%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU898^5 : 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 : n015.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 0.25s 0.32s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 73 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 327 ( 31 ~; 21 |; 32 &; 219 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 50 !; 12 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > a ).
thf(func_def_5,type,
sK2: a > a ).
thf(func_def_6,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > a,X1: a > $o,X2: a > a] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X0 @ ( X2 @ X3 ) )
= ( X2 @ ( X0 @ X3 ) ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X0 @ X3 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X0 @ ( X0 @ ( X2 @ X3 ) ) )
= ( X2 @ ( X0 @ ( X0 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM132_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a,X1: a > $o,X2: a > a] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X0 @ ( X2 @ X3 ) )
= ( X2 @ ( X0 @ X3 ) ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X0 @ X3 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X0 @ ( X0 @ ( X2 @ X3 ) ) )
= ( X2 @ ( X0 @ ( X0 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a,X1: a > $o,X2: a > a] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( ( X2 @ ( X0 @ X4 ) )
= ( X0 @ ( X2 @ X4 ) ) ) )
& ! [X5: a] :
( ( X1 @ X5 )
=> ( X1 @ ( X0 @ X5 ) ) )
& ! [X6: a] :
( ( X1 @ X6 )
=> ( X1 @ ( X2 @ X6 ) ) ) )
=> ! [X7: a] :
( ( X1 @ X7 )
=> ( ( X2 @ ( X0 @ ( X0 @ X7 ) ) )
= ( X0 @ ( X0 @ ( X2 @ X7 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: a > a,X1: a > $o,X0: a > a] :
( ( ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
=> ( $true
= ( X1 @ ( X0 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X1 @ ( X2 @ X3 ) )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
=> ( ( X2 @ ( X0 @ X4 ) )
= ( X0 @ ( X2 @ X4 ) ) ) )
& ! [X6: a] :
( ( $true
= ( X1 @ X6 ) )
=> ( $true
= ( X1 @ ( X2 @ X6 ) ) ) ) )
=> ! [X7: a] :
( ( $true
= ( X1 @ X7 ) )
=> ( ( X2 @ ( X0 @ ( X0 @ X7 ) ) )
= ( X0 @ ( X0 @ ( X2 @ X7 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > a,X1: a > $o,X0: a > a] :
( ? [X7: a] :
( ( $true
= ( X1 @ X7 ) )
& ( ( X2 @ ( X0 @ ( X0 @ X7 ) ) )
!= ( X0 @ ( X0 @ ( X2 @ X7 ) ) ) ) )
& ! [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X1 @ ( X0 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X1 @ ( X2 @ X3 ) )
= $true ) )
& ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( ( X2 @ ( X0 @ X4 ) )
= ( X0 @ ( X2 @ X4 ) ) ) )
& ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X1 @ ( X2 @ X6 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X1: a > $o,X0: a > a,X2: a > a] :
( ? [X7: a] :
( ( $true
= ( X1 @ X7 ) )
& ( ( X2 @ ( X0 @ ( X0 @ X7 ) ) )
!= ( X0 @ ( X0 @ ( X2 @ X7 ) ) ) ) )
& ! [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X1 @ ( X0 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X1 @ ( X2 @ X3 ) )
= $true ) )
& ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X1 @ ( X2 @ X6 ) ) ) )
& ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( ( X2 @ ( X0 @ X4 ) )
= ( X0 @ ( X2 @ X4 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > a,X2: a > a] :
( ? [X3: a] :
( ( $true
= ( X0 @ X3 ) )
& ( ( X2 @ ( X1 @ ( X1 @ X3 ) ) )
!= ( X1 @ ( X1 @ ( X2 @ X3 ) ) ) ) )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
= ( X0 @ ( X1 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
| ( $true
= ( X0 @ ( X2 @ X5 ) ) ) )
& ! [X6: a] :
( ( $true
!= ( X0 @ X6 ) )
| ( $true
= ( X0 @ ( X2 @ X6 ) ) ) )
& ! [X7: a] :
( ( $true
!= ( X0 @ X7 ) )
| ( ( X1 @ ( X2 @ X7 ) )
= ( X2 @ ( X1 @ X7 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
= ( sK0 @ sK3 ) )
& ( ( sK2 @ ( sK1 @ ( sK1 @ sK3 ) ) )
!= ( sK1 @ ( sK1 @ ( sK2 @ sK3 ) ) ) )
& ! [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( sK0 @ ( sK1 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
!= ( sK0 @ X5 ) )
| ( $true
= ( sK0 @ ( sK2 @ X5 ) ) ) )
& ! [X6: a] :
( ( $true
!= ( sK0 @ X6 ) )
| ( $true
= ( sK0 @ ( sK2 @ X6 ) ) ) )
& ! [X7: a] :
( ( $true
!= ( sK0 @ X7 ) )
| ( ( sK1 @ ( sK2 @ X7 ) )
= ( sK2 @ ( sK1 @ X7 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
! [X7: a] :
( ( $true
!= ( sK0 @ X7 ) )
| ( ( sK1 @ ( sK2 @ X7 ) )
= ( sK2 @ ( sK1 @ X7 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( sK0 @ ( sK1 @ X4 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( sK2 @ ( sK1 @ ( sK1 @ sK3 ) ) )
!= ( sK1 @ ( sK1 @ ( sK2 @ sK3 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,plain,
( ( $true
= ( sK0 @ ( sK1 @ sK3 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f12,f14]) ).
thf(f23,plain,
( $true
= ( sK0 @ ( sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f29,plain,
( ( $true != $true )
| ( ( sK2 @ ( sK1 @ sK3 ) )
= ( sK1 @ ( sK2 @ sK3 ) ) ) ),
inference(constrained_superposition,[],[f9,f14]) ).
thf(f31,plain,
( ( ( sK1 @ ( sK2 @ ( sK1 @ sK3 ) ) )
= ( sK2 @ ( sK1 @ ( sK1 @ sK3 ) ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f9,f23]) ).
thf(f32,plain,
( ( sK1 @ ( sK2 @ ( sK1 @ sK3 ) ) )
= ( sK2 @ ( sK1 @ ( sK1 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f33,plain,
( ( sK2 @ ( sK1 @ sK3 ) )
= ( sK1 @ ( sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f77,plain,
( ( sK1 @ ( sK2 @ ( sK1 @ sK3 ) ) )
!= ( sK1 @ ( sK1 @ ( sK2 @ sK3 ) ) ) ),
inference(constrained_superposition,[],[f13,f32]) ).
thf(f78,plain,
( ( sK1 @ ( sK1 @ ( sK2 @ sK3 ) ) )
!= ( sK1 @ ( sK1 @ ( sK2 @ sK3 ) ) ) ),
inference(forward_demodulation,[],[f77,f33]) ).
thf(f79,plain,
$false,
inference(trivial_inequality_removal,[],[f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU898^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n015.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 14:48:03 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running higher-order theorem proving
% 0.25/0.27 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
% 0.25/0.32 % (3619297)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.32 % (3619303)lrs+10_16_si=on:nwc=1.5:random_seed=1773338079:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.32 % (3619302)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=115494201:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.32 % (3619304)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3743580747:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.32 % (3619304) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3619297-3619304"...
% 0.25/0.32 % (3619304)...printing done.
% 0.25/0.32 % (3619304)Refutation found. Thanks to Tanya!
% 0.25/0.32 % SZS status Theorem for theBenchmark
% 0.25/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.32 % (3619304)------------------------------
% 0.25/0.32 % (3619304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.32 % (3619304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.32 % (3619304)CaDiCaL version: 2.1.3
% 0.25/0.32 % (3619304)Termination reason: Refutation
% 0.25/0.32 % (3619304)Time elapsed: 0.004 s
% 0.25/0.32 % (3619304)Peak memory usage: 12 MB
% 0.25/0.32 % (3619304)Instructions burned: 6 (million)
% 0.25/0.32 % (3619297)Success in time 0.036 s
% 0.25/0.32 % Vampire exiting
%------------------------------------------------------------------------------