%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO087^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n017.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 11:07:36 AM UTC 2026
% Result : Theorem 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 72 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 506 ( 86 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 655 ( 393 ~; 216 |; 38 &; 0 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 0 !; 4 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: $o ).
thf(tp_cQ,type,
cQ: $o ).
thf(tp_cR,type,
cR: $o ).
thf(1,conjecture,
? [Xx: $i] :
( ( ~ cP
& ( ( cQ
& ~ cR )
| ( ~ cQ
& cR ) ) )
=> ( ( ( cP
& cQ )
| ( ~ cP
& ~ cQ ) )
=> cR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM50_13) ).
thf(2,negated_conjecture,
( ( ? [Xx: $i] :
( ( ~ cP
& ( ( cQ
& ~ cR )
| ( ~ cQ
& cR ) ) )
=> ( ( ( cP
& cQ )
| ( ~ cP
& ~ cQ ) )
=> cR ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Xx: $i] :
( ( ~ cP
& ( ( cQ
& ~ cR )
| ( ~ cQ
& cR ) ) )
=> ( ( ( cP
& cQ )
| ( ~ cP
& ~ cQ ) )
=> cR ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [Xx: $i] :
( ( ~ cP
& ( ( cQ
& ~ cR )
| ( ~ cQ
& cR ) ) )
=> ( ( ( cP
& cQ )
| ( ~ cP
& ~ cQ ) )
=> cR ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ cP
& ( cQ
| ~ cQ )
& ( cQ
| cR )
& ( ~ cR
| ~ cQ )
& ( ~ cR
| cR )
& ( cP
| ~ cP )
& ( cP
| ~ cQ )
& ( cQ
| ~ cP )
& ( cQ
| ~ cQ )
& ~ cR )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ~ cP
& ( cQ
| ~ cQ )
& ( cQ
| cR )
& ( ~ cR
| ~ cQ )
& ( ~ cR
| cR )
& ( cP
| ~ cP )
& ( cP
| ~ cQ )
& ( cQ
| ~ cP )
& ( cQ
| ~ cQ )
& ~ cR )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ~ ~ ( ~ ~ cP
| ~ ~ ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
| ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
| ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) )
| ~ ~ cR ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ~ ( ~ ~ cP
| ~ ~ ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
| ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
| ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) )
| ~ ~ cR ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ~ ( ~ ~ cP
| ~ ~ ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
| ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
| ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) )
| ~ ~ cR ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ~ cP
| ~ ~ ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
| ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
| ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) )
| ~ ~ cR ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ~ cP
| ~ ~ ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
| ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
| ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) )
| ~ ~ cR )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ cP )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
| ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ~ ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
| ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ~ cR )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(19,plain,
( ( ~ cP ) = $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
| ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
| ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ cR ) = $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
cP = $false,
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
| ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
| ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
cR = $false,
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( cQ
| ~ cQ )
| ~ ( cQ
| cR ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ( ~ cR
| ~ cQ )
| ~ ( ~ cR
| cR ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ ( cP
| ~ cP )
| ~ ( cP
| ~ cQ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ( cQ
| ~ cP )
| ~ ( cQ
| ~ cQ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ( cQ
| ~ cQ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ( cQ
| cR ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ( ~ cR
| ~ cQ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ( ~ cR
| cR ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(43,plain,
( ( ~ ( cP
| ~ cP ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(44,plain,
( ( ~ ( cP
| ~ cQ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(45,plain,
( ( ~ ( cQ
| ~ cP ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(46,plain,
( ( ~ ( cQ
| ~ cQ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(47,plain,
( ( cQ
| ~ cQ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(48,plain,
( ( cQ
| cR )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(49,plain,
( ( ~ cR
| ~ cQ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(50,plain,
( ( ~ cR
| cR )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(51,plain,
( ( cP
| ~ cP )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(52,plain,
( ( cP
| ~ cQ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(53,plain,
( ( cQ
| ~ cP )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(54,plain,
( ( cQ
| ~ cQ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(55,plain,
( ( cQ = $true )
| ( ( ~ cQ ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(56,plain,
( ( cQ = $true )
| ( cR = $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(57,plain,
( ( ( ~ cR ) = $true )
| ( ( ~ cQ ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(58,plain,
( ( ( ~ cR ) = $true )
| ( cR = $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(59,plain,
( ( cP = $true )
| ( ( ~ cP ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(60,plain,
( ( cP = $true )
| ( ( ~ cQ ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(61,plain,
( ( cQ = $true )
| ( ( ~ cP ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(62,plain,
( ( cQ = $true )
| ( ( ~ cQ ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(63,plain,
( ( cQ = $false )
| ( cQ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(64,plain,
( ( cR = $false )
| ( ( ~ cQ ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(65,plain,
( ( cR = $false )
| ( cR = $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(66,plain,
( ( cP = $false )
| ( cP = $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(67,plain,
( ( cQ = $false )
| ( cP = $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(68,plain,
( ( cP = $false )
| ( cQ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(69,plain,
( ( cQ = $false )
| ( cQ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(70,plain,
( ( cQ = $false )
| ( cR = $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(71,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,70,69,68,67,66,65,63,56,26]) ).
thf(72,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO087^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.18 % Computer : n017.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 17:27:46 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22
% 0.10/0.22 No.of.Axioms: 0
% 0.10/0.22
% 0.10/0.22 Length.of.Defs: 0
% 0.10/0.22
% 0.10/0.22 Contains.Choice.Funs: false
% 0.10/0.22 .
% 0.10/0.22
% 0.10/0.22 ********************************
% 0.10/0.22 * All subproblems solved! *
% 0.10/0.22 ********************************
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:71,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.10/0.22
% 0.10/0.22 %**** Beginning of derivation protocol ****
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22
% 0.10/0.22 %**** End of derivation protocol ****
% 0.10/0.22 %**** no. of clauses in derivation: 72 ****
% 0.10/0.22 %**** clause counter: 71 ****
% 0.10/0.22
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:71,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------