%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN073+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : 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 Oct 7 11:02:53 AM UTC 2026
% Result : Theorem 0.09s 0.19s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 77 ( 9 ~; 8 |; 0 &; 57 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 39 ( 0 ^; 33 !; 6 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_sK1_SY5,type,
sK1_SY5: $i > $i ).
thf(1,conjecture,
( ! [X: $i] :
( ( big_f @ a @ X )
| ! [Y: $i] : ( big_f @ X @ Y ) )
=> ? [X1: $i] :
! [Y1: $i] : ( big_f @ X1 @ Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel50) ).
thf(2,negated_conjecture,
( ( ! [X: $i] :
( ( big_f @ a @ X )
| ! [Y: $i] : ( big_f @ X @ Y ) )
=> ? [X1: $i] :
! [Y1: $i] : ( big_f @ X1 @ Y1 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: $i] :
( ( big_f @ a @ X )
| ! [Y: $i] : ( big_f @ X @ Y ) )
=> ? [X1: $i] :
! [Y1: $i] : ( big_f @ X1 @ Y1 ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $i] :
( ( big_f @ a @ X )
| ! [Y: $i] : ( big_f @ X @ Y ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [X1: $i] :
! [Y1: $i] : ( big_f @ X1 @ Y1 ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ? [X1: $i] :
! [Y1: $i] : ( big_f @ X1 @ Y1 ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [X: $i] :
( ( big_f @ a @ X )
| ! [Y: $i] : ( big_f @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ? [X1: $i] :
! [Y1: $i] : ( big_f @ X1 @ Y1 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( big_f @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i] :
( ( ( big_f @ a @ SV1 )
| ! [SY4: $i] : ( big_f @ SV1 @ SY4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( big_f @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ( big_f @ a @ SV1 )
= $true )
| ( ( ! [SY4: $i] : ( big_f @ SV1 @ SY4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] : ( big_f @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ( big_f @ SV1 @ SV2 )
= $true )
| ( ( big_f @ a @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV3: $i] :
( ( ~ ! [SY5: $i] : ( big_f @ SV3 @ SY5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV3: $i] :
( ( ! [SY5: $i] : ( big_f @ SV3 @ SY5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV3: $i] :
( ( big_f @ SV3 @ ( sK1_SY5 @ SV3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,17]) ).
thf(19,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN073+1 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.09/0.16 % Computer : n009.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 17:16:17 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19
% 0.09/0.19 No.of.Axioms: 0
% 0.09/0.19
% 0.09/0.19 Length.of.Defs: 0
% 0.09/0.19
% 0.09/0.19 Contains.Choice.Funs: false
% 0.09/0.19
% 0.09/0.19 ********************************
% 0.09/0.19 * All subproblems solved! *
% 0.09/0.19 ********************************
% 0.09/0.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.19
% 0.09/0.19 %**** Beginning of derivation protocol ****
% 0.09/0.19 % SZS output start CNFRefutation
% See solution above
% 0.09/0.19
% 0.09/0.19 %**** End of derivation protocol ****
% 0.09/0.19 %**** no. of clauses in derivation: 19 ****
% 0.09/0.19 %**** clause counter: 18 ****
% 0.09/0.19
% 0.09/0.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------