%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV225^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:38:04 AM UTC 2026
% Result : Theorem 0.24s 0.34s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 25 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 68 ( 14 ~; 0 |; 8 &; 39 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 6 con; 0-4 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 14 ( 4 ^; 9 !; 1 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
r: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c0: r ).
thf(func_def_1,type,
less: r > r > $o ).
thf(func_def_2,type,
cIRREFLEXIVE_LAW: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: r ).
thf(f1,axiom,
! [X0: r] :
( ( ~ ( less @ X0 @ X0 ) )
= cIRREFLEXIVE_LAW ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cIRREFLEXIVE_LAW_def) ).
thf(f2,conjecture,
( cIRREFLEXIVE_LAW
=> ! [X0: r] :
~ ( ( less @ X0 @ c0 )
& ( X0 = c0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPARNAS_FIG3_A) ).
thf(f3,negated_conjecture,
~ ( cIRREFLEXIVE_LAW
=> ! [X0: r] :
~ ( ( less @ X0 @ c0 )
& ( X0 = c0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ( cIRREFLEXIVE_LAW
=> ! [X0: r] :
~ ( ( less @ X0 @ c0 )
& ( X0 = c0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ( ( cIRREFLEXIVE_LAW = $true )
=> ! [X0: r] :
~ ( ( ( less @ X0 @ c0 )
= $true )
& ( c0 = X0 ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
! [X0: r] :
( ( ~ ( less @ X0 @ X0 ) )
= cIRREFLEXIVE_LAW ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( cIRREFLEXIVE_LAW
= ( !! @ r
@ ^ [Y0: r] :
~ ( less @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: r] :
( ( ( less @ X0 @ c0 )
= $true )
& ( c0 = X0 ) )
& ( cIRREFLEXIVE_LAW = $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
( ( $true
= ( less @ sK0 @ c0 ) )
& ( c0 = sK0 )
& ( cIRREFLEXIVE_LAW = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( cIRREFLEXIVE_LAW
= ( !! @ r
@ ^ [Y0: r] :
~ ( less @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
cIRREFLEXIVE_LAW = $true,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
c0 = sK0,
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( $true
= ( less @ sK0 @ c0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( $true
= ( !! @ r
@ ^ [Y0: r] :
~ ( less @ Y0 @ Y0 ) ) ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f17,plain,
( $true
= ( less @ sK0 @ sK0 ) ),
inference(definition_unfolding,[],[f13,f12]) ).
thf(f18,plain,
! [X1: r] :
( $true
= ( ^ [Y0: r] :
~ ( less @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f19,plain,
! [X1: r] :
( $true
= ( ~ ( less @ X1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X1: r] :
( $false
= ( less @ X1 @ X1 ) ),
inference(not_proxy_clausification,[],[f19]) ).
thf(f21,plain,
$false = $true,
inference(constrained_superposition,[],[f20,f17]) ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV225^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n009.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 15:23:00 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 Running higher-order theorem proving
% 0.24/0.30 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
% 0.24/0.34 % (4133510)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.34 % (4133516)lrs+10_16_si=on:nwc=1.5:random_seed=1712029816:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.34 % (4133516) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4133510-4133516"...
% 0.24/0.34 % (4133516)...printing done.
% 0.24/0.34 % (4133516)Refutation found. Thanks to Tanya!
% 0.24/0.34 % SZS status Theorem for theBenchmark
% 0.24/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.34 % (4133516)------------------------------
% 0.24/0.34 % (4133516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.34 % (4133516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.34 % (4133516)CaDiCaL version: 2.1.3
% 0.24/0.34 % (4133516)Termination reason: Refutation
% 0.24/0.34 % (4133516)Time elapsed: 0.002 s
% 0.24/0.34 % (4133516)Peak memory usage: 12 MB
% 0.24/0.34 % (4133516)Instructions burned: 1 (million)
% 0.24/0.34 % (4133510)Success in time 0.026 s
% 0.24/0.34 % Vampire exiting
%------------------------------------------------------------------------------