%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO379^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:47:33 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 78 equ; 8 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 113 ( 20 ~; 21 |; 7 &; 59 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 12 usr; 5 con; 0-4 aty)
% ( 0 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 47 ( 15 ^; 26 !; 6 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQDP0: $i > $o ).
thf(func_def_2,type,
cQDP1: ( $i > $o ) > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
sK0: ( $i > $o ) > $i ).
thf(f1,axiom,
( ( ^ [X0: $i] : ( X0 = c ) )
= cQDP0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cQDP0_def) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
& ( X0 = cQDP0 ) ) )
= cQDP1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cQDP1_def) ).
thf(f3,conjecture,
? [X0: $i > $o] : ( cQDP1 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cQDTHM1) ).
thf(f4,negated_conjecture,
~ ? [X0: $i > $o] : ( cQDP1 @ X0 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ? [X0: $i > $o] : ( cQDP1 @ X0 ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ? [X0: $i > $o] :
( ( cQDP1 @ X0 )
= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( cQDP0
= ( ^ [Y0: $i] : ( c = Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
( ( ^ [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
& ( X0 = cQDP0 ) ) )
= cQDP1 ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( cQDP0 = Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ( cQDP1 @ X0 )
!= $true ),
inference(ennf_transformation,[],[f6]) ).
thf(f11,plain,
( cQDP0
= ( ^ [Y0: $i] : ( c = Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ( cQDP1 @ X0 )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( cQDP0 = Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( ( ^ [Y1: $i] : ( c = Y1 ) )
= Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f13,f11]) ).
thf(f17,plain,
! [X0: $i > $o] :
( $true
!= ( ^ [Y0: $i > $o] :
( ( ( ^ [Y1: $i] : ( c = Y1 ) )
= Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
@ X0 ) ),
inference(definition_unfolding,[],[f12,f16]) ).
thf(f18,plain,
! [X0: $i > $o] :
( $true
!= ( ( ( (=) @ c )
= X0 )
& ( ?? @ $i @ X0 ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X0: $i > $o] :
( ( $false
= ( ?? @ $i @ X0 ) )
| ( $false
= ( ( (=) @ c )
= X0 ) ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $false )
| ( $false
= ( ( (=) @ c )
= X0 ) ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X0: $i > $o,X1: $i] :
( ( ( (=) @ c )
!= X0 )
| ( ( X0 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X0: $i > $o,X1: $i] :
( ( ( c
= ( sK0 @ X0 ) )
!= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X1 )
= $false ) ),
inference(negative_extensionality,[],[f21]) ).
thf(f23,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X1 )
= $false )
| ( ( c
= ( sK0 @ X0 ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $false )
| ( $false
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( c
= ( sK0 @ X0 ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f25,plain,
! [X0: $i > $o,X1: $i] :
( ( c
!= ( sK0 @ X0 ) )
| ( $false
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X1 )
= $false )
| ( c
= ( sK0 @ X0 ) ) ),
inference(equality_proxy_clausification,[],[f23]) ).
thf(f27,plain,
! [X0: $i] :
( ( ( sK0 @ ( (=) @ X0 ) )
= X0 )
| ( c
= ( sK0 @ ( (=) @ X0 ) ) ) ),
inference(leibniz_equality_elimination,[],[f26]) ).
thf(f89,plain,
! [X0: $i] :
( ( c != X0 )
| ( c
= ( sK0 @ ( (=) @ X0 ) ) ) ),
inference(equality_factoring,[],[f27]) ).
thf(f101,plain,
( c
= ( sK0 @ ( (=) @ c ) ) ),
inference(equality_resolution,[],[f89]) ).
thf(f103,plain,
! [X0: $i] :
( ( $false
= ( c = X0 ) )
| ( $false
= ( c = c ) )
| ( c != c ) ),
inference(constrained_superposition,[],[f25,f101]) ).
thf(f104,plain,
! [X0: $i] :
( ( $false
= ( c = c ) )
| ( c != c )
| ( c != X0 ) ),
inference(equality_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X0: $i] :
( ( c != c )
| ( c != X0 )
| ( c != c ) ),
inference(equality_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X0: $i] :
( ( c != c )
| ( c != X0 ) ),
inference(duplicate_literal_removal,[],[f105]) ).
thf(f107,plain,
! [X0: $i] : ( c != X0 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f108,plain,
$false,
inference(equality_resolution,[],[f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO379^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n003.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 16:51:44 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.24 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
% 0.21/0.28 % (2746945)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (2746961)lrs+10_16_si=on:nwc=1.5:random_seed=2630923636:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (2746961) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2746945-2746961"...
% 0.21/0.28 % (2746961)...printing done.
% 0.21/0.28 % (2746961)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (2746961)------------------------------
% 0.21/0.28 % (2746961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2746961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2746961)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2746961)Termination reason: Refutation
% 0.21/0.28 % (2746961)Time elapsed: 0.003 s
% 0.21/0.28 % (2746961)Peak memory usage: 12 MB
% 0.21/0.28 % (2746961)Instructions burned: 5 (million)
% 0.21/0.28 % (2746945)Success in time 0.032 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------