TSTP Solution File: GRP001^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP001^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 : Sat Jul 16 10:15:17 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 23 unt; 4 typ; 0 def)
% Number of atoms : 80 ( 56 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 147 ( 3 ~; 0 |; 9 &; 132 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 0 ^ 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: $i > $i > $i ).
thf(tp_e,type,
e: $i ).
thf(tp_sK1_Xa,type,
sK1_Xa: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(1,conjecture,
( ( ! [Xx: $i] :
( ( cP @ e @ Xx )
= Xx )
& ! [Xy: $i] :
( ( cP @ Xy @ e )
= Xy )
& ! [Xz: $i] :
( ( cP @ Xz @ Xz )
= e )
& ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
=> ! [Xa: $i,Xb: $i] :
( ( cP @ Xa @ Xb )
= ( cP @ Xb @ Xa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_COMM2) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: $i] :
( ( cP @ e @ Xx )
= Xx )
& ! [Xy: $i] :
( ( cP @ Xy @ e )
= Xy )
& ! [Xz: $i] :
( ( cP @ Xz @ Xz )
= e )
& ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
=> ! [Xa: $i,Xb: $i] :
( ( cP @ Xa @ Xb )
= ( cP @ Xb @ Xa ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: $i] :
( ( cP @ e @ Xx )
= Xx )
& ! [Xy: $i] :
( ( cP @ Xy @ e )
= Xy )
& ! [Xz: $i] :
( ( cP @ Xz @ Xz )
= e )
& ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
=> ! [Xa: $i,Xb: $i] :
( ( cP @ Xa @ Xb )
= ( cP @ Xb @ Xa ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i] :
( ( cP @ e @ Xx )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xy: $i] :
( ( cP @ Xy @ e )
= Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xz: $i] :
( ( cP @ Xz @ Xz )
= e ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xa: $i,Xb: $i] :
( ( cP @ Xa @ Xb )
= ( cP @ Xb @ Xa ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ! [Xa: $i,Xb: $i] :
( ( cP @ Xa @ Xb )
= ( cP @ Xb @ Xa ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( ( cP @ sK1_Xa @ sK2_SY8 )
!= ( cP @ sK2_SY8 @ sK1_Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(12,plain,
( ( ! [Xz: $i] :
( ( cP @ Xz @ Xz )
= e ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(13,plain,
( ( ! [Xy: $i] :
( ( cP @ Xy @ e )
= Xy ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [Xx: $i] :
( ( cP @ e @ Xx )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(15,plain,
( ( ( ( cP @ sK1_Xa @ sK2_SY8 )
!= ( cP @ sK2_SY8 @ sK1_Xa ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
! [SV1: $i] :
( ( ! [SY9: $i,SY10: $i] :
( ( cP @ ( cP @ SV1 @ SY9 ) @ SY10 )
= ( cP @ SV1 @ ( cP @ SY9 @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(17,plain,
! [SV2: $i] :
( ( ( cP @ SV2 @ SV2 )
= e )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(18,plain,
! [SV3: $i] :
( ( ( cP @ SV3 @ e )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(19,plain,
! [SV4: $i] :
( ( ( cP @ e @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(20,plain,
( ( ( cP @ sK1_Xa @ sK2_SY8 )
= ( cP @ sK2_SY8 @ sK1_Xa ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY11: $i] :
( ( cP @ ( cP @ SV1 @ SV5 ) @ SY11 )
= ( cP @ SV1 @ ( cP @ SV5 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV6: $i,SV5: $i,SV1: $i] :
( ( ( cP @ ( cP @ SV1 @ SV5 ) @ SV6 )
= ( cP @ SV1 @ ( cP @ SV5 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,22,20,19,18]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP001^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n022.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
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 07:03:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 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: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).
% 0.13/0.39
% 0.13/0.39 ********************************
% 0.13/0.39 * All subproblems solved! *
% 0.13/0.39 ********************************
% 0.13/0.39 % 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:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39
% 0.13/0.39 %**** Beginning of derivation protocol ****
% 0.13/0.39 % SZS output start CNFRefutation
% See solution above
% 0.13/0.39
% 0.13/0.39 %**** End of derivation protocol ****
% 0.13/0.39 %**** no. of clauses in derivation: 24 ****
% 0.13/0.39 %**** clause counter: 23 ****
% 0.13/0.39
% 0.13/0.39 % 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:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------