TSTP Solution File: SET607^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET607^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:03:24 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 21 unt; 4 typ; 0 def)
% Number of atoms : 370 ( 101 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 452 ( 116 ~; 131 |; 8 &; 197 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 22 ^ 8 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_X,type,
sK1_X: a > $o ).
thf(tp_sK2_SY4,type,
sK2_SY4: a > $o ).
thf(tp_sK3_SV1,type,
sK3_SV1: a ).
thf(1,conjecture,
! [X: a > $o,Y: a > $o] :
( ( ^ [Xz: a] :
( ( X @ Xz )
| ( ( Y @ Xz )
& ~ ( X @ Xz ) ) ) )
= ( ^ [Xz: a] :
( ( X @ Xz )
| ( Y @ Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_79_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o] :
( ( ^ [Xz: a] :
( ( X @ Xz )
| ( ( Y @ Xz )
& ~ ( X @ Xz ) ) ) )
= ( ^ [Xz: a] :
( ( X @ Xz )
| ( Y @ Xz ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ( ^ [Xz: a] :
( ( X @ Xz )
| ( ( Y @ Xz )
& ~ ( X @ Xz ) ) ) )
= ( ^ [Xz: a] :
( ( X @ Xz )
| ( Y @ Xz ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY4: a > $o] :
( ( ^ [SY5: a] :
( ( sK1_X @ SY5 )
| ( ( SY4 @ SY5 )
& ~ ( sK1_X @ SY5 ) ) ) )
= ( ^ [SY6: a] :
( ( sK1_X @ SY6 )
| ( SY4 @ SY6 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [SY7: a] :
( ( sK1_X @ SY7 )
| ( ( sK2_SY4 @ SY7 )
& ~ ( sK1_X @ SY7 ) ) ) )
= ( ^ [SY8: a] :
( ( sK1_X @ SY8 )
| ( sK2_SY4 @ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ( ^ [SY7: a] :
( ( sK1_X @ SY7 )
| ( ( sK2_SY4 @ SY7 )
& ~ ( sK1_X @ SY7 ) ) ) )
!= ( ^ [SY8: a] :
( ( sK1_X @ SY8 )
| ( sK2_SY4 @ SY8 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( ( ^ [SY7: a] :
( ( ( sK2_SY4 @ SY7 )
& ~ ( sK1_X @ SY7 ) )
| ( sK1_X @ SY7 ) ) )
!= ( ^ [SY8: a] :
( ( sK1_X @ SY8 )
| ( sK2_SY4 @ SY8 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ( ( ^ [SY7: a] :
( ( ( sK2_SY4 @ SY7 )
& ~ ( sK1_X @ SY7 ) )
| ( sK1_X @ SY7 ) ) )
!= ( ^ [SY8: a] :
( ( sK1_X @ SY8 )
| ( sK2_SY4 @ SY8 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(9,plain,
( ( ( ( ^ [SX0: a] :
( ~ ( ~ ( sK2_SY4 @ SX0 )
| ~ ~ ( sK1_X @ SX0 ) )
| ( sK1_X @ SX0 ) ) )
!= ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY4 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ( ^ [SX0: a] :
( ~ ( ~ ( sK2_SY4 @ SX0 )
| ~ ~ ( sK1_X @ SX0 ) )
| ( sK1_X @ SX0 ) ) )
= ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY4 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SV1: a] :
( ( ~ ( ~ ( sK2_SY4 @ SV1 )
| ~ ~ ( sK1_X @ SV1 ) )
| ( sK1_X @ SV1 ) )
= ( ( sK1_X @ SV1 )
| ( sK2_SY4 @ SV1 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(12,plain,
( ( ( ^ [SX0: a] :
( ~ ( ~ ( sK2_SY4 @ SX0 )
| ~ ~ ( sK1_X @ SX0 ) )
| ( sK1_X @ SX0 ) ) )
= ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY4 @ SX0 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 ) )
= ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
( ( ~ ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 )
| ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
| ~ ( ~ ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 ) )
| ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[13]) ).
thf(15,plain,
( ( ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 ) )
= ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 )
| ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ~ ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 ) )
| ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 )
| ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 ) )
| ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 ) )
= $true )
| ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ( ~ ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 ) ) )
= $true )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) ) )
= $true )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
| ( sK1_X @ sK3_SV1 ) )
= $false )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( ( ~ ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) ) )
= $false )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( ( sK1_X @ sK3_SV1 )
= $false )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ( ~ ( sK2_SY4 @ sK3_SV1 ) )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ( ~ ~ ( sK1_X @ sK3_SV1 ) )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ( ~ ( sK2_SY4 @ sK3_SV1 )
| ~ ~ ( sK1_X @ sK3_SV1 ) )
= $true )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ( sK2_SY4 @ sK3_SV1 )
= $true )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ( ~ ( sK1_X @ sK3_SV1 ) )
= $true )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ( ~ ( sK2_SY4 @ sK3_SV1 ) )
= $true )
| ( ( ~ ~ ( sK1_X @ sK3_SV1 ) )
= $true )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
( ( ( sK1_X @ sK3_SV1 )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(36,plain,
( ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( sK2_SY4 @ sK3_SV1 )
= $true )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( sK2_SY4 @ sK3_SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(37,plain,
( ( ( sK1_X @ sK3_SV1 )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( ~ ~ ( sK1_X @ sK3_SV1 ) )
= $true )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( sK2_SY4 @ sK3_SV1 )
= $true )
| ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( sK1_X @ sK3_SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ( ~ ( sK1_X @ sK3_SV1 ) )
= $false )
| ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
( ( ( sK1_X @ sK3_SV1 )
= $true )
| ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( ~ ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(42,plain,
( ( ( ( sK1_X @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $false )
| ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(43,plain,
( ( ( sK1_X @ sK3_SV1 )
= $false )
| ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(44,plain,
( ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(45,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,44,43,39,36,35,34,15]) ).
thf(46,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET607^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 16:38:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)
% 0.12/0.37 ********************************
% 0.12/0.37 * All subproblems solved! *
% 0.12/0.37 ********************************
% 0.12/0.37 % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.37
% 0.12/0.37 %**** Beginning of derivation protocol ****
% 0.12/0.37 % SZS output start CNFRefutation
% See solution above
% 0.12/0.37
% 0.12/0.37 %**** End of derivation protocol ****
% 0.12/0.37 %**** no. of clauses in derivation: 46 ****
% 0.12/0.37 %**** clause counter: 45 ****
% 0.12/0.37
% 0.12/0.37 % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------