TSTP Solution File: NUM020-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM020-1 : 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 : n012.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 11:46:26 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 81 ( 59 unt; 7 typ; 0 def)
% Number of atoms : 263 ( 73 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 438 ( 44 ~; 43 |; 0 &; 351 @)
% ( 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 : 112 ( 0 ^ 112 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $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_n1,type,
n1: $i ).
thf(tp_successor,type,
successor: $i > $i ).
thf(1,axiom,
equalish @ n1 @ ( successor @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_succeeds_zero) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(4,axiom,
! [X: $i] : ( equalish @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_equality1) ).
thf(7,axiom,
! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(8,axiom,
! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(9,axiom,
! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition) ).
thf(10,axiom,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adding_zero) ).
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,
! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_contradiction) ).
thf(14,negated_conjecture,
~ ( equalish @ ( add @ a @ ( successor @ n0 ) ) @ ( successor @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deny_addition_lemma) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
( ( equalish @ n1 @ ( successor @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(27,plain,
( ( ~ ( equalish @ ( add @ a @ ( successor @ n0 ) ) @ ( successor @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(30,plain,
( ( ~ ( equalish @ ( add @ a @ ( successor @ n0 ) ) @ ( successor @ a ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(32,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(34,plain,
( ( ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(38,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(41,plain,
( ( equalish @ n1 @ ( successor @ n0 ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(42,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( equalish @ ( add @ a @ ( successor @ n0 ) ) @ ( successor @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(44,plain,
! [SV1: $i] :
( ( ~ ( equalish @ ( successor @ SV1 ) @ n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(45,plain,
! [SV2: $i] :
( ( equalish @ ( add @ SV2 @ n0 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(46,plain,
! [SV3: $i] :
( ( ! [SY17: $i] : ( equalish @ ( add @ SV3 @ ( successor @ SY17 ) ) @ ( successor @ ( add @ SV3 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(47,plain,
! [SV4: $i] :
( ( equalish @ ( multiply @ SV4 @ n0 ) @ n0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(48,plain,
! [SV5: $i] :
( ( ! [SY18: $i] : ( equalish @ ( multiply @ SV5 @ ( successor @ SY18 ) ) @ ( add @ ( multiply @ SV5 @ SY18 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(49,plain,
! [SV6: $i] :
( ( ! [SY19: $i] :
( ~ ( equalish @ ( successor @ SV6 ) @ ( successor @ SY19 ) )
| ( equalish @ SV6 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(50,plain,
! [SV7: $i] :
( ( ! [SY20: $i] :
( ~ ( equalish @ SV7 @ SY20 )
| ( equalish @ ( successor @ SV7 ) @ ( successor @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(51,plain,
! [SV8: $i] :
( ( equalish @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(52,plain,
! [SV9: $i] :
( ( ! [SY21: $i] :
( ~ ( equalish @ SV9 @ SY21 )
| ( equalish @ SY21 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(53,plain,
! [SV10: $i] :
( ( ! [SY22: $i] :
( ~ ( equalish @ SV10 @ SY22 )
| ! [SY23: $i] :
( ~ ( equalish @ SY22 @ SY23 )
| ( equalish @ SV10 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(54,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(55,plain,
! [SV1: $i] :
( ( equalish @ ( successor @ SV1 ) @ n0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV11: $i,SV3: $i] :
( ( equalish @ ( add @ SV3 @ ( successor @ SV11 ) ) @ ( successor @ ( add @ SV3 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(57,plain,
! [SV12: $i,SV5: $i] :
( ( equalish @ ( multiply @ SV5 @ ( successor @ SV12 ) ) @ ( add @ ( multiply @ SV5 @ SV12 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV13: $i,SV6: $i] :
( ( ~ ( equalish @ ( successor @ SV6 ) @ ( successor @ SV13 ) )
| ( equalish @ SV6 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV14: $i,SV7: $i] :
( ( ~ ( equalish @ SV7 @ SV14 )
| ( equalish @ ( successor @ SV7 ) @ ( successor @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV15: $i,SV9: $i] :
( ( ~ ( equalish @ SV9 @ SV15 )
| ( equalish @ SV15 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV16: $i,SV10: $i] :
( ( ~ ( equalish @ SV10 @ SV16 )
| ! [SY24: $i] :
( ~ ( equalish @ SV16 @ SY24 )
| ( equalish @ SV10 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV13: $i,SV6: $i] :
( ( ( ~ ( equalish @ ( successor @ SV6 ) @ ( successor @ SV13 ) ) )
= $true )
| ( ( equalish @ SV6 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV14: $i,SV7: $i] :
( ( ( ~ ( equalish @ SV7 @ SV14 ) )
= $true )
| ( ( equalish @ ( successor @ SV7 ) @ ( successor @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV15: $i,SV9: $i] :
( ( ( ~ ( equalish @ SV9 @ SV15 ) )
= $true )
| ( ( equalish @ SV15 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV16: $i,SV10: $i] :
( ( ( ~ ( equalish @ SV10 @ SV16 ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( equalish @ SV16 @ SY24 )
| ( equalish @ SV10 @ SY24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV13: $i,SV6: $i] :
( ( ( equalish @ ( successor @ SV6 ) @ ( successor @ SV13 ) )
= $false )
| ( ( equalish @ SV6 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV14: $i,SV7: $i] :
( ( ( equalish @ SV7 @ SV14 )
= $false )
| ( ( equalish @ ( successor @ SV7 ) @ ( successor @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV15: $i,SV9: $i] :
( ( ( equalish @ SV9 @ SV15 )
= $false )
| ( ( equalish @ SV15 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV16: $i,SV10: $i] :
( ( ( equalish @ SV10 @ SV16 )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( equalish @ SV16 @ SY24 )
| ( equalish @ SV10 @ SY24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV10: $i,SV17: $i,SV16: $i] :
( ( ( ~ ( equalish @ SV16 @ SV17 )
| ( equalish @ SV10 @ SV17 ) )
= $true )
| ( ( equalish @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(71,plain,
! [SV10: $i,SV17: $i,SV16: $i] :
( ( ( ~ ( equalish @ SV16 @ SV17 ) )
= $true )
| ( ( equalish @ SV10 @ SV17 )
= $true )
| ( ( equalish @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(72,plain,
! [SV10: $i,SV17: $i,SV16: $i] :
( ( ( equalish @ SV16 @ SV17 )
= $false )
| ( ( equalish @ SV10 @ SV17 )
= $true )
| ( ( equalish @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(73,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,72,68,67,66,57,56,55,54,51,47,45,43]) ).
thf(74,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jul 7 21:35:14 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34
% 0.11/0.34 No.of.Axioms: 12
% 0.11/0.34
% 0.11/0.34 Length.of.Defs: 0
% 0.11/0.34
% 0.11/0.34 Contains.Choice.Funs: false
% 0.11/0.34 (rf:0,axioms:12,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:14,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.19/0.40
% 0.19/0.40 ********************************
% 0.19/0.40 * All subproblems solved! *
% 0.19/0.40 ********************************
% 0.19/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:73,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40
% 0.19/0.40 %**** Beginning of derivation protocol ****
% 0.19/0.40 % SZS output start CNFRefutation
% See solution above
% 0.19/0.40
% 0.19/0.40 %**** End of derivation protocol ****
% 0.19/0.40 %**** no. of clauses in derivation: 74 ****
% 0.19/0.40 %**** clause counter: 73 ****
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:73,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------