%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO237^5 : 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 : n004.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 08:47:15 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 24 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 82 ( 11 ~; 1 |; 6 &; 52 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 21 ( 14 ^; 7 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
g: $i > $i ).
thf(func_def_1,type,
p: ( $i > $i ) > $o ).
thf(func_def_3,type,
q: $i > $o ).
thf(func_def_4,type,
f: $i > $i ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p
@ ^ [X0: $i] : ( f @ X0 ) )
=> ( ( q @ x )
=> ( p
@ ^ [X0: $i] : ( g @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM508) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p
@ ^ [X0: $i] : ( f @ X0 ) )
=> ( ( q @ x )
=> ( p
@ ^ [X0: $i] : ( g @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p
@ ^ [X1: $i] : ( f @ X1 ) )
=> ( ( q @ x )
=> ( p
@ ^ [X2: $i] : ( g @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( $true
= ( p
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
=> ( ( ( q @ x )
= $true )
=> ( ( p
@ ^ [Y0: $i] : ( g @ Y0 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( p
@ ^ [Y0: $i] : ( g @ Y0 ) )
!= $true )
& ( ( q @ x )
= $true )
& ( $true
= ( p
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
& ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( q @ x )
= $true )
& ( $true
= ( p
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
& ( ( p
@ ^ [Y0: $i] : ( g @ Y0 ) )
!= $true )
& ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( p
@ ^ [Y0: $i] : ( g @ Y0 ) )
!= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( $true
= ( p
@ ^ [Y0: $i] : ( f @ Y0 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
( $true
!= ( p @ g ) ),
inference(beta-eta_normalization,[],[f8]) ).
thf(f14,plain,
( $true
= ( p @ f ) ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f15,plain,
( ( f != g )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f13,f14]) ).
thf(f16,plain,
f != g,
inference(trivial_inequality_removal,[],[f15]) ).
thf(f17,plain,
( ( f @ sK0 )
!= ( g @ sK0 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f18,plain,
$false,
inference(forward_subsumption_resolution,[],[f17,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO237^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:40:37 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.19/0.28 % (1533995)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (1534017)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1865308659:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.28 % (1534017) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1533995-1534017"...
% 0.19/0.28 % (1534017)...printing done.
% 0.19/0.28 % (1534017)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (1534017)------------------------------
% 0.19/0.28 % (1534017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1534017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1534017)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1534017)Termination reason: Refutation
% 0.19/0.28 % (1534017)Time elapsed: 0.001 s
% 0.19/0.28 % (1534017)Peak memory usage: 12 MB
% 0.19/0.28 % (1534017)Instructions burned: 1 (million)
% 0.19/0.28 % (1533995)Success in time 0.04 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------