TSTP Solution File: ALG012-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG012-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.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 14 17:22:39 EDT 2022
% Result : Unsatisfiable 0.96s 1.12s
% Output : CNFRefutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 47 unt; 7 typ; 0 def)
% Number of atoms : 383 ( 109 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 468 ( 82 ~; 99 |; 0 &; 287 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 101 ( 0 ^ 101 !; 0 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a1,type,
a1: $i ).
thf(tp_a2,type,
a2: $i ).
thf(tp_a3,type,
a3: $i ).
thf(tp_c,type,
c: $i > $o ).
thf(tp_d1,type,
d1: $i > $o ).
thf(tp_d2,type,
d2: $i > $o ).
thf(tp_f,type,
f: $i > $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( c @ X )
| ( d1 @ X )
| ( d2 @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_union) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_is_associative) ).
thf(3,axiom,
d2 @ a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d2_not_empty) ).
thf(4,axiom,
d1 @ a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d1_not_empty) ).
thf(5,axiom,
c @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_c_not_empty) ).
thf(6,axiom,
! [X: $i] :
( ~ ( d1 @ X )
| ~ ( d2 @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive_d1_d2) ).
thf(7,axiom,
! [X: $i] :
( ~ ( c @ X )
| ~ ( d2 @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
thf(8,axiom,
! [X: $i] :
( ~ ( c @ X )
| ~ ( d1 @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
! [X: $i,Y: $i] :
( ( c @ ( f @ X @ Y ) )
| ~ ( d2 @ X )
| ~ ( d2 @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_3) ).
thf(12,negated_conjecture,
! [X: $i,Y: $i] :
( ( c @ ( f @ X @ Y ) )
| ~ ( d1 @ X )
| ~ ( d1 @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_2) ).
thf(13,negated_conjecture,
! [X: $i,Y: $i] :
( ( d2 @ ( f @ X @ Y ) )
| ( d1 @ ( f @ X @ Y ) )
| ~ ( c @ X )
| ~ ( c @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
thf(14,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( c @ X )
| ( d1 @ X )
| ( d2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( d2 @ a3 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( d1 @ a2 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( c @ a1 )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [X: $i] :
( ~ ( d1 @ X )
| ~ ( d2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [X: $i] :
( ~ ( c @ X )
| ~ ( d2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [X: $i] :
( ~ ( c @ X )
| ~ ( d1 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( c @ ( f @ X @ Y ) )
| ~ ( d2 @ X )
| ~ ( d2 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ( c @ ( f @ X @ Y ) )
| ~ ( d1 @ X )
| ~ ( d1 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] :
( ( d2 @ ( f @ X @ Y ) )
| ( d1 @ ( f @ X @ Y ) )
| ~ ( c @ X )
| ~ ( c @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(26,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( d2 @ ( f @ X @ Y ) )
| ( d1 @ ( f @ X @ Y ) )
| ~ ( c @ X )
| ~ ( c @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ( c @ ( f @ X @ Y ) )
| ~ ( d1 @ X )
| ~ ( d1 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( c @ ( f @ X @ Y ) )
| ~ ( d2 @ X )
| ~ ( d2 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [X: $i] :
( ~ ( c @ X )
| ~ ( d1 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(31,plain,
( ( ! [X: $i] :
( ~ ( c @ X )
| ~ ( d2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(32,plain,
( ( ! [X: $i] :
( ~ ( d1 @ X )
| ~ ( d2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(33,plain,
( ( c @ a1 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(34,plain,
( ( d1 @ a2 )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(35,plain,
( ( d2 @ a3 )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( c @ X )
| ( d1 @ X )
| ( d2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(38,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(39,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ( d2 @ ( f @ SV1 @ SY13 ) )
| ( d1 @ ( f @ SV1 @ SY13 ) )
| ~ ( c @ SV1 )
| ~ ( c @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(40,plain,
! [SV2: $i] :
( ( ! [SY14: $i] :
( ( c @ ( f @ SV2 @ SY14 ) )
| ~ ( d1 @ SV2 )
| ~ ( d1 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(41,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
( ( c @ ( f @ SV3 @ SY15 ) )
| ~ ( d2 @ SV3 )
| ~ ( d2 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(42,plain,
! [SV4: $i] :
( ( ~ ( c @ SV4 )
| ~ ( d1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(43,plain,
! [SV5: $i] :
( ( ~ ( c @ SV5 )
| ~ ( d2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(44,plain,
! [SV6: $i] :
( ( ~ ( d1 @ SV6 )
| ~ ( d2 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(45,plain,
! [SV7: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( f @ SV7 @ ( f @ SY16 @ SY17 ) )
= ( f @ ( f @ SV7 @ SY16 ) @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(46,plain,
! [SV8: $i] :
( ( ( c @ SV8 )
| ( d1 @ SV8 )
| ( d2 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(47,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(48,plain,
! [SV9: $i,SV1: $i] :
( ( ( d2 @ ( f @ SV1 @ SV9 ) )
| ( d1 @ ( f @ SV1 @ SV9 ) )
| ~ ( c @ SV1 )
| ~ ( c @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(49,plain,
! [SV10: $i,SV2: $i] :
( ( ( c @ ( f @ SV2 @ SV10 ) )
| ~ ( d1 @ SV2 )
| ~ ( d1 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV11: $i,SV3: $i] :
( ( ( c @ ( f @ SV3 @ SV11 ) )
| ~ ( d2 @ SV3 )
| ~ ( d2 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( ~ ( c @ SV4 ) )
= $true )
| ( ( ~ ( d1 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV5: $i] :
( ( ( ~ ( c @ SV5 ) )
= $true )
| ( ( ~ ( d2 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV6: $i] :
( ( ( ~ ( d1 @ SV6 ) )
= $true )
| ( ( ~ ( d2 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV12: $i,SV7: $i] :
( ( ! [SY18: $i] :
( ( f @ SV7 @ ( f @ SV12 @ SY18 ) )
= ( f @ ( f @ SV7 @ SV12 ) @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV8: $i] :
( ( ( c @ SV8 )
= $true )
| ( ( ( d1 @ SV8 )
| ( d2 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV9: $i,SV1: $i] :
( ( ( d2 @ ( f @ SV1 @ SV9 ) )
= $true )
| ( ( ( d1 @ ( f @ SV1 @ SV9 ) )
| ~ ( c @ SV1 )
| ~ ( c @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV10: $i,SV2: $i] :
( ( ( c @ ( f @ SV2 @ SV10 ) )
= $true )
| ( ( ~ ( d1 @ SV2 )
| ~ ( d1 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV11: $i,SV3: $i] :
( ( ( c @ ( f @ SV3 @ SV11 ) )
= $true )
| ( ( ~ ( d2 @ SV3 )
| ~ ( d2 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV4: $i] :
( ( ( c @ SV4 )
= $false )
| ( ( ~ ( d1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV5: $i] :
( ( ( c @ SV5 )
= $false )
| ( ( ~ ( d2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV6: $i] :
( ( ( d1 @ SV6 )
= $false )
| ( ( ~ ( d2 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV13: $i,SV12: $i,SV7: $i] :
( ( ( f @ SV7 @ ( f @ SV12 @ SV13 ) )
= ( f @ ( f @ SV7 @ SV12 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV8: $i] :
( ( ( d1 @ SV8 )
= $true )
| ( ( d2 @ SV8 )
= $true )
| ( ( c @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV9: $i,SV1: $i] :
( ( ( d1 @ ( f @ SV1 @ SV9 ) )
= $true )
| ( ( ~ ( c @ SV1 )
| ~ ( c @ SV9 ) )
= $true )
| ( ( d2 @ ( f @ SV1 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( d1 @ SV2 ) )
= $true )
| ( ( ~ ( d1 @ SV10 ) )
= $true )
| ( ( c @ ( f @ SV2 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( d2 @ SV3 ) )
= $true )
| ( ( ~ ( d2 @ SV11 ) )
= $true )
| ( ( c @ ( f @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(67,plain,
! [SV4: $i] :
( ( ( d1 @ SV4 )
= $false )
| ( ( c @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV5: $i] :
( ( ( d2 @ SV5 )
= $false )
| ( ( c @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV6: $i] :
( ( ( d2 @ SV6 )
= $false )
| ( ( d1 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV9: $i,SV1: $i] :
( ( ( ~ ( c @ SV1 ) )
= $true )
| ( ( ~ ( c @ SV9 ) )
= $true )
| ( ( d1 @ ( f @ SV1 @ SV9 ) )
= $true )
| ( ( d2 @ ( f @ SV1 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV10: $i,SV2: $i] :
( ( ( d1 @ SV2 )
= $false )
| ( ( ~ ( d1 @ SV10 ) )
= $true )
| ( ( c @ ( f @ SV2 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV11: $i,SV3: $i] :
( ( ( d2 @ SV3 )
= $false )
| ( ( ~ ( d2 @ SV11 ) )
= $true )
| ( ( c @ ( f @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV9: $i,SV1: $i] :
( ( ( c @ SV1 )
= $false )
| ( ( ~ ( c @ SV9 ) )
= $true )
| ( ( d1 @ ( f @ SV1 @ SV9 ) )
= $true )
| ( ( d2 @ ( f @ SV1 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV2: $i,SV10: $i] :
( ( ( d1 @ SV10 )
= $false )
| ( ( d1 @ SV2 )
= $false )
| ( ( c @ ( f @ SV2 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV3: $i,SV11: $i] :
( ( ( d2 @ SV11 )
= $false )
| ( ( d2 @ SV3 )
= $false )
| ( ( c @ ( f @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV1: $i,SV9: $i] :
( ( ( c @ SV9 )
= $false )
| ( ( c @ SV1 )
= $false )
| ( ( d1 @ ( f @ SV1 @ SV9 ) )
= $true )
| ( ( d2 @ ( f @ SV1 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,76,75,74,69,68,67,63,62,47,35,34]) ).
thf(78,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG012-1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 22:16:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 11
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:11,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:13,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.96/1.12
% 0.96/1.12 ********************************
% 0.96/1.12 * All subproblems solved! *
% 0.96/1.12 ********************************
% 0.96/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,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:77,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.96/1.12
% 0.96/1.12 %**** Beginning of derivation protocol ****
% 0.96/1.12 % SZS output start CNFRefutation
% See solution above
% 0.96/1.12
% 0.96/1.12 %**** End of derivation protocol ****
% 0.96/1.12 %**** no. of clauses in derivation: 78 ****
% 0.96/1.12 %**** clause counter: 77 ****
% 0.96/1.12
% 0.96/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,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:77,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------