/0.26 ( ! [X1 : (($i > $i) > $o)] : ((((X1 @ (sK1 @ X1))) = $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f7])).
% 0.20/0.26 thf(f13,plain,(
% 0.20/0.26 ((((^[Y0 : $i > $i]: ($false)) @ (sK1 @ (^[Y0 : $i > $i]: ($false))))) = $true)),
% 0.20/0.26 inference(primitive_instantiation,[],[f10])).
% 0.20/0.26 thf(f15,plain,(
% 0.20/0.26 ($false = $true)),
% 0.20/0.26 inference(beta-eta_normalization,[],[f13])).
% 0.20/0.26 thf(f16,plain,(
% 0.20/0.26 $false),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f15])).
% 0.20/0.26 % SZS output end Proof for theBenchmark
% 0.20/0.26 % (180693)------------------------------
% 0.20/0.26 % (180693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (180693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (180693)CaDiCaL version: 2.1.3
% 0.20/0.26 % (180693)Termination reason: Refutation
% 0.20/0.26 % (180693)Time elapsed: 0.001 s
% 0.20/0.26 % (180693)Peak memory usage: 12 MB
% 0.20/0.26 % (180693)Instructions burned: 1 (million)
% 0.20/0.26 % (180684)Success in time 0.037 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------