%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO132^5 : 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 : 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 11:07:41 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 62 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 343 ( 102 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 237 ( 54 ~; 50 |; 10 &; 120 @)
% ( 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 : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: ( $i > $o ) > $o ).
thf(tp_cS,type,
cS: $i > $o ).
thf(tp_cT,type,
cT: $i > $o ).
thf(tp_cX,type,
cX: $i ).
thf(1,conjecture,
( ( ( cP @ cS )
& ( cT @ cX )
& ( cS = cT ) )
=> ( ( cP @ cT )
& ( cS @ cX ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM503) ).
thf(2,negated_conjecture,
( ( ( ( cP @ cS )
& ( cT @ cX )
& ( cS = cT ) )
=> ( ( cP @ cT )
& ( cS @ cX ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( cP @ cS )
& ( cT @ cX )
& ( cS = cT ) )
=> ( ( cP @ cT )
& ( cS @ cX ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( cP @ cS )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( cT @ cX )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( cS = cT )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ( cP @ cT )
& ( cS @ cX ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( cP @ cT )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( cS @ cX )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ~ ( cP @ cT ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( cS @ cX ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( cS = cT )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(13,plain,
( ( cT @ cX )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(14,plain,
( ( cP @ cS )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(15,plain,
( ( ~ ( cP @ cT ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [SV1: $i] :
( ( cS @ SV1 )
= ( cT @ SV1 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( cS = cT )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[12]) ).
thf(18,plain,
( ( cP @ cT )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $i] :
( ( ( cS @ SV2 )
= ( cT @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: $i] :
( ( ~ ( ( cS @ SV2 )
| ( cT @ SV2 ) )
| ~ ( ~ ( cS @ SV2 )
| ~ ( cT @ SV2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV2: $i] :
( ( ( cS @ SV2 )
= ( cT @ SV2 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: $i] :
( ( ( ~ ( ( cS @ SV2 )
| ( cT @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ( cS @ SV2 )
| ~ ( cT @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: $i] :
( ( ( ( cS @ SV2 )
| ( cT @ SV2 ) )
= $false )
| ( ( ~ ( ~ ( cS @ SV2 )
| ~ ( cT @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
! [SV2: $i] :
( ( ( cS @ SV2 )
= $false )
| ( ( ~ ( ~ ( cS @ SV2 )
| ~ ( cT @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(25,plain,
! [SV2: $i] :
( ( ( cT @ SV2 )
= $false )
| ( ( ~ ( ~ ( cS @ SV2 )
| ~ ( cT @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: $i] :
( ( ( ~ ( cS @ SV2 )
| ~ ( cT @ SV2 ) )
= $false )
| ( ( cS @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( ~ ( cS @ SV2 )
| ~ ( cT @ SV2 ) )
= $false )
| ( ( cT @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i] :
( ( ( ~ ( cS @ SV2 ) )
= $false )
| ( ( cS @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: $i] :
( ( ( ~ ( cT @ SV2 ) )
= $false )
| ( ( cS @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( ~ ( cS @ SV2 ) )
= $false )
| ( ( cT @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i] :
( ( ( ~ ( cT @ SV2 ) )
= $false )
| ( ( cT @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( cS @ SV2 )
= $true )
| ( ( cS @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( cT @ SV2 )
= $true )
| ( ( cS @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( cS @ SV2 )
= $true )
| ( ( cT @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $i] :
( ( ( cT @ SV2 )
= $true )
| ( ( cT @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,35,34,33,32,21,18,17,14]) ).
thf(37,plain,
( ( cS = cT )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(38,plain,
( ( cT @ cX )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(39,plain,
( ( cP @ cS )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(40,plain,
( ( ~ ( cS @ cX ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(41,plain,
( ( ! [SV3: $i] :
( ( cS @ SV3 )
= ( cT @ SV3 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[37]) ).
thf(42,plain,
( ( cS = cT )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[37]) ).
thf(43,plain,
( ( cS @ cX )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV4: $i] :
( ( ( cS @ SV4 )
= ( cT @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV4: $i] :
( ( ~ ( ( cS @ SV4 )
| ( cT @ SV4 ) )
| ~ ( ~ ( cS @ SV4 )
| ~ ( cT @ SV4 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV4: $i] :
( ( ( cS @ SV4 )
= ( cT @ SV4 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV4: $i] :
( ( ( ~ ( ( cS @ SV4 )
| ( cT @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( cS @ SV4 )
| ~ ( cT @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV4: $i] :
( ( ( ( cS @ SV4 )
| ( cT @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( cS @ SV4 )
| ~ ( cT @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV4: $i] :
( ( ( cS @ SV4 )
= $false )
| ( ( ~ ( ~ ( cS @ SV4 )
| ~ ( cT @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(50,plain,
! [SV4: $i] :
( ( ( cT @ SV4 )
= $false )
| ( ( ~ ( ~ ( cS @ SV4 )
| ~ ( cT @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( ~ ( cS @ SV4 )
| ~ ( cT @ SV4 ) )
= $false )
| ( ( cS @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( ~ ( cS @ SV4 )
| ~ ( cT @ SV4 ) )
= $false )
| ( ( cT @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( ~ ( cS @ SV4 ) )
= $false )
| ( ( cS @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(54,plain,
! [SV4: $i] :
( ( ( ~ ( cT @ SV4 ) )
= $false )
| ( ( cS @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV4: $i] :
( ( ( ~ ( cS @ SV4 ) )
= $false )
| ( ( cT @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(56,plain,
! [SV4: $i] :
( ( ( ~ ( cT @ SV4 ) )
= $false )
| ( ( cT @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( cS @ SV4 )
= $true )
| ( ( cS @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( cT @ SV4 )
= $true )
| ( ( cS @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV4: $i] :
( ( ( cS @ SV4 )
= $true )
| ( ( cT @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV4: $i] :
( ( ( cT @ SV4 )
= $true )
| ( ( cT @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,60,59,58,57,46,43,42,39]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO132^5 : 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
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 17:38:54 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.27
% 0.08/0.27 No.of.Axioms: 0
% 0.08/0.27
% 0.08/0.27 Length.of.Defs: 0
% 0.08/0.27
% 0.08/0.27 Contains.Choice.Funs: false
% 0.08/0.27
% 0.08/0.27 ********************************
% 0.08/0.27 * All subproblems solved! *
% 0.08/0.27 ********************************
% 0.08/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.27
% 0.08/0.27 %**** Beginning of derivation protocol ****
% 0.08/0.27 % SZS output start CNFRefutation
% See solution above
% 0.08/0.27
% 0.08/0.27 %**** End of derivation protocol ****
% 0.08/0.27 %**** no. of clauses in derivation: 62 ****
% 0.08/0.27 %**** clause counter: 61 ****
% 0.08/0.27
% 0.08/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------