%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO547^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n001.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 11:08:42 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 17 unt; 0 typ; 1 def)
% Number of atoms : 101 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 132 ( 56 ~; 8 |; 0 &; 64 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 15 ^; 13 !; 6 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_eps,type,
eps: ( $i > $o ) > $i ).
thf(tp_epscomp,type,
epscomp: ( $i > $o ) > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(epscomp,definition,
( epscomp
= ( ^ [P: $i > $o] :
( eps
@ ^ [X: $i] :
~ ( P @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epscompd) ).
thf(2,conjecture,
! [P: $i > $o] :
( ? [X: $i] :
~ ( P @ X )
=> ~ ( P @ ( epscomp @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choicecomp) ).
thf(3,negated_conjecture,
( ( ! [P: $i > $o] :
( ? [X: $i] :
~ ( P @ X )
=> ~ ( P @ ( epscomp @ P ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [SY0: $i > $o] :
( ? [X: $i] :
~ ( SY0 @ X )
=> ~ ( SY0
@ ( eps
@ ^ [SY2: $i] :
~ ( SY0 @ SY2 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,epscomp]) ).
thf(6,plain,
( ( ? [SY8: $i] :
~ ( sK1_SY0 @ SY8 )
=> ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( ? [SY8: $i] :
~ ( sK1_SY0 @ SY8 ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ? [SY8: $i] :
~ ( sK1_SY0 @ SY8 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(12,plain,
( ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( sK1_SY0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[11,epscomp]) ).
thf(15,plain,
( ( ! [SX0: $i] :
~ ~ ( sK1_SY0 @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ~ ( sK1_SY0 @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(19,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( sK1_SY0 @ sK2_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( ~ ~ ! [SY11: $i] :
~ ~ ( sK1_SY0 @ SY11 )
| ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $true ),
inference(choice,[status(thm)],[12]) ).
thf(26,plain,
( ( ( ~ ~ ! [SY11: $i] :
~ ~ ( sK1_SY0 @ SY11 ) )
= $true )
| ( ( ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(27,plain,
( ( ( ~ ! [SY11: $i] :
~ ~ ( sK1_SY0 @ SY11 ) )
= $false )
| ( ( ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(28,plain,
( ( ( ! [SY11: $i] :
~ ~ ( sK1_SY0 @ SY11 ) )
= $true )
| ( ( ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(29,plain,
! [SV4: $i] :
( ( ( ~ ~ ( sK1_SY0 @ SV4 ) )
= $true )
| ( ( ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV4: $i] :
( ( ( ~ ( sK1_SY0 @ SV4 ) )
= $false )
| ( ( ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV4: $i] :
( ( ( sK1_SY0 @ SV4 )
= $true )
| ( ( ~ ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(32,plain,
! [SV4: $i] :
( ( ( sK1_SY0
@ ( eps
@ ^ [SY9: $i] :
~ ( sK1_SY0 @ SY9 ) ) )
= $false )
| ( ( sK1_SY0 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,32,21]) ).
thf(34,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO547^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 17:48:09 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 1
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 149
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: true
% 0.09/0.21
% 0.09/0.21 *** Modified list of choice operators: eps ***
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 24 ****
% 0.09/0.21 %**** clause counter: 33 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------