%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU504^2 : 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 : 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 08:29:50 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU504^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:49:42 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
% 0.09/0.25 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
% 0.22/0.29 % (615933)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (615950)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2463769029:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (615950) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-615933-615950"...
% 0.22/0.29 % (615950)...printing done.
% 0.22/0.29 % (615950)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_0, type, exu: (($i > $o) > $o)).
% 0.22/0.29 thf(func_def_2, type, exuE1: $o).
% 0.22/0.29 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.29 thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.29 thf(func_def_8, type, vAND: ($o > $o > $o)).
% 0.22/0.29 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_10, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.29 thf(func_def_11, type, vIMP: ($o > $o > $o)).
% 0.22/0.29 thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.29 thf(func_def_14, type, sK0: (($i > $o) > $i)).
% 0.22/0.29 thf(func_def_15, type, sK1: ($i > $o)).
% 0.22/0.29 thf(func_def_16, type, sK2: ($i > $i)).
% 0.22/0.29 thf(func_def_17, type, sK3: ($i > $o)).
% 0.22/0.29 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.22/0.29 thf(f2,axiom,(
% 0.22/0.29 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2)))) = exuE1)),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1)).
% 0.22/0.29 thf(f3,conjecture,(
% 0.22/0.29 exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (X0 @ X1))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e)).
% 0.22/0.29 thf(f4,negated_conjecture,(
% 0.22/0.29 ~(exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (X0 @ X1)))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.29 thf(f5,plain,(
% 0.22/0.29 ~(exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : (X0 @ X2)))),
% 0.22/0.29 inference(rectify,[],[f4])).
% 0.22/0.29 thf(f6,plain,(
% 0.22/0.29 ~((exuE1 = $true) => ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X2 : $i] : (((X0 @ X2)) = $true)))),
% 0.22/0.29 inference(fool_elimination,[],[f5])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : ((X0 @ X2) & ! [X3 : $i] : ((X0 @ X3) => (X2 = X3)))) = exuE1)),
% 0.22/0.29 inference(rectify,[],[f2])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X2 : $i] : ((((X0 @ X2)) = $true) & ! [X3 : $i] : (($true = ((X0 @ X3))) => (X2 = X3)))) <=> (exuE1 = $true)),
% 0.22/0.29 inference(fool_elimination,[],[f9])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 ~((exuE1 = $true) => ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X1 : $i] : (((X0 @ X1)) = $true)))),
% 0.22/0.29 inference(rectify,[],[f6])).
% 0.22/0.29 thf(f12,plain,(
% 0.22/0.29 ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X1 : $i] : (! [X2 : $i] : ((((X0 @ X2)) = $true) => (X1 = X2)) & (((X0 @ X1)) = $true))) <=> (exuE1 = $true)),
% 0.22/0.29 inference(rectify,[],[f10])).
% 0.22/0.29 thf(f13,plain,(
% 0.22/0.29 (exuE1 = $true) & ? [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X1 : $i] : (((X0 @ X1)) != $true))),
% 0.22/0.29 inference(ennf_transformation,[],[f11])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 ! [X0 : ($i > $o)] : (($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & ! [X2 : $i] : ((X1 = X2) | (((X0 @ X2)) != $true)))) <=> (exuE1 = $true)),
% 0.22/0.29 inference(ennf_transformation,[],[f12])).
% 0.22/0.29 thf(f15,plain,(
% 0.22/0.29 (! [X0 : ($i > $o)] : (($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & ! [X2 : $i] : ((X1 = X2) | (((X0 @ X2)) != $true)))) | (exuE1 != $true)) & ((exuE1 = $true) | ? [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X1 : $i] : ((((X0 @ X1)) != $true) | ? [X2 : $i] : ((X1 != X2) & (((X0 @ X2)) = $true)))))),
% 0.22/0.29 inference(nnf_transformation,[],[f14])).
% 0.22/0.29 thf(f16,plain,(
% 0.22/0.29 (! [X0 : ($i > $o)] : (($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & ! [X2 : $i] : ((X1 = X2) | (((X0 @ X2)) != $true)))) | (exuE1 != $true)) & ((exuE1 = $true) | ? [X3 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X3 @ Y0))))) & ! [X4 : $i] : (($true != ((X3 @ X4))) | ? [X5 : $i] : ((X4 != X5) & ($true = ((X3 @ X5)))))))),
% 0.22/0.29 inference(rectify,[],[f15])).
% 0.22/0.29 thf(f17,plain,(
% 0.22/0.29 (! [X0 : ($i > $o)] : (($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) | (($true = ((X0 @ (sK0 @ X0)))) & ! [X2 : $i] : ((((sK0 @ X0)) = X2) | (((X0 @ X2)) != $true)))) | (exuE1 != $true)) & ((exuE1 = $true) | (($true = ((exu @ (^[Y0 : $i]: (sK1 @ Y0))))) & ! [X4 : $i] : (($true != ((sK1 @ X4))) | ((((sK2 @ X4)) != X4) & ($true = ((sK1 @ (sK2 @ X4))))))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,vAPP]),skolemize(X5,sK2 @ X4),skolemize(X3,sK1),skolemize(X5,sK2 @ X4)],[f16])).
% 0.22/0.29 thf(f18,plain,(
% 0.22/0.29 (exuE1 = $true) & (($true = ((exu @ (^[Y0 : $i]: (sK3 @ Y0))))) & ! [X1 : $i] : ($true != ((sK3 @ X1))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f13])).
% 0.22/0.29 thf(f24,plain,(
% 0.22/0.29 ( ! [X0 : ($i > $o)] : ((exuE1 != $true) | ($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f17])).
% 0.22/0.29 thf(f25,plain,(
% 0.22/0.29 ( ! [X1 : $i] : (($true != ((sK3 @ X1)))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f18])).
% 0.22/0.29 thf(f26,plain,(
% 0.22/0.29 ($true = ((exu @ (^[Y0 : $i]: (sK3 @ Y0)))))),
% 0.22/0.29 inference(cnf_transformation,[],[f18])).
% 0.22/0.29 thf(f27,plain,(
% 0.22/0.29 (exuE1 = $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f18])).
% 0.22/0.29 thf(f31,plain,(
% 0.22/0.29 ( ! [X0 : ($i > $o)] : ((exuE1 != $true) | ($true != ((exu @ X0))) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.22/0.29 inference(beta-eta_normalization,[],[f24])).
% 0.22/0.29 thf(f32,plain,(
% 0.22/0.29 ($true = ((exu @ sK3)))),
% 0.22/0.29 inference(beta-eta_normalization,[],[f26])).
% 0.22/0.29 thf(f34,plain,(
% 0.22/0.29 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK0 @ X0)))) | ($true != ((exu @ X0)))) )),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f31,f27])).
% 0.22/0.29 thf(f38,plain,(
% 0.22/0.29 ($true != $true) | ($true != ((exu @ sK3)))),
% 0.22/0.29 inference(superposition,[],[f25,f34])).
% 0.22/0.29 thf(f44,plain,(
% 0.22/0.29 ($true != ((exu @ sK3)))),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f38])).
% 0.22/0.29 thf(f45,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f44,f32])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (615950)------------------------------
% 0.22/0.29 % (615950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (615950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (615950)CaDiCaL version: 2.1.3
% 0.22/0.29 % (615950)Termination reason: Refutation
% 0.22/0.29 % (615950)Time elapsed: 0.002 s
% 0.22/0.29 % (615950)Peak memory usage: 12 MB
% 0.22/0.29 % (615950)Instructions burned: 3 (million)
% 0.22/0.29 % (615933)Success in time 0.032 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------