%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU901^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:31:54 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 228 ( 117 equ; 0 cnn)
% Maximal formula atoms : 18 ( 10 avg)
% Number of connectives : 518 ( 46 ~; 38 |; 64 &; 330 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 130 ( 0 ^; 103 !; 27 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: b > a ).
thf(func_def_4,type,
sK1: b > b ).
thf(func_def_5,type,
sK2: g > b ).
thf(func_def_6,type,
sK3: a > $o ).
thf(func_def_7,type,
sK4: a > a ).
thf(func_def_8,type,
sK5: g > g ).
thf(func_def_9,type,
sK6: b > $o ).
thf(func_def_10,type,
sK7: g > $o ).
thf(func_def_11,type,
sK8: g ).
thf(f1,conjecture,
! [X3: g > g,X0: g > b,X7: a > a,X6: a > $o,X4: b > $o,X2: g > $o,X1: b > a,X5: b > b] :
( ( ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X0 @ ( X3 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM131D_pme) ).
thf(f2,negated_conjecture,
~ ! [X3: g > g,X0: g > b,X7: a > a,X6: a > $o,X4: b > $o,X2: g > $o,X1: b > a,X5: b > b] :
( ( ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X0 @ ( X3 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: g > g,X1: g > b,X2: a > a,X3: a > $o,X4: b > $o,X5: g > $o,X6: b > a,X7: b > b] :
( ( ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X7 @ X8 ) ) )
& ! [X9: b] :
( ( X4 @ X9 )
=> ( X4 @ ( X7 @ X9 ) ) )
& ! [X10: a] :
( ( X3 @ X10 )
=> ( X3 @ ( X2 @ X10 ) ) )
& ! [X11: g] :
( ( X5 @ X11 )
=> ( X5 @ ( X0 @ X11 ) ) )
& ! [X12: b] :
( ( X4 @ X12 )
=> ( ( X6 @ ( X7 @ X12 ) )
= ( X2 @ ( X6 @ X12 ) ) ) )
& ! [X13: g] :
( ( X5 @ X13 )
=> ( ( X1 @ ( X0 @ X13 ) )
= ( X7 @ ( X1 @ X13 ) ) ) )
& ! [X14: g] :
( ( X5 @ X14 )
=> ( X4 @ ( X1 @ X14 ) ) )
& ! [X15: b] :
( ( X4 @ X15 )
=> ( X3 @ ( X6 @ X15 ) ) ) )
=> ! [X16: g] :
( ( X5 @ X16 )
=> ( ( X6 @ ( X1 @ ( X0 @ X16 ) ) )
= ( X2 @ ( X6 @ ( X1 @ X16 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X4: b > $o,X3: a > $o,X5: g > $o,X1: g > b,X7: b > b,X2: a > a,X6: b > a,X0: g > g] :
( ( ! [X15: b] :
( ( $true
= ( X4 @ X15 ) )
=> ( $true
= ( X3 @ ( X6 @ X15 ) ) ) )
& ! [X13: g] :
( ( $true
= ( X5 @ X13 ) )
=> ( ( X1 @ ( X0 @ X13 ) )
= ( X7 @ ( X1 @ X13 ) ) ) )
& ! [X8: b] :
( ( ( X4 @ X8 )
= $true )
=> ( $true
= ( X4 @ ( X7 @ X8 ) ) ) )
& ! [X9: b] :
( ( ( X4 @ X9 )
= $true )
=> ( ( X4 @ ( X7 @ X9 ) )
= $true ) )
& ! [X11: g] :
( ( $true
= ( X5 @ X11 ) )
=> ( $true
= ( X5 @ ( X0 @ X11 ) ) ) )
& ! [X12: b] :
( ( $true
= ( X4 @ X12 ) )
=> ( ( X6 @ ( X7 @ X12 ) )
= ( X2 @ ( X6 @ X12 ) ) ) )
& ! [X14: g] :
( ( $true
= ( X5 @ X14 ) )
=> ( $true
= ( X4 @ ( X1 @ X14 ) ) ) )
& ! [X10: a] :
( ( ( X3 @ X10 )
= $true )
=> ( $true
= ( X3 @ ( X2 @ X10 ) ) ) ) )
=> ! [X16: g] :
( ( $true
= ( X5 @ X16 ) )
=> ( ( X6 @ ( X1 @ ( X0 @ X16 ) ) )
= ( X2 @ ( X6 @ ( X1 @ X16 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X4: b > $o,X3: a > $o,X5: g > $o,X1: g > b,X7: b > b,X2: a > a,X6: b > a,X0: g > g] :
( ? [X16: g] :
( ( $true
= ( X5 @ X16 ) )
& ( ( X6 @ ( X1 @ ( X0 @ X16 ) ) )
!= ( X2 @ ( X6 @ ( X1 @ X16 ) ) ) ) )
& ! [X15: b] :
( ( $true
= ( X3 @ ( X6 @ X15 ) ) )
| ( $true
!= ( X4 @ X15 ) ) )
& ! [X13: g] :
( ( ( X1 @ ( X0 @ X13 ) )
= ( X7 @ ( X1 @ X13 ) ) )
| ( $true
!= ( X5 @ X13 ) ) )
& ! [X8: b] :
( ( $true
= ( X4 @ ( X7 @ X8 ) ) )
| ( ( X4 @ X8 )
!= $true ) )
& ! [X9: b] :
( ( ( X4 @ ( X7 @ X9 ) )
= $true )
| ( ( X4 @ X9 )
!= $true ) )
& ! [X11: g] :
( ( $true
!= ( X5 @ X11 ) )
| ( $true
= ( X5 @ ( X0 @ X11 ) ) ) )
& ! [X12: b] :
( ( ( X6 @ ( X7 @ X12 ) )
= ( X2 @ ( X6 @ X12 ) ) )
| ( $true
!= ( X4 @ X12 ) ) )
& ! [X14: g] :
( ( $true
!= ( X5 @ X14 ) )
| ( $true
= ( X4 @ ( X1 @ X14 ) ) ) )
& ! [X10: a] :
( ( ( X3 @ X10 )
!= $true )
| ( $true
= ( X3 @ ( X2 @ X10 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X6: b > a,X7: b > b,X1: g > b,X3: a > $o,X2: a > a,X0: g > g,X4: b > $o,X5: g > $o] :
( ! [X10: a] :
( ( ( X3 @ X10 )
!= $true )
| ( $true
= ( X3 @ ( X2 @ X10 ) ) ) )
& ? [X16: g] :
( ( $true
= ( X5 @ X16 ) )
& ( ( X6 @ ( X1 @ ( X0 @ X16 ) ) )
!= ( X2 @ ( X6 @ ( X1 @ X16 ) ) ) ) )
& ! [X15: b] :
( ( $true
= ( X3 @ ( X6 @ X15 ) ) )
| ( $true
!= ( X4 @ X15 ) ) )
& ! [X14: g] :
( ( $true
!= ( X5 @ X14 ) )
| ( $true
= ( X4 @ ( X1 @ X14 ) ) ) )
& ! [X12: b] :
( ( ( X6 @ ( X7 @ X12 ) )
= ( X2 @ ( X6 @ X12 ) ) )
| ( $true
!= ( X4 @ X12 ) ) )
& ! [X9: b] :
( ( ( X4 @ ( X7 @ X9 ) )
= $true )
| ( ( X4 @ X9 )
!= $true ) )
& ! [X13: g] :
( ( ( X1 @ ( X0 @ X13 ) )
= ( X7 @ ( X1 @ X13 ) ) )
| ( $true
!= ( X5 @ X13 ) ) )
& ! [X11: g] :
( ( $true
!= ( X5 @ X11 ) )
| ( $true
= ( X5 @ ( X0 @ X11 ) ) ) )
& ! [X8: b] :
( ( $true
= ( X4 @ ( X7 @ X8 ) ) )
| ( ( X4 @ X8 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: b > a,X1: b > b,X2: g > b,X3: a > $o,X4: a > a,X5: g > g,X6: b > $o,X7: g > $o] :
( ! [X8: a] :
( ( $true
!= ( X3 @ X8 ) )
| ( ( X3 @ ( X4 @ X8 ) )
= $true ) )
& ? [X9: g] :
( ( $true
= ( X7 @ X9 ) )
& ( ( X4 @ ( X0 @ ( X2 @ X9 ) ) )
!= ( X0 @ ( X2 @ ( X5 @ X9 ) ) ) ) )
& ! [X10: b] :
( ( $true
= ( X3 @ ( X0 @ X10 ) ) )
| ( $true
!= ( X6 @ X10 ) ) )
& ! [X11: g] :
( ( $true
!= ( X7 @ X11 ) )
| ( $true
= ( X6 @ ( X2 @ X11 ) ) ) )
& ! [X12: b] :
( ( ( X4 @ ( X0 @ X12 ) )
= ( X0 @ ( X1 @ X12 ) ) )
| ( $true
!= ( X6 @ X12 ) ) )
& ! [X13: b] :
( ( $true
= ( X6 @ ( X1 @ X13 ) ) )
| ( ( X6 @ X13 )
!= $true ) )
& ! [X14: g] :
( ( ( X2 @ ( X5 @ X14 ) )
= ( X1 @ ( X2 @ X14 ) ) )
| ( $true
!= ( X7 @ X14 ) ) )
& ! [X15: g] :
( ( $true
!= ( X7 @ X15 ) )
| ( $true
= ( X7 @ ( X5 @ X15 ) ) ) )
& ! [X16: b] :
( ( ( X6 @ ( X1 @ X16 ) )
= $true )
| ( $true
!= ( X6 @ X16 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X8: a] :
( ( ( sK3 @ X8 )
!= $true )
| ( $true
= ( sK3 @ ( sK4 @ X8 ) ) ) )
& ( $true
= ( sK7 @ sK8 ) )
& ( ( sK0 @ ( sK2 @ ( sK5 @ sK8 ) ) )
!= ( sK4 @ ( sK0 @ ( sK2 @ sK8 ) ) ) )
& ! [X10: b] :
( ( $true
= ( sK3 @ ( sK0 @ X10 ) ) )
| ( ( sK6 @ X10 )
!= $true ) )
& ! [X11: g] :
( ( $true
!= ( sK7 @ X11 ) )
| ( ( sK6 @ ( sK2 @ X11 ) )
= $true ) )
& ! [X12: b] :
( ( ( sK4 @ ( sK0 @ X12 ) )
= ( sK0 @ ( sK1 @ X12 ) ) )
| ( ( sK6 @ X12 )
!= $true ) )
& ! [X13: b] :
( ( $true
= ( sK6 @ ( sK1 @ X13 ) ) )
| ( $true
!= ( sK6 @ X13 ) ) )
& ! [X14: g] :
( ( ( sK1 @ ( sK2 @ X14 ) )
= ( sK2 @ ( sK5 @ X14 ) ) )
| ( $true
!= ( sK7 @ X14 ) ) )
& ! [X15: g] :
( ( $true
!= ( sK7 @ X15 ) )
| ( $true
= ( sK7 @ ( sK5 @ X15 ) ) ) )
& ! [X16: b] :
( ( $true
= ( sK6 @ ( sK1 @ X16 ) ) )
| ( $true
!= ( sK6 @ X16 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X9,sK8)],[f7]) ).
thf(f11,plain,
! [X14: g] :
( ( $true
!= ( sK7 @ X14 ) )
| ( ( sK1 @ ( sK2 @ X14 ) )
= ( sK2 @ ( sK5 @ X14 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X12: b] :
( ( ( sK6 @ X12 )
!= $true )
| ( ( sK4 @ ( sK0 @ X12 ) )
= ( sK0 @ ( sK1 @ X12 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X11: g] :
( ( $true
!= ( sK7 @ X11 ) )
| ( ( sK6 @ ( sK2 @ X11 ) )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( sK0 @ ( sK2 @ ( sK5 @ sK8 ) ) )
!= ( sK4 @ ( sK0 @ ( sK2 @ sK8 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( $true
= ( sK7 @ sK8 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f27,plain,
( ( ( sK6 @ ( sK2 @ sK8 ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f14,f17]) ).
thf(f30,plain,
( ( sK6 @ ( sK2 @ sK8 ) )
= $true ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f45,plain,
( ( $true != $true )
| ( ( sK2 @ ( sK5 @ sK8 ) )
= ( sK1 @ ( sK2 @ sK8 ) ) ) ),
inference(constrained_superposition,[],[f11,f17]) ).
thf(f48,plain,
( ( sK2 @ ( sK5 @ sK8 ) )
= ( sK1 @ ( sK2 @ sK8 ) ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f53,plain,
( ( $true != $true )
| ( ( sK0 @ ( sK1 @ ( sK2 @ sK8 ) ) )
= ( sK4 @ ( sK0 @ ( sK2 @ sK8 ) ) ) ) ),
inference(constrained_superposition,[],[f13,f30]) ).
thf(f56,plain,
( ( sK0 @ ( sK1 @ ( sK2 @ sK8 ) ) )
= ( sK4 @ ( sK0 @ ( sK2 @ sK8 ) ) ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f59,plain,
( ( sK0 @ ( sK2 @ ( sK5 @ sK8 ) ) )
= ( sK4 @ ( sK0 @ ( sK2 @ sK8 ) ) ) ),
inference(forward_demodulation,[],[f56,f48]) ).
thf(f62,plain,
$false,
inference(forward_subsumption_resolution,[],[f59,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU901^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:45:09 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 % (3256397)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (3256404)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2542961406:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (3256404) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3256397-3256404"...
% 0.20/0.27 % (3256404)...printing done.
% 0.20/0.27 % (3256404)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (3256404)------------------------------
% 0.20/0.27 % (3256404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (3256404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (3256404)CaDiCaL version: 2.1.3
% 0.20/0.27 % (3256404)Termination reason: Refutation
% 0.20/0.27 % (3256404)Time elapsed: 0.002 s
% 0.20/0.27 % (3256404)Peak memory usage: 12 MB
% 0.20/0.27 % (3256404)Instructions burned: 7 (million)
% 0.20/0.27 % (3256397)Success in time 0.03 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------