%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO354^5 : 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 : n006.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 08:47:30 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 24 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 99 ( 15 ~; 4 |; 4 &; 64 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 34 ( 14 ^; 19 !; 1 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
n: $i > $i ).
thf(func_def_1,type,
m: $i > $i ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: ( $i > $i ) > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(f1,conjecture,
( ! [X1: $i > $o,X0: $i] :
( ( X1 @ ( m @ X0 ) )
=> ( X1 @ ( n @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2
@ ^ [X0: $i] : ( m @ X0 ) )
=> ( X2
@ ^ [X0: $i] : ( n @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE4EXT) ).
thf(f2,negated_conjecture,
~ ( ! [X1: $i > $o,X0: $i] :
( ( X1 @ ( m @ X0 ) )
=> ( X1 @ ( n @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2
@ ^ [X0: $i] : ( m @ X0 ) )
=> ( X2
@ ^ [X0: $i] : ( n @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i > $o,X1: $i] :
( ( X0 @ ( m @ X1 ) )
=> ( X0 @ ( n @ X1 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2
@ ^ [X3: $i] : ( m @ X3 ) )
=> ( X2
@ ^ [X4: $i] : ( n @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( m @ X1 ) )
= $true )
=> ( $true
= ( X0 @ ( n @ X1 ) ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true )
=> ( ( X2
@ ^ [Y0: $i] : ( n @ Y0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( m @ X1 ) )
!= $true )
| ( $true
= ( X0 @ ( n @ X1 ) ) ) )
& ? [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : ( n @ Y0 ) )
!= $true )
& ( ( X2
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( m @ X1 ) )
!= $true )
| ( $true
= ( X0 @ ( n @ X1 ) ) ) )
& ( ( sK0
@ ^ [Y0: $i] : ( n @ Y0 ) )
!= $true )
& ( ( sK0
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f5]) ).
thf(f7,plain,
( ( sK0
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( sK0
@ ^ [Y0: $i] : ( n @ Y0 ) )
!= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( m @ X1 ) )
!= $true )
| ( $true
= ( X0 @ ( n @ X1 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,plain,
( ( sK0 @ n )
!= $true ),
inference(beta-eta_normalization,[],[f8]) ).
thf(f13,plain,
( ( sK0 @ m )
= $true ),
inference(beta-eta_normalization,[],[f7]) ).
thf(f14,plain,
( ( m != n )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f12,f13]) ).
thf(f15,plain,
m != n,
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
( ( n @ sK1 )
!= ( m @ sK1 ) ),
inference(negative_extensionality,[],[f15]) ).
thf(f17,plain,
! [X0: $i] :
( ( m @ X0 )
= ( n @ X0 ) ),
inference(leibniz_equality_elimination,[],[f9]) ).
thf(f37,plain,
( ( m @ sK1 )
!= ( m @ sK1 ) ),
inference(backward_demodulation,[],[f16,f17]) ).
thf(f38,plain,
$false,
inference(trivial_inequality_removal,[],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO354^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:48:39 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.28 % (1003335)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1003345)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3613454451:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.28 % (1003345) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1003335-1003345"...
% 0.22/0.28 % (1003345)...printing done.
% 0.22/0.28 % (1003345)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (1003345)------------------------------
% 0.22/0.28 % (1003345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1003345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1003345)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1003345)Termination reason: Refutation
% 0.22/0.28 % (1003345)Time elapsed: 0.002 s
% 0.22/0.28 % (1003345)Peak memory usage: 12 MB
% 0.22/0.28 % (1003345)Instructions burned: 2 (million)
% 0.22/0.28 % (1003335)Success in time 0.031 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------