TSTP Solution File: NUM830^5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM830^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 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 : Mon Jul 18 11:55:49 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 36 ( 26 unt; 9 typ; 4 def)
% Number of atoms : 89 ( 54 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 196 ( 2 ~; 0 |; 9 &; 182 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 0 ^ 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_n,type,
n: $tType ).
thf(tp_c0,type,
c0: n ).
thf(tp_cPA_1,type,
cPA_1: $o ).
thf(tp_cPA_2,type,
cPA_2: $o ).
thf(tp_cPA_3,type,
cPA_3: $o ).
thf(tp_cPA_4,type,
cPA_4: $o ).
thf(tp_cS,type,
cS: n > n ).
thf(tp_c_plus,type,
c_plus: n > n > n ).
thf(tp_c_star,type,
c_star: n > n > n ).
thf(cPA_1,definition,
( cPA_1
= ( ! [Xx: n] :
( ( c_plus @ Xx @ c0 )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_1) ).
thf(cPA_2,definition,
( cPA_2
= ( ! [Xx: n,Xy: n] :
( ( c_plus @ Xx @ ( cS @ Xy ) )
= ( cS @ ( c_plus @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_2) ).
thf(cPA_3,definition,
( cPA_3
= ( ! [Xx: n] :
( ( c_star @ Xx @ c0 )
= c0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_3) ).
thf(cPA_4,definition,
( cPA_4
= ( ! [Xx: n,Xy: n] :
( ( c_star @ Xx @ ( cS @ Xy ) )
= ( c_plus @ ( c_star @ Xx @ Xy ) @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_4) ).
thf(1,conjecture,
( ( cPA_1
& cPA_2
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_THM1) ).
thf(2,negated_conjecture,
( ( ( cPA_1
& cPA_2
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: n] :
( ( c_plus @ Xx @ c0 )
= Xx )
& ! [Xx: n,Xy: n] :
( ( c_plus @ Xx @ ( cS @ Xy ) )
= ( cS @ ( c_plus @ Xx @ Xy ) ) )
& ! [Xx: n] :
( ( c_star @ Xx @ c0 )
= c0 )
& ! [Xx: n,Xy: n] :
( ( c_star @ Xx @ ( cS @ Xy ) )
= ( c_plus @ ( c_star @ Xx @ Xy ) @ Xx ) ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cPA_1,cPA_2,cPA_3,cPA_4]) ).
thf(4,plain,
( ( ! [Xx: n] :
( ( c_plus @ Xx @ c0 )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: n,Xy: n] :
( ( c_plus @ Xx @ ( cS @ Xy ) )
= ( cS @ ( c_plus @ Xx @ Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: n] :
( ( c_star @ Xx @ c0 )
= c0 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: n,Xy: n] :
( ( c_star @ Xx @ ( cS @ Xy ) )
= ( c_plus @ ( c_star @ Xx @ Xy ) @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [Xx: n,Xy: n] :
( ( c_star @ Xx @ ( cS @ Xy ) )
= ( c_plus @ ( c_star @ Xx @ Xy ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [Xx: n] :
( ( c_star @ Xx @ c0 )
= c0 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( ! [Xx: n,Xy: n] :
( ( c_plus @ Xx @ ( cS @ Xy ) )
= ( cS @ ( c_plus @ Xx @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [Xx: n] :
( ( c_plus @ Xx @ c0 )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(14,plain,
( ( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
! [SV1: n] :
( ( ! [SY6: n] :
( ( c_star @ SV1 @ ( cS @ SY6 ) )
= ( c_plus @ ( c_star @ SV1 @ SY6 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(16,plain,
! [SV2: n] :
( ( ( c_star @ SV2 @ c0 )
= c0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(17,plain,
! [SV3: n] :
( ( ! [SY7: n] :
( ( c_plus @ SV3 @ ( cS @ SY7 ) )
= ( cS @ ( c_plus @ SV3 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(18,plain,
! [SV4: n] :
( ( ( c_plus @ SV4 @ c0 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(19,plain,
( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV5: n,SV1: n] :
( ( ( c_star @ SV1 @ ( cS @ SV5 ) )
= ( c_plus @ ( c_star @ SV1 @ SV5 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV6: n,SV3: n] :
( ( ( c_plus @ SV3 @ ( cS @ SV6 ) )
= ( cS @ ( c_plus @ SV3 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,21,20,19,18]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM830^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jul 7 15:33:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 599
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (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).
% 0.21/0.39
% 0.21/0.39 ********************************
% 0.21/0.39 * All subproblems solved! *
% 0.21/0.39 ********************************
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:22,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.39
% 0.21/0.39 %**** Beginning of derivation protocol ****
% 0.21/0.39 % SZS output start CNFRefutation
% See solution above
% 0.21/0.39
% 0.21/0.39 %**** End of derivation protocol ****
% 0.21/0.39 %**** no. of clauses in derivation: 23 ****
% 0.21/0.39 %**** clause counter: 22 ****
% 0.21/0.39
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:22,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------