%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV196^5 : 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 08:38:00 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 201 ( 116 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 489 ( 60 ~; 55 |; 43 &; 321 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 133 ( 0 ^; 101 !; 32 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
y: a ).
thf(func_def_1,type,
x: a ).
thf(func_def_2,type,
cP: a > a > a ).
thf(func_def_3,type,
c0: a ).
thf(func_def_7,type,
sK0: a > a > a > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X0: a > a > a > $o] :
( ( ! [X2: a,X3: a,X1: a] :
( ( ( ( X1 = X3 )
& ( X2 = c0 ) )
| ( ( X1 = c0 )
& ( X2 = X3 ) )
| ? [X9: a,X7: a,X8: a,X4: a,X6: a,X5: a] :
( ( X3
= ( cP @ X8 @ X9 ) )
& ( X0 @ X5 @ X7 @ X9 )
& ( X1
= ( cP @ X4 @ X5 ) )
& ( X0 @ X4 @ X6 @ X8 )
& ( X2
= ( cP @ X6 @ X7 ) ) ) )
=> ( X0 @ X1 @ X2 @ X3 ) )
& $true )
=> ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_JOIN_LEM2_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > a > $o] :
( ( ! [X2: a,X3: a,X1: a] :
( ( ( ( X1 = X3 )
& ( X2 = c0 ) )
| ( ( X1 = c0 )
& ( X2 = X3 ) )
| ? [X9: a,X7: a,X8: a,X4: a,X6: a,X5: a] :
( ( X3
= ( cP @ X8 @ X9 ) )
& ( X0 @ X5 @ X7 @ X9 )
& ( X1
= ( cP @ X4 @ X5 ) )
& ( X0 @ X4 @ X6 @ X8 )
& ( X2
= ( cP @ X6 @ X7 ) ) ) )
=> ( X0 @ X1 @ X2 @ X3 ) )
& $true )
=> ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > a > $o] :
( ( ! [X1: a,X2: a,X3: a] :
( ( ( ( X2 = X3 )
& ( c0 = X1 ) )
| ( ( c0 = X3 )
& ( X1 = X2 ) )
| ? [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X6 @ X4 )
= X2 )
& ( X0 @ X9 @ X5 @ X4 )
& ( ( cP @ X7 @ X9 )
= X3 )
& ( X0 @ X7 @ X8 @ X6 )
& ( ( cP @ X8 @ X5 )
= X1 ) ) )
=> ( X0 @ X3 @ X1 @ X2 ) )
& $true )
=> ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > a > a > $o] :
( ( ! [X2: a,X3: a,X1: a] :
( ( ? [X5: a,X9: a,X4: a,X8: a,X7: a,X6: a] :
( ( ( cP @ X7 @ X9 )
= X3 )
& ( ( X0 @ X7 @ X8 @ X6 )
= $true )
& ( $true
= ( X0 @ X9 @ X5 @ X4 ) )
& ( ( cP @ X6 @ X4 )
= X2 )
& ( ( cP @ X8 @ X5 )
= X1 ) )
| ( ( X1 = X2 )
& ( c0 = X3 ) )
| ( ( X2 = X3 )
& ( c0 = X1 ) ) )
=> ( $true
= ( X0 @ X3 @ X1 @ X2 ) ) )
& $true )
=> ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > a > a > $o] :
( ! [X2: a,X3: a,X1: a] :
( ( ? [X5: a,X9: a,X4: a,X8: a,X7: a,X6: a] :
( ( ( cP @ X7 @ X9 )
= X3 )
& ( ( X0 @ X7 @ X8 @ X6 )
= $true )
& ( $true
= ( X0 @ X9 @ X5 @ X4 ) )
& ( ( cP @ X6 @ X4 )
= X2 )
& ( ( cP @ X8 @ X5 )
= X1 ) )
| ( ( X1 = X2 )
& ( c0 = X3 ) )
| ( ( X2 = X3 )
& ( c0 = X1 ) ) )
=> ( $true
= ( X0 @ X3 @ X1 @ X2 ) ) )
=> ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
= $true ) ),
inference(true_and_false_elimination,[],[f4]) ).
thf(f6,plain,
? [X0: a > a > a > $o] :
( ! [X1: a,X2: a,X3: a] :
( ( ! [X4: a,X7: a,X6: a,X8: a,X9: a,X5: a] :
( ( ( X0 @ X7 @ X8 @ X6 )
!= $true )
| ( ( cP @ X7 @ X9 )
!= X3 )
| ( ( cP @ X8 @ X5 )
!= X1 )
| ( $true
!= ( X0 @ X9 @ X5 @ X4 ) )
| ( ( cP @ X6 @ X4 )
!= X2 ) )
& ( ( X2 != X3 )
| ( c0 != X1 ) )
& ( ( X1 != X2 )
| ( c0 != X3 ) ) )
| ( $true
= ( X0 @ X3 @ X1 @ X2 ) ) )
& ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > a > a > $o] :
( ! [X1: a,X2: a,X3: a] :
( ( ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( $true
!= ( X0 @ X5 @ X7 @ X6 ) )
| ( ( cP @ X5 @ X8 )
!= X3 )
| ( ( cP @ X7 @ X9 )
!= X1 )
| ( $true
!= ( X0 @ X8 @ X9 @ X4 ) )
| ( ( cP @ X6 @ X4 )
!= X2 ) )
& ( ( X2 != X3 )
| ( c0 != X1 ) )
& ( ( X1 != X2 )
| ( c0 != X3 ) ) )
| ( $true
= ( X0 @ X3 @ X1 @ X2 ) ) )
& ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X1: a,X2: a,X3: a] :
( ( ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( sK0 @ X5 @ X7 @ X6 )
!= $true )
| ( ( cP @ X5 @ X8 )
!= X3 )
| ( ( cP @ X7 @ X9 )
!= X1 )
| ( $true
!= ( sK0 @ X8 @ X9 @ X4 ) )
| ( ( cP @ X6 @ X4 )
!= X2 ) )
& ( ( X2 != X3 )
| ( c0 != X1 ) )
& ( ( X1 != X2 )
| ( c0 != X3 ) ) )
| ( ( sK0 @ X3 @ X1 @ X2 )
= $true ) )
& ( ( sK0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
thf(f9,plain,
( ( sK0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X2: a,X3: a,X1: a] :
( ( X1 != X2 )
| ( c0 != X3 )
| ( ( sK0 @ X3 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X2: a,X3: a,X1: a] :
( ( X2 != X3 )
| ( c0 != X1 )
| ( ( sK0 @ X3 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X2: a,X3: a,X1: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( ( sK0 @ X5 @ X7 @ X6 )
!= $true )
| ( ( cP @ X5 @ X8 )
!= X3 )
| ( ( cP @ X7 @ X9 )
!= X1 )
| ( $true
!= ( sK0 @ X8 @ X9 @ X4 ) )
| ( ( cP @ X6 @ X4 )
!= X2 )
| ( ( sK0 @ X3 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X2: a,X1: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( ( sK0 @ X5 @ X7 @ X6 )
!= $true )
| ( ( cP @ X7 @ X9 )
!= X1 )
| ( $true
!= ( sK0 @ X8 @ X9 @ X4 ) )
| ( ( cP @ X6 @ X4 )
!= X2 )
| ( ( sK0 @ ( cP @ X5 @ X8 ) @ X1 @ X2 )
= $true ) ),
inference(equality_resolution,[],[f12]) ).
thf(f16,plain,
! [X2: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( ( sK0 @ X5 @ X7 @ X6 )
!= $true )
| ( $true
!= ( sK0 @ X8 @ X9 @ X4 ) )
| ( ( cP @ X6 @ X4 )
!= X2 )
| ( ( sK0 @ ( cP @ X5 @ X8 ) @ ( cP @ X7 @ X9 ) @ X2 )
= $true ) ),
inference(equality_resolution,[],[f15]) ).
thf(f17,plain,
! [X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( $true
!= ( sK0 @ X8 @ X9 @ X4 ) )
| ( $true
= ( sK0 @ ( cP @ X5 @ X8 ) @ ( cP @ X7 @ X9 ) @ ( cP @ X6 @ X4 ) ) )
| ( ( sK0 @ X5 @ X7 @ X6 )
!= $true ) ),
inference(equality_resolution,[],[f16]) ).
thf(f18,plain,
! [X3: a,X1: a] :
( ( c0 != X1 )
| ( ( sK0 @ X3 @ X1 @ X3 )
= $true ) ),
inference(equality_resolution,[],[f11]) ).
thf(f19,plain,
! [X3: a] :
( $true
= ( sK0 @ X3 @ c0 @ X3 ) ),
inference(equality_resolution,[],[f18]) ).
thf(f20,plain,
! [X2: a,X3: a] :
( ( c0 != X3 )
| ( $true
= ( sK0 @ X3 @ X2 @ X2 ) ) ),
inference(equality_resolution,[],[f10]) ).
thf(f21,plain,
! [X2: a] :
( $true
= ( sK0 @ c0 @ X2 @ X2 ) ),
inference(equality_resolution,[],[f20]) ).
thf(f23,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true
= ( sK0 @ ( cP @ X1 @ c0 ) @ ( cP @ X2 @ X0 ) @ ( cP @ X3 @ X0 ) ) )
| ( ( sK0 @ X1 @ X2 @ X3 )
!= $true ) ),
inference(constrained_superposition,[],[f17,f21]) ).
thf(f24,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( ( sK0 @ X1 @ X2 @ X3 )
!= $true )
| ( $true
= ( sK0 @ ( cP @ X1 @ c0 ) @ ( cP @ X2 @ X0 ) @ ( cP @ X3 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f26,plain,
! [X0: a,X1: a] :
( ( ( sK0 @ ( cP @ X0 @ c0 ) @ ( cP @ c0 @ X1 ) @ ( cP @ X0 @ X1 ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f24,f19]) ).
thf(f28,plain,
! [X0: a,X1: a] :
( ( sK0 @ ( cP @ X0 @ c0 ) @ ( cP @ c0 @ X1 ) @ ( cP @ X0 @ X1 ) )
= $true ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f30,plain,
$true != $true,
inference(constrained_superposition,[],[f9,f28]) ).
thf(f35,plain,
$false,
inference(trivial_inequality_removal,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV196^5 : 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 : n015.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 15:23:33 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 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
% 0.09/0.27 % (3655104)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.27 % (3655110)lrs+10_16_si=on:nwc=1.5:random_seed=918648195:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.27 % (3655110) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3655104-3655110"...
% 0.09/0.27 % (3655110)...printing done.
% 0.09/0.27 % (3655110)Refutation found. Thanks to Tanya!
% 0.09/0.27 % SZS status Theorem for theBenchmark
% 0.09/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.27 % (3655110)------------------------------
% 0.09/0.27 % (3655110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.27 % (3655110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.27 % (3655110)CaDiCaL version: 2.1.3
% 0.09/0.27 % (3655110)Termination reason: Refutation
% 0.09/0.27 % (3655110)Time elapsed: 0.002 s
% 0.09/0.27 % (3655110)Peak memory usage: 12 MB
% 0.09/0.27 % (3655110)Instructions burned: 5 (million)
% 0.09/0.27 % (3655104)Success in time 0.034 s
% 0.09/0.27 % Vampire exiting
%------------------------------------------------------------------------------