%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN958+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/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 11:07:14 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 61 ( 10 ~; 6 |; 8 &; 34 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 12 !; 9 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i > $o ).
thf(tp_b,type,
b: $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(1,conjecture,
( ( ? [X: $i] : ( a @ X )
& ! [X: $i] : ( b @ X ) )
=> ? [X: $i] :
( ( a @ X )
& ( b @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
( ( ( ? [X: $i] : ( a @ X )
& ! [X: $i] : ( b @ X ) )
=> ? [X: $i] :
( ( a @ X )
& ( b @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ? [X: $i] : ( a @ X )
& ! [X: $i] : ( b @ X ) )
=> ? [X: $i] :
( ( a @ X )
& ( b @ X ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [X: $i] : ( a @ X ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [X: $i] : ( b @ X ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ? [X: $i] :
( ( a @ X )
& ( b @ X ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ? [X: $i] :
( ( a @ X )
& ( b @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [X: $i] :
( ~ ( a @ X )
| ~ ( b @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( a @ sK1_X )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [X: $i] : ( b @ X ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( a @ sK1_X )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i] :
( ~ ( a @ X )
| ~ ( b @ X ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
! [SV1: $i] :
( ( b @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV2: $i] :
( ( ~ ( a @ SV2 )
| ~ ( b @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: $i] :
( ( ( ~ ( a @ SV2 ) )
= $true )
| ( ( ~ ( b @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV2: $i] :
( ( ( a @ SV2 )
= $false )
| ( ( ~ ( b @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV2: $i] :
( ( ( b @ SV2 )
= $false )
| ( ( a @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(18,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,17,13]) ).
thf(19,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN958+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 17:30:31 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20
% 0.08/0.20 No.of.Axioms: 0
% 0.08/0.20
% 0.08/0.20 Length.of.Defs: 0
% 0.08/0.20
% 0.08/0.20 Contains.Choice.Funs: false
% 0.08/0.20
% 0.08/0.20 ********************************
% 0.08/0.20 * All subproblems solved! *
% 0.08/0.20 ********************************
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.20
% 0.08/0.20 %**** Beginning of derivation protocol ****
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20
% 0.08/0.20 %**** End of derivation protocol ****
% 0.08/0.20 %**** no. of clauses in derivation: 19 ****
% 0.08/0.20 %**** clause counter: 18 ****
% 0.08/0.20
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------