%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV258^5 : 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 : n013.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 08:38:08 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV258^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n013.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 15:27:36 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.22 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
% 0.21/0.26 % (2250314)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.26 % (2250323)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1837668404:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.26 % (2250323) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2250314-2250323"...
% 0.21/0.26 % (2250323)...printing done.
% 0.21/0.26 % (2250323)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% 0.21/0.26 tff(type_def_5, type, a: $tType).
% 0.21/0.26 tff(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.26 tff(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.26 tff(func_def_4, type, vAND: ($o > ($o > $o))).
% 0.21/0.26 tff(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.26 tff(func_def_6, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.26 tff(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.26 tff(func_def_8, type, vNOT: ($o > $o)).
% 0.21/0.26 fof(f1,conjecture,(
% 0.21/0.26 ! [X0 : (a > $o)] : ((^[X1 : a] : (~$false)) = X0 => $true) & ! [X2 : ((a > $o) > $o),X0 : (a > $o)] : (((^[X1 : a] : (? [X3 : (a > $o)] : (vAPP(a > $o,$o,X2,X3) & vAPP(a,$o,X3,X1)))) = X0 & ! [X1 : (a > $o)] : (vAPP(a > $o,$o,X2,X1) => $true)) => $true) & ! [X4 : (a > $o),X5 : (a > $o),X3 : (a > $o)] : (((^[X1 : a] : (vAPP(a,$o,X4,X1) & vAPP(a,$o,X5,X1))) = X3 & $true & $true) => $true) & ! [X0 : (a > $o)] : ((^[X1 : a] : ($false)) = X0 => $true)),
% 0.21/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDISCRETE_TOPOLOGY_pme)).
% 0.21/0.26 fof(f2,negated_conjecture,(
% 0.21/0.26 ~(! [X0 : (a > $o)] : ((^[X1 : a] : (~$false)) = X0 => $true) & ! [X2 : ((a > $o) > $o),X0 : (a > $o)] : (((^[X1 : a] : (? [X3 : (a > $o)] : (vAPP(a > $o,$o,X2,X3) & vAPP(a,$o,X3,X1)))) = X0 & ! [X1 : (a > $o)] : (vAPP(a > $o,$o,X2,X1) => $true)) => $true) & ! [X4 : (a > $o),X5 : (a > $o),X3 : (a > $o)] : (((^[X1 : a] : (vAPP(a,$o,X4,X1) & vAPP(a,$o,X5,X1))) = X3 & $true & $true) => $true) & ! [X0 : (a > $o)] : ((^[X1 : a] : ($false)) = X0 => $true))),
% 0.21/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.26 fof(f3,plain,(
% 0.21/0.26 ~(! [X0 : (a > $o)] : ((^[X1 : a] : (~$false)) = X0 => $true) & ! [X2 : ((a > $o) > $o),X3 : (a > $o)] : (((^[X4 : a] : (? [X5 : (a > $o)] : (vAPP(a > $o,$o,X2,X5) & vAPP(a,$o,X5,X4)))) = X3 & ! [X6 : (a > $o)] : (vAPP(a > $o,$o,X2,X6) => $true)) => $true) & ! [X7 : (a > $o),X8 : (a > $o),X9 : (a > $o)] : (((^[X10 : a] : (vAPP(a,$o,X7,X10) & vAPP(a,$o,X8,X10))) = X9 & $true & $true) => $true) & ! [X11 : (a > $o)] : ((^[X12 : a] : ($false)) = X11 => $true))),
% 0.21/0.26 inference(rectify,[],[f2])).
% 0.21/0.26 fof(f4,plain,(
% 0.21/0.26 ~(! [X0 : (a > $o)] : (vLAM(a,$o,vAPP($o,$o,vNOT,$false)) = X0 => $true) & ! [X2 : ((a > $o) > $o),X3 : (a > $o)] : ((vLAM(a,$o,vAPP((a > $o) > $o,$o,vSIGMA(a > $o),vLAM(a > $o,$o,vAPP($o,$o,vAPP($o,$o > $o,vAND,vAPP(a,$o,db0(a > $o),db1(a))),vAPP(a > $o,$o,X2,db0(a > $o)))))) = X3 & ! [X6 : (a > $o)] : (($true = vAPP(a > $o,$o,X2,X6)) => $true)) => $true) & ! [X7 : (a > $o),X8 : (a > $o),X9 : (a > $o)] : ((vLAM(a,$o,vAPP($o,$o,vAPP($o,$o > $o,vAND,vAPP(a,$o,X8,db0(a))),vAPP(a,$o,X7,db0(a)))) = X9 & $true & $true) => $true) & ! [X11 : (a > $o)] : (vLAM(a,$o,$false) = X11 => $true))),
% 0.21/0.26 inference(fool_elimination,[],[f3])).
% 0.21/0.26 fof(f5,plain,(
% 0.21/0.26 ~(! [X0 : (a > $o)] : (vLAM(a,$o,vAPP($o,$o,vNOT,$false)) = X0 => $true) & ! [X1 : ((a > $o) > $o),X2 : (a > $o)] : ((vLAM(a,$o,vAPP((a > $o) > $o,$o,vSIGMA(a > $o),vLAM(a > $o,$o,vAPP($o,$o,vAPP($o,$o > $o,vAND,vAPP(a,$o,db0(a > $o),db1(a))),vAPP(a > $o,$o,X1,db0(a > $o)))))) = X2 & ! [X3 : (a > $o)] : ((vAPP(a > $o,$o,X1,X3) = $true) => $true)) => $true) & ! [X4 : (a > $o),X5 : (a > $o),X6 : (a > $o)] : ((vLAM(a,$o,vAPP($o,$o,vAPP($o,$o > $o,vAND,vAPP(a,$o,X5,db0(a))),vAPP(a,$o,X4,db0(a)))) = X6 & $true & $true) => $true) & ! [X7 : (a > $o)] : (vLAM(a,$o,$false) = X7 => $true))),
% 0.21/0.26 inference(rectify,[],[f4])).
% 0.21/0.26 fof(f6,plain,(
% 0.21/0.26 $false),
% 0.21/0.26 inference(true_and_false_elimination,[],[f5])).
% 0.21/0.26 fof(f7,plain,(
% 0.21/0.26 $false),
% 0.21/0.26 inference(cnf_transformation,[],[f6])).
% 0.21/0.26 % SZS output end Proof for theBenchmark
% 0.21/0.26 % (2250323)------------------------------
% 0.21/0.26 % (2250323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (2250323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (2250323)CaDiCaL version: 2.1.3
% 0.21/0.26 % (2250323)Termination reason: Refutation
% 0.21/0.26 % (2250323)Time elapsed: 0.001 s
% 0.21/0.26 % (2250323)Peak memory usage: 11 MB
% 0.21/0.26 % (2250323)Instructions burned: 1 (million)
% 0.21/0.26 % (2250314)Success in time 0.032 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------