%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM655^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:18:25 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 114 ( 27 ~; 11 |; 1 &; 62 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
less: nat > nat > $o ).
thf(func_def_4,type,
more: nat > nat > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
~ ( less @ x @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a) ).
thf(f4,conjecture,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10f) ).
thf(f5,negated_conjecture,
~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f8,plain,
~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
~ ( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X1 @ X0 )
=> ( less @ X1 @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true
!= ( more @ X1 @ X0 ) )
=> ( ( less @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( less @ x @ y ),
inference(rectify,[],[f1]) ).
thf(f13,plain,
( ( less @ x @ y )
!= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f15,plain,
~ ( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f9]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true
!= ( more @ X1 @ X0 ) )
=> ( ( less @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[],[f11]) ).
thf(f17,plain,
( ( less @ x @ y )
!= $true ),
inference(flattening,[],[f13]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X1 @ X0 )
= $true )
| ( $true
= ( more @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f19,plain,
! [X1: nat,X0: nat] :
( ( $true
= ( more @ X1 @ X0 ) )
| ( X0 = X1 )
| ( ( less @ X1 @ X0 )
= $true ) ),
inference(flattening,[],[f18]) ).
thf(f21,plain,
( ( x != y )
& ( ( more @ x @ y )
!= $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( X0 = X1 )
| ( ( less @ X0 @ X1 )
= $true ) ),
inference(rectify,[],[f19]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( ( less @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f25,plain,
( ( less @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f26,plain,
( ( more @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
x != y,
inference(cnf_transformation,[],[f21]) ).
thf(f31,plain,
( ( ( less @ x @ y )
= $true )
| ( $true != $true )
| ( x = y ) ),
inference(constrained_superposition,[],[f26,f24]) ).
thf(f32,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f33,plain,
( ( less @ x @ y )
= $true ),
inference(forward_subsumption_resolution,[],[f32,f27]) ).
thf(f34,plain,
$false,
inference(forward_subsumption_resolution,[],[f33,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM655^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n008.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 12:33:09 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (3079099)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3079104)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=512198285:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (3079104) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3079099-3079104"...
% 0.20/0.28 % (3079104)...printing done.
% 0.20/0.28 % (3079110)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (3079110)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.28 % (3079104)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3079104)------------------------------
% 0.20/0.28 % (3079104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3079104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3079104)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3079104)Termination reason: Refutation
% 0.20/0.28 % (3079104)Time elapsed: 0.001 s
% 0.20/0.28 % (3079104)Peak memory usage: 12 MB
% 0.20/0.28 % (3079104)Instructions burned: 1 (million)
% 0.20/0.28 % (3079099)Success in time 0.034 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------