%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN047+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 : n013.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 11:02:45 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 82 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 619 ( 137 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 484 ( 221 ~; 218 |; 18 &; 0 @)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_p,type,
p: $o ).
thf(tp_q,type,
q: $o ).
thf(tp_r,type,
r: $o ).
thf(tp_s,type,
s: $o ).
thf(1,conjecture,
( ( ( p
& ( q
=> r ) )
=> s )
<=> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel17) ).
thf(2,negated_conjecture,
( ( ( ( p
& ( q
=> r ) )
=> s )
<=> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( p
& ( q
=> r ) )
=> s )
<=> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ( p
& ( q
=> r ) )
=> s )
=> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) )
=> ( ( p
& ( q
=> r ) )
=> s ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ( ( p
& ( q
=> r ) )
=> s )
=> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) )
=> ( ( p
& ( q
=> r ) )
=> s ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ( ( p
& ( q
=> r ) )
=> s )
=> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ~ ( ~ ~ ( ~ p
| ~ ( ~ q
| r ) )
| s )
| ~ ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ( ~ ~ ( ~ p
| ~ ( ~ q
| r ) )
| s )
| ~ ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ p
| ~ ( ~ q
| r ) )
| s ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ~ ( ~ p
| ~ ( ~ q
| r ) )
| s )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ( ~ ~ ( ~ p
| ~ ( ~ q
| r ) ) )
= $true )
| ( s = $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ( ~ ( ~ p
| q
| s ) )
= $true )
| ( ( ~ ( ~ p
| ~ r
| s ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ( ~ ( ~ p
| ~ ( ~ q
| r ) ) )
= $false )
| ( s = $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ( ~ p
| q
| s )
= $false )
| ( ( ~ ( ~ p
| ~ r
| s ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ~ p
| ~ ( ~ q
| r ) )
= $true )
| ( s = $true ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ( ~ p
| q )
= $false )
| ( ( ~ ( ~ p
| ~ r
| s ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( s = $false )
| ( ( ~ ( ~ p
| ~ r
| s ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ( ~ p ) = $true )
| ( ( ~ ( ~ q
| r ) )
= $true )
| ( s = $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ( ~ p ) = $false )
| ( ( ~ ( ~ p
| ~ r
| s ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( q = $false )
| ( ( ~ ( ~ p
| ~ r
| s ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ( ~ p
| ~ r
| s )
= $false )
| ( s = $false ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( p = $false )
| ( ( ~ ( ~ q
| r ) )
= $true )
| ( s = $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( p = $true )
| ( ( ~ ( ~ p
| ~ r
| s ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ( ~ p
| ~ r
| s )
= $false )
| ( q = $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ( ~ p
| ~ r )
= $false )
| ( s = $false ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( s = $false )
| ( s = $false ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ( ~ q
| r )
= $false )
| ( p = $false )
| ( s = $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
( ( ( ~ p
| ~ r
| s )
= $false )
| ( p = $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(33,plain,
( ( ( ~ p
| ~ r )
= $false )
| ( q = $false ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(34,plain,
( ( s = $false )
| ( q = $false ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(35,plain,
( ( ( ~ p ) = $false )
| ( s = $false ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(36,plain,
( ( ( ~ r ) = $false )
| ( s = $false ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(37,plain,
( ( ( ~ q ) = $false )
| ( p = $false )
| ( s = $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(38,plain,
( ( r = $false )
| ( p = $false )
| ( s = $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(39,plain,
( ( ( ~ p
| ~ r )
= $false )
| ( p = $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(40,plain,
( ( s = $false )
| ( p = $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(41,plain,
( ( ( ~ p ) = $false )
| ( q = $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(42,plain,
( ( ( ~ r ) = $false )
| ( q = $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(43,plain,
( ( p = $true )
| ( s = $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(44,plain,
( ( r = $true )
| ( s = $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(45,plain,
( ( q = $true )
| ( p = $false )
| ( s = $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(46,plain,
( ( ( ~ p ) = $false )
| ( p = $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(47,plain,
( ( ( ~ r ) = $false )
| ( p = $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(48,plain,
( ( p = $true )
| ( q = $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(49,plain,
( ( r = $true )
| ( q = $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(50,plain,
( ( p = $true )
| ( p = $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(51,plain,
( ( r = $true )
| ( p = $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(52,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,51,50,49,48,45,44,43,40,38,34]) ).
thf(53,plain,
( ( ~ ( ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) )
=> ( ( p
& ( q
=> r ) )
=> s ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(54,plain,
( ( ~ ( ~ ~ ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) )
| ~ ~ ( ~ p
| ~ ( ~ q
| r ) )
| s ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(55,plain,
( ( ~ ~ ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) )
| ~ ~ ( ~ p
| ~ ( ~ q
| r ) )
| s )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(56,plain,
( ( ~ ~ ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(57,plain,
( ( ~ ~ ( ~ p
| ~ ( ~ q
| r ) )
| s )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(58,plain,
( ( ~ ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(59,plain,
( ( ~ ~ ( ~ p
| ~ ( ~ q
| r ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(60,plain,
s = $false,
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(61,plain,
( ( ~ ( ~ p
| q
| s )
| ~ ( ~ p
| ~ r
| s ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(62,plain,
( ( ~ ( ~ p
| ~ ( ~ q
| r ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(63,plain,
( ( ~ ( ~ p
| q
| s ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(64,plain,
( ( ~ ( ~ p
| ~ r
| s ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(65,plain,
( ( ~ p
| ~ ( ~ q
| r ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
( ( ~ p
| q
| s )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(67,plain,
( ( ~ p
| ~ r
| s )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(68,plain,
( ( ~ p ) = $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(69,plain,
( ( ~ ( ~ q
| r ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(70,plain,
( ( ( ~ p
| q )
= $true )
| ( s = $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(71,plain,
( ( ( ~ p
| ~ r )
= $true )
| ( s = $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(72,plain,
p = $true,
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
( ( ~ q
| r )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
( ( ( ~ p ) = $true )
| ( q = $true )
| ( s = $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(75,plain,
( ( ( ~ p ) = $true )
| ( ( ~ r ) = $true )
| ( s = $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(76,plain,
( ( ( ~ q ) = $true )
| ( r = $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(77,plain,
( ( p = $false )
| ( q = $true )
| ( s = $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(78,plain,
( ( p = $false )
| ( ( ~ r ) = $true )
| ( s = $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
( ( q = $false )
| ( r = $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
( ( r = $false )
| ( p = $false )
| ( s = $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(81,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,80,79,77,72]) ).
thf(82,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[81,52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN047+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
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 17:15:06 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 0
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 0
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:0,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:81,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 82 ****
% 0.07/0.21 %**** clause counter: 81 ****
% 0.07/0.21
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:0,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:81,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------