TSTP Solution File: NUM019-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM019-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.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 : Mon Jul 18 11:46:25 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 74 ( 55 unt; 7 typ; 0 def)
% Number of atoms : 233 ( 65 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 378 ( 38 ~; 36 |; 0 &; 304 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 0 ^ 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_aa,type,
aa: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_n0,type,
n0: $i ).
thf(tp_successor,type,
successor: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_equality1) ).
thf(3,axiom,
! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(4,axiom,
! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(5,axiom,
! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition) ).
thf(6,axiom,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adding_zero) ).
thf(7,axiom,
equalish @ a @ aa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_aa) ).
thf(8,axiom,
! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_the_first_number) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ X @ Z )
| ( equalish @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(10,axiom,
! [X: $i] : ( equalish @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(11,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(12,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,negated_conjecture,
~ ( equalish @ aa @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_a) ).
thf(14,plain,
$false = $false,
inference(unfold_def,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( equalish @ a @ aa )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ X @ Z )
| ( equalish @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ~ ( equalish @ aa @ a ) )
= $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] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ X @ Z )
| ( equalish @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(28,plain,
( ( ~ ( equalish @ aa @ a ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ X @ Z )
| ( equalish @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(32,plain,
( ( equalish @ a @ aa )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(33,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(35,plain,
( ( ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(39,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( equalish @ aa @ a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(41,plain,
! [SV1: $i] :
( ( equalish @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
( ~ ( equalish @ SV2 @ SY15 )
| ! [SY16: $i] :
( ~ ( equalish @ SV2 @ SY16 )
| ( equalish @ SY15 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(43,plain,
! [SV3: $i] :
( ( ~ ( equalish @ ( successor @ SV3 ) @ n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(44,plain,
! [SV4: $i] :
( ( equalish @ ( add @ SV4 @ n0 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV5: $i] :
( ( ! [SY17: $i] : ( equalish @ ( add @ SV5 @ ( successor @ SY17 ) ) @ ( successor @ ( add @ SV5 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV6: $i] :
( ( equalish @ ( multiply @ SV6 @ n0 ) @ n0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV7: $i] :
( ( ! [SY18: $i] : ( equalish @ ( multiply @ SV7 @ ( successor @ SY18 ) ) @ ( add @ ( multiply @ SV7 @ SY18 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(48,plain,
! [SV8: $i] :
( ( ! [SY19: $i] :
( ~ ( equalish @ ( successor @ SV8 ) @ ( successor @ SY19 ) )
| ( equalish @ SV8 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(49,plain,
! [SV9: $i] :
( ( ! [SY20: $i] :
( ~ ( equalish @ SV9 @ SY20 )
| ( equalish @ ( successor @ SV9 ) @ ( successor @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(50,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(51,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ( equalish @ SV2 @ SV10 )
| ! [SY21: $i] :
( ~ ( equalish @ SV2 @ SY21 )
| ( equalish @ SV10 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV3: $i] :
( ( equalish @ ( successor @ SV3 ) @ n0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV11: $i,SV5: $i] :
( ( equalish @ ( add @ SV5 @ ( successor @ SV11 ) ) @ ( successor @ ( add @ SV5 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV12: $i,SV7: $i] :
( ( equalish @ ( multiply @ SV7 @ ( successor @ SV12 ) ) @ ( add @ ( multiply @ SV7 @ SV12 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( equalish @ ( successor @ SV8 ) @ ( successor @ SV13 ) )
| ( equalish @ SV8 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( equalish @ SV9 @ SV14 )
| ( equalish @ ( successor @ SV9 ) @ ( successor @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV10 ) )
= $true )
| ( ( ! [SY21: $i] :
( ~ ( equalish @ SV2 @ SY21 )
| ( equalish @ SV10 @ SY21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( equalish @ ( successor @ SV8 ) @ ( successor @ SV13 ) ) )
= $true )
| ( ( equalish @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( equalish @ SV9 @ SV14 ) )
= $true )
| ( ( equalish @ ( successor @ SV9 ) @ ( successor @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV10: $i,SV2: $i] :
( ( ( equalish @ SV2 @ SV10 )
= $false )
| ( ( ! [SY21: $i] :
( ~ ( equalish @ SV2 @ SY21 )
| ( equalish @ SV10 @ SY21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV13: $i,SV8: $i] :
( ( ( equalish @ ( successor @ SV8 ) @ ( successor @ SV13 ) )
= $false )
| ( ( equalish @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV14: $i,SV9: $i] :
( ( ( equalish @ SV9 @ SV14 )
= $false )
| ( ( equalish @ ( successor @ SV9 ) @ ( successor @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV10: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV15 )
| ( equalish @ SV10 @ SV15 ) )
= $true )
| ( ( equalish @ SV2 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV10: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV15 ) )
= $true )
| ( ( equalish @ SV10 @ SV15 )
= $true )
| ( ( equalish @ SV2 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(65,plain,
! [SV10: $i,SV15: $i,SV2: $i] :
( ( ( equalish @ SV2 @ SV15 )
= $false )
| ( ( equalish @ SV10 @ SV15 )
= $true )
| ( ( equalish @ SV2 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,65,62,61,54,53,52,50,46,44,41,40]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM019-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 06:03:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 11
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 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)...
% 0.13/0.38
% 0.13/0.38 ********************************
% 0.13/0.38 * All subproblems solved! *
% 0.13/0.38 ********************************
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/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:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38
% 0.13/0.38 %**** Beginning of derivation protocol ****
% 0.13/0.38 % SZS output start CNFRefutation
% See solution above
% 0.13/0.38
% 0.13/0.38 %**** End of derivation protocol ****
% 0.13/0.38 %**** no. of clauses in derivation: 67 ****
% 0.13/0.38 %**** clause counter: 66 ****
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/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:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------