%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO171^5 : 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 : n010.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 08:46:47 AM UTC 2026
% Result : Theorem 0.28s 0.40s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 214 ( 50 equ; 0 cnn)
% Maximal formula atoms : 13 ( 12 avg)
% Number of connectives : 281 ( 41 ~; 40 |; 24 &; 176 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
g: $i > $i > $o ).
thf(func_def_2,type,
f: $i > $i ).
thf(f1,conjecture,
~ ( ! [X0: $i] :
( ( g @ ( f @ X0 ) @ X0 )
| ( g @ X0 @ a ) )
& ! [X0: $i,X1: $i] :
( ~ ( g @ X0 @ X1 )
| ( g @ ( f @ X1 ) @ X1 ) )
& ! [X1: $i,X0: $i] :
( ~ ( g @ X0 @ X1 )
| ( g @ X1 @ ( f @ X1 ) ) )
& ! [X0: $i,X1: $i] :
( ~ ( g @ X0 @ X1 )
| ~ ( g @ X1 @ a ) )
& ! [X0: $i] :
( ( g @ X0 @ ( f @ X0 ) )
| ( g @ X0 @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSYN031_1) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X0: $i] :
( ( g @ ( f @ X0 ) @ X0 )
| ( g @ X0 @ a ) )
& ! [X0: $i,X1: $i] :
( ~ ( g @ X0 @ X1 )
| ( g @ ( f @ X1 ) @ X1 ) )
& ! [X1: $i,X0: $i] :
( ~ ( g @ X0 @ X1 )
| ( g @ X1 @ ( f @ X1 ) ) )
& ! [X0: $i,X1: $i] :
( ~ ( g @ X0 @ X1 )
| ~ ( g @ X1 @ a ) )
& ! [X0: $i] :
( ( g @ X0 @ ( f @ X0 ) )
| ( g @ X0 @ a ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i] :
( ( g @ ( f @ X0 ) @ X0 )
| ( g @ X0 @ a ) )
& ! [X1: $i,X2: $i] :
( ~ ( g @ X1 @ X2 )
| ( g @ ( f @ X2 ) @ X2 ) )
& ! [X3: $i,X4: $i] :
( ~ ( g @ X4 @ X3 )
| ( g @ X3 @ ( f @ X3 ) ) )
& ! [X5: $i,X6: $i] :
( ~ ( g @ X5 @ X6 )
| ~ ( g @ X6 @ a ) )
& ! [X7: $i] :
( ( g @ X7 @ ( f @ X7 ) )
| ( g @ X7 @ a ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i] :
( ( ( g @ ( f @ X0 ) @ X0 )
= $true )
| ( ( g @ X0 @ a )
= $true ) )
& ! [X1: $i,X2: $i] :
( ( $true
!= ( g @ X1 @ X2 ) )
| ( ( g @ ( f @ X2 ) @ X2 )
= $true ) )
& ! [X3: $i,X4: $i] :
( ( $true
!= ( g @ X4 @ X3 ) )
| ( $true
= ( g @ X3 @ ( f @ X3 ) ) ) )
& ! [X5: $i,X6: $i] :
( ( $true
!= ( g @ X5 @ X6 ) )
| ( $true
!= ( g @ X6 @ a ) ) )
& ! [X7: $i] :
( ( $true
= ( g @ X7 @ a ) )
| ( $true
= ( g @ X7 @ ( f @ X7 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X4: $i,X3: $i] :
( ( $true
= ( g @ X3 @ ( f @ X3 ) ) )
| ( $true
!= ( g @ X4 @ X3 ) ) )
& ! [X2: $i,X1: $i] :
( ( ( g @ ( f @ X2 ) @ X2 )
= $true )
| ( $true
!= ( g @ X1 @ X2 ) ) )
& ! [X0: $i] :
( ( ( g @ ( f @ X0 ) @ X0 )
= $true )
| ( ( g @ X0 @ a )
= $true ) )
& ! [X6: $i,X5: $i] :
( ( $true
!= ( g @ X5 @ X6 ) )
| ( $true
!= ( g @ X6 @ a ) ) )
& ! [X7: $i] :
( ( $true
= ( g @ X7 @ a ) )
| ( $true
= ( g @ X7 @ ( f @ X7 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( ( ( g @ X1 @ ( f @ X1 ) )
= $true )
| ( ( g @ X0 @ X1 )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( g @ ( f @ X2 ) @ X2 )
= $true )
| ( $true
!= ( g @ X3 @ X2 ) ) )
& ! [X4: $i] :
( ( $true
= ( g @ ( f @ X4 ) @ X4 ) )
| ( $true
= ( g @ X4 @ a ) ) )
& ! [X5: $i,X6: $i] :
( ( $true
!= ( g @ X6 @ X5 ) )
| ( $true
!= ( g @ X5 @ a ) ) )
& ! [X7: $i] :
( ( $true
= ( g @ X7 @ a ) )
| ( $true
= ( g @ X7 @ ( f @ X7 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
! [X7: $i] :
( ( $true
= ( g @ X7 @ ( f @ X7 ) ) )
| ( $true
= ( g @ X7 @ a ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X6: $i,X5: $i] :
( ( $true
!= ( g @ X6 @ X5 ) )
| ( $true
!= ( g @ X5 @ a ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X4: $i] :
( ( $true
= ( g @ ( f @ X4 ) @ X4 ) )
| ( $true
= ( g @ X4 @ a ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( g @ X0 @ a )
= $true )
| ( $true != $true )
| ( $true
!= ( g @ ( f @ X0 ) @ a ) ) ),
inference(superposition,[],[f8,f7]) ).
thf(f14,plain,
! [X0: $i] :
( ( $true
!= ( g @ ( f @ X0 ) @ a ) )
| ( ( g @ X0 @ a )
= $true ) ),
inference(trivial_inequality_removal,[],[f13]) ).
thf(f22,plain,
( ( $true
= ( g @ a @ a ) )
| ( $true != $true )
| ( $true
= ( g @ a @ a ) ) ),
inference(superposition,[],[f14,f9]) ).
thf(f23,plain,
( ( $true != $true )
| ( $true
= ( g @ a @ a ) ) ),
inference(duplicate_literal_removal,[],[f22]) ).
thf(f24,plain,
( $true
= ( g @ a @ a ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f27,plain,
( ( $true != $true )
| ( $true != $true ) ),
inference(superposition,[],[f8,f24]) ).
thf(f28,plain,
$true != $true,
inference(duplicate_literal_removal,[],[f27]) ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO171^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n010.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Tue Sep 29 16:37:03 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.33 Running higher-order theorem proving
% 0.28/0.35 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
% 0.28/0.40 % (3105827)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.40 % (3105836)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1771366748:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.28/0.40 % (3105836) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3105827-3105836"...
% 0.28/0.40 % (3105836)...printing done.
% 0.28/0.40 % (3105836)Refutation found. Thanks to Tanya!
% 0.28/0.40 % SZS status Theorem for theBenchmark
% 0.28/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.40 % (3105836)------------------------------
% 0.28/0.40 % (3105836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.40 % (3105836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.40 % (3105836)CaDiCaL version: 2.1.3
% 0.28/0.40 % (3105836)Termination reason: Refutation
% 0.28/0.40 % (3105836)Time elapsed: 0.003 s
% 0.28/0.40 % (3105836)Peak memory usage: 12 MB
% 0.28/0.40 % (3105836)Instructions burned: 3 (million)
% 0.28/0.40 % (3105827)Success in time 0.035 s
% 0.28/0.40 % Vampire exiting
%------------------------------------------------------------------------------