%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM787^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 Oct 7 10:35:14 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 41 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 140 ( 26 ~; 23 |; 0 &; 82 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_rat,type,
rat: $tType ).
thf(tp_is,type,
is: rat > rat > $o ).
thf(tp_less,type,
less: rat > rat > $o ).
thf(tp_more,type,
more: rat > rat > $o ).
thf(tp_x0,type,
x0: rat ).
thf(tp_y0,type,
y0: rat ).
thf(1,axiom,
! [Xx0: rat,Xy0: rat] :
( ~ ( is @ Xx0 @ Xy0 )
=> ( ~ ( more @ Xx0 @ Xy0 )
=> ( less @ Xx0 @ Xy0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81a) ).
thf(2,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',et) ).
thf(3,axiom,
~ ( less @ x0 @ y0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(4,conjecture,
( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81f) ).
thf(5,negated_conjecture,
( ( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx0: rat,Xy0: rat] :
( ~ ( is @ Xx0 @ Xy0 )
=> ( ~ ( more @ Xx0 @ Xy0 )
=> ( less @ Xx0 @ Xy0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ~ ( less @ x0 @ y0 ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ( more @ x0 @ y0 ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(11,plain,
( ( is @ x0 @ y0 )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ ( is @ x0 @ y0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [Xx0: rat,Xy0: rat] :
( ( is @ Xx0 @ Xy0 )
| ( more @ Xx0 @ Xy0 )
| ( less @ Xx0 @ Xy0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(14,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(15,plain,
( ( ~ ( less @ x0 @ y0 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(16,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [Xx0: rat,Xy0: rat] :
( ( is @ Xx0 @ Xy0 )
| ( more @ Xx0 @ Xy0 )
| ( less @ Xx0 @ Xy0 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(18,plain,
( ( ~ ( more @ x0 @ y0 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ~ ( is @ x0 @ y0 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
( ( less @ x0 @ y0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV1: $o] :
( ( ~ SV1
| SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[16]) ).
thf(22,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[16]) ).
thf(23,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[16]) ).
thf(24,plain,
! [SV2: rat] :
( ( ! [SY3: rat] :
( ( is @ SV2 @ SY3 )
| ( more @ SV2 @ SY3 )
| ( less @ SV2 @ SY3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(25,plain,
( ( more @ x0 @ y0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(26,plain,
( ( is @ x0 @ y0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(29,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV3: rat,SV2: rat] :
( ( ( is @ SV2 @ SV3 )
| ( more @ SV2 @ SV3 )
| ( less @ SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV3: rat,SV2: rat] :
( ( ( is @ SV2 @ SV3 )
= $true )
| ( ( ( more @ SV2 @ SV3 )
| ( less @ SV2 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: rat,SV2: rat] :
( ( ( more @ SV2 @ SV3 )
= $true )
| ( ( less @ SV2 @ SV3 )
= $true )
| ( ( is @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(36,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,35,33,32,31,26,25]) ).
thf(37,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM787^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 13:38:46 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 3
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 0
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:36,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 37 ****
% 0.07/0.23 %**** clause counter: 36 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:36,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------