TSTP Solution File: SYN095-1.002 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN095-1.002 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n019.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 : Thu Jul 21 08:23:34 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 88 ( 49 unt; 7 typ; 0 def)
% Number of atoms : 373 ( 102 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 327 ( 78 ~; 88 |; 0 &; 161 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 ^ 61 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_p_1_1,type,
p_1_1: $i > $o ).
thf(tp_p_1_2,type,
p_1_2: $i > $o ).
thf(tp_p_2_2,type,
p_2_2: $i > $o ).
thf(tp_q_1_1,type,
q_1_1: $i > $o ).
thf(tp_q_1_2,type,
q_1_2: $i > $o ).
thf(tp_q_2_2,type,
q_2_2: $i > $o ).
thf(1,axiom,
q_2_2 @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t2_4) ).
thf(2,axiom,
p_2_2 @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t2_3) ).
thf(3,axiom,
q_1_1 @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t2_2) ).
thf(4,axiom,
p_1_1 @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t2_1) ).
thf(5,axiom,
! [X: $i] :
( ( q_2_2 @ X )
| ~ ( q_1_2 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type22_2) ).
thf(6,axiom,
! [X: $i] :
( ( p_2_2 @ X )
| ~ ( p_1_2 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type22_1) ).
thf(7,axiom,
! [X: $i] :
( ( q_1_1 @ X )
| ~ ( q_1_2 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type21_2) ).
thf(8,axiom,
! [X: $i] :
( ( p_1_1 @ X )
| ~ ( p_1_2 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type21_1) ).
thf(9,axiom,
! [X: $i] :
( ( q_1_2 @ X )
| ~ ( q_2_2 @ X )
| ~ ( p_1_1 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type12_2) ).
thf(10,axiom,
! [X: $i] :
( ( q_1_2 @ X )
| ~ ( p_2_2 @ X )
| ~ ( q_1_1 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type12_1) ).
thf(11,axiom,
! [X: $i] :
( ( p_1_2 @ X )
| ~ ( q_2_2 @ X )
| ~ ( q_1_1 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type11_2) ).
thf(12,axiom,
! [X: $i] :
( ( p_1_2 @ X )
| ~ ( p_2_2 @ X )
| ~ ( p_1_1 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type11_1) ).
thf(13,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(14,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,negated_conjecture,
! [X: $i] :
~ ( p_1_2 @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_goal_1) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( q_2_2 @ a )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( p_2_2 @ a )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( q_1_1 @ a )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( p_1_1 @ a )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( q_2_2 @ X )
| ~ ( q_1_2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( p_2_2 @ X )
| ~ ( p_1_2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [X: $i] :
( ( q_1_1 @ X )
| ~ ( q_1_2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( p_1_1 @ X )
| ~ ( p_1_2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( q_1_2 @ X )
| ~ ( q_2_2 @ X )
| ~ ( p_1_1 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( q_1_2 @ X )
| ~ ( p_2_2 @ X )
| ~ ( q_1_1 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( p_1_2 @ X )
| ~ ( q_2_2 @ X )
| ~ ( q_1_1 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( p_1_2 @ X )
| ~ ( p_2_2 @ X )
| ~ ( p_1_1 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [X: $i] :
~ ( p_1_2 @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i] :
~ ( p_1_2 @ X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( p_1_2 @ X )
| ~ ( p_2_2 @ X )
| ~ ( p_1_1 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(33,plain,
( ( ! [X: $i] :
( ( p_1_2 @ X )
| ~ ( q_2_2 @ X )
| ~ ( q_1_1 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(34,plain,
( ( ! [X: $i] :
( ( q_1_2 @ X )
| ~ ( p_2_2 @ X )
| ~ ( q_1_1 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(35,plain,
( ( ! [X: $i] :
( ( q_1_2 @ X )
| ~ ( q_2_2 @ X )
| ~ ( p_1_1 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( p_1_1 @ X )
| ~ ( p_1_2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( q_1_1 @ X )
| ~ ( q_1_2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( p_2_2 @ X )
| ~ ( p_1_2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(39,plain,
( ( ! [X: $i] :
( ( q_2_2 @ X )
| ~ ( q_1_2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(40,plain,
( ( p_1_1 @ a )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(41,plain,
( ( q_1_1 @ a )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(42,plain,
( ( p_2_2 @ a )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(43,plain,
( ( q_2_2 @ a )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(44,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(45,plain,
! [SV1: $i] :
( ( ~ ( p_1_2 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(46,plain,
! [SV2: $i] :
( ( ( p_1_2 @ SV2 )
| ~ ( p_2_2 @ SV2 )
| ~ ( p_1_1 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(47,plain,
! [SV3: $i] :
( ( ( p_1_2 @ SV3 )
| ~ ( q_2_2 @ SV3 )
| ~ ( q_1_1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(48,plain,
! [SV4: $i] :
( ( ( q_1_2 @ SV4 )
| ~ ( p_2_2 @ SV4 )
| ~ ( q_1_1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(49,plain,
! [SV5: $i] :
( ( ( q_1_2 @ SV5 )
| ~ ( q_2_2 @ SV5 )
| ~ ( p_1_1 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( p_1_1 @ SV6 )
| ~ ( p_1_2 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV7: $i] :
( ( ( q_1_1 @ SV7 )
| ~ ( q_1_2 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV8: $i] :
( ( ( p_2_2 @ SV8 )
| ~ ( p_1_2 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(53,plain,
! [SV9: $i] :
( ( ( q_2_2 @ SV9 )
| ~ ( q_1_2 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV1: $i] :
( ( p_1_2 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( p_1_2 @ SV2 )
= $true )
| ( ( ~ ( p_2_2 @ SV2 )
| ~ ( p_1_1 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(57,plain,
! [SV3: $i] :
( ( ( p_1_2 @ SV3 )
= $true )
| ( ( ~ ( q_2_2 @ SV3 )
| ~ ( q_1_1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( q_1_2 @ SV4 )
= $true )
| ( ( ~ ( p_2_2 @ SV4 )
| ~ ( q_1_1 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV5: $i] :
( ( ( q_1_2 @ SV5 )
= $true )
| ( ( ~ ( q_2_2 @ SV5 )
| ~ ( p_1_1 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( p_1_1 @ SV6 )
= $true )
| ( ( ~ ( p_1_2 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV7: $i] :
( ( ( q_1_1 @ SV7 )
= $true )
| ( ( ~ ( q_1_2 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV8: $i] :
( ( ( p_2_2 @ SV8 )
= $true )
| ( ( ~ ( p_1_2 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV9: $i] :
( ( ( q_2_2 @ SV9 )
= $true )
| ( ( ~ ( q_1_2 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV2: $i] :
( ( ( ~ ( p_2_2 @ SV2 ) )
= $true )
| ( ( ~ ( p_1_1 @ SV2 ) )
= $true )
| ( ( p_1_2 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV3: $i] :
( ( ( ~ ( q_2_2 @ SV3 ) )
= $true )
| ( ( ~ ( q_1_1 @ SV3 ) )
= $true )
| ( ( p_1_2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV4: $i] :
( ( ( ~ ( p_2_2 @ SV4 ) )
= $true )
| ( ( ~ ( q_1_1 @ SV4 ) )
= $true )
| ( ( q_1_2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(67,plain,
! [SV5: $i] :
( ( ( ~ ( q_2_2 @ SV5 ) )
= $true )
| ( ( ~ ( p_1_1 @ SV5 ) )
= $true )
| ( ( q_1_2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV6: $i] :
( ( ( p_1_2 @ SV6 )
= $false )
| ( ( p_1_1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV7: $i] :
( ( ( q_1_2 @ SV7 )
= $false )
| ( ( q_1_1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV8: $i] :
( ( ( p_1_2 @ SV8 )
= $false )
| ( ( p_2_2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV9: $i] :
( ( ( q_1_2 @ SV9 )
= $false )
| ( ( q_2_2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV2: $i] :
( ( ( p_2_2 @ SV2 )
= $false )
| ( ( ~ ( p_1_1 @ SV2 ) )
= $true )
| ( ( p_1_2 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV3: $i] :
( ( ( q_2_2 @ SV3 )
= $false )
| ( ( ~ ( q_1_1 @ SV3 ) )
= $true )
| ( ( p_1_2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV4: $i] :
( ( ( p_2_2 @ SV4 )
= $false )
| ( ( ~ ( q_1_1 @ SV4 ) )
= $true )
| ( ( q_1_2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV5: $i] :
( ( ( q_2_2 @ SV5 )
= $false )
| ( ( ~ ( p_1_1 @ SV5 ) )
= $true )
| ( ( q_1_2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV2: $i] :
( ( ( p_1_1 @ SV2 )
= $false )
| ( ( p_2_2 @ SV2 )
= $false )
| ( ( p_1_2 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV3: $i] :
( ( ( q_1_1 @ SV3 )
= $false )
| ( ( q_2_2 @ SV3 )
= $false )
| ( ( p_1_2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV4: $i] :
( ( ( q_1_1 @ SV4 )
= $false )
| ( ( p_2_2 @ SV4 )
= $false )
| ( ( q_1_2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV5: $i] :
( ( ( p_1_1 @ SV5 )
= $false )
| ( ( q_2_2 @ SV5 )
= $false )
| ( ( q_1_2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,79,78,77,76,71,70,69,68,55,54,43,42,41]) ).
thf(81,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN095-1.002 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 12 05:43:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 13
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:13,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:15,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.12/0.38
% 0.12/0.38 ********************************
% 0.12/0.38 * All subproblems solved! *
% 0.12/0.38 ********************************
% 0.12/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:80,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.38
% 0.12/0.38 %**** Beginning of derivation protocol ****
% 0.12/0.38 % SZS output start CNFRefutation
% See solution above
% 0.12/0.38
% 0.12/0.38 %**** End of derivation protocol ****
% 0.12/0.38 %**** no. of clauses in derivation: 81 ****
% 0.12/0.38 %**** clause counter: 80 ****
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:80,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------