%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO357^5 : 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 : n011.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 11:08:07 AM UTC 2026
% Result : Theorem 0.11s 0.19s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 42 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 89 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 319 ( 112 ~; 108 |; 10 &; 75 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 ^; 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_atype,type,
atype: $tType ).
thf(tp_a,type,
a: $o ).
thf(tp_b,type,
b: $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: atype > $o ).
thf(tp_u,type,
u: atype ).
thf(tp_v,type,
v: atype ).
thf(1,conjecture,
( ! [P: atype > $o] :
( ( ( a
| ~ a )
& ( P @ u ) )
=> ( ( b
| ~ b )
& ( P @ v ) ) )
=> ! [Xq: atype > $o] :
( ( Xq @ u )
=> ( Xq @ v ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE2LEIBEQ2_pme) ).
thf(2,negated_conjecture,
( ( ! [P: atype > $o] :
( ( ( a
| ~ a )
& ( P @ u ) )
=> ( ( b
| ~ b )
& ( P @ v ) ) )
=> ! [Xq: atype > $o] :
( ( Xq @ u )
=> ( Xq @ v ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [P: atype > $o] :
( ( ( a
| ~ a )
& ( P @ u ) )
=> ( ( b
| ~ b )
& ( P @ v ) ) )
=> ! [Xq: atype > $o] :
( ( Xq @ u )
=> ( Xq @ v ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [P: atype > $o] :
( ( ( a
| ~ a )
& ( P @ u ) )
=> ( ( b
| ~ b )
& ( P @ v ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xq: atype > $o] :
( ( Xq @ u )
=> ( Xq @ v ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xq: atype > $o] :
( ( Xq @ u )
=> ( Xq @ v ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [P: atype > $o] :
( ( ( a
| ~ a )
& ( P @ u ) )
=> ( ( b
| ~ b )
& ( P @ v ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [Xq: atype > $o] :
( ( Xq @ u )
=> ( Xq @ v ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: atype > $o] :
( ~ ( SX0 @ u )
| ( SX0 @ v ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SX0: atype > $o] :
( ~ ~ ( ~ ( a
| ~ a )
| ~ ( SX0 @ u ) )
| ~ ( ~ ( b
| ~ b )
| ~ ( SX0 @ v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: atype > $o] :
( ~ ( SX0 @ u )
| ( SX0 @ v ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: atype > $o] :
( ( ~ ~ ( ~ ( a
| ~ a )
| ~ ( SV1 @ u ) )
| ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( sK1_SX0 @ u )
| ( sK1_SX0 @ v ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: atype > $o] :
( ( ( ~ ~ ( ~ ( a
| ~ a )
| ~ ( SV1 @ u ) ) )
= $true )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( sK1_SX0 @ u ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( sK1_SX0 @ v )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: atype > $o] :
( ( ( ~ ( ~ ( a
| ~ a )
| ~ ( SV1 @ u ) ) )
= $false )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( sK1_SX0 @ u )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: atype > $o] :
( ( ( ~ ( a
| ~ a )
| ~ ( SV1 @ u ) )
= $true )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV1: atype > $o] :
( ( ( ~ ( a
| ~ a ) )
= $true )
| ( ( ~ ( SV1 @ u ) )
= $true )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV1: atype > $o] :
( ( ( a
| ~ a )
= $false )
| ( ( ~ ( SV1 @ u ) )
= $true )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
! [SV1: atype > $o] :
( ( a = $false )
| ( ( ~ ( SV1 @ u ) )
= $true )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(23,plain,
! [SV1: atype > $o] :
( ( ( ~ a ) = $false )
| ( ( ~ ( SV1 @ u ) )
= $true )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: atype > $o] :
( ( ( SV1 @ u )
= $false )
| ( a = $false )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV1: atype > $o] :
( ( a = $true )
| ( ( ~ ( SV1 @ u ) )
= $true )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: atype > $o] :
( ( ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) )
= $false )
| ( a = $false )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: atype > $o] :
( ( ( SV1 @ u )
= $false )
| ( a = $true )
| ( ( ~ ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: atype > $o] :
( ( ( ~ ( b
| ~ b ) )
= $false )
| ( a = $false )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV1: atype > $o] :
( ( ( ~ ( SV1 @ v ) )
= $false )
| ( a = $false )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: atype > $o] :
( ( ( ~ ( b
| ~ b )
| ~ ( SV1 @ v ) )
= $false )
| ( a = $true )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: atype > $o] :
( ( ( b
| ~ b )
= $true )
| ( a = $false )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: atype > $o] :
( ( ( SV1 @ v )
= $true )
| ( a = $false )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: atype > $o] :
( ( ( ~ ( b
| ~ b ) )
= $false )
| ( a = $true )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV1: atype > $o] :
( ( ( ~ ( SV1 @ v ) )
= $false )
| ( a = $true )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: atype > $o] :
( ( b = $true )
| ( ( ~ b ) = $true )
| ( a = $false )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: atype > $o] :
( ( ( b
| ~ b )
= $true )
| ( a = $true )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: atype > $o] :
( ( ( SV1 @ v )
= $true )
| ( a = $true )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: atype > $o] :
( ( b = $false )
| ( b = $true )
| ( a = $false )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: atype > $o] :
( ( b = $true )
| ( ( ~ b ) = $true )
| ( a = $true )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV1: atype > $o] :
( ( b = $false )
| ( b = $true )
| ( a = $true )
| ( ( SV1 @ u )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,40,38,37,32,18]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO357^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n011.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 17:35:51 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.19
% 0.11/0.19 No.of.Axioms: 0
% 0.11/0.19
% 0.11/0.19 Length.of.Defs: 0
% 0.11/0.19
% 0.11/0.19 Contains.Choice.Funs: false
% 0.11/0.19
% 0.11/0.19 ********************************
% 0.11/0.19 * All subproblems solved! *
% 0.11/0.19 ********************************
% 0.11/0.19 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.19
% 0.11/0.19 %**** Beginning of derivation protocol ****
% 0.11/0.19 % SZS output start CNFRefutation
% See solution above
% 0.11/0.19
% 0.11/0.19 %**** End of derivation protocol ****
% 0.11/0.19 %**** no. of clauses in derivation: 42 ****
% 0.11/0.19 %**** clause counter: 41 ****
% 0.11/0.19
% 0.11/0.19 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------