TSTP Solution File: GRP001-4 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n010.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 : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 30 unt; 5 typ; 0 def)
% Number of atoms : 76 ( 45 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 86 ( 6 ~; 0 |; 0 &; 80 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 ^ 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(3,axiom,
( ( multiply @ a @ b )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(4,axiom,
! [X: $i] :
( ( multiply @ X @ X )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',squareness) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
( multiply @ b @ a )
!= c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ( multiply @ a @ b )
= c )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [X: $i] :
( ( multiply @ X @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ( ( multiply @ b @ a )
!= c ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ( ( multiply @ b @ a )
!= c ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(16,plain,
( ( ( ( multiply @ b @ a )
!= c ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X: $i] :
( ( multiply @ X @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ( multiply @ a @ b )
= c )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(21,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
( ( ( multiply @ b @ a )
= c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV1: $i] :
( ( ( multiply @ SV1 @ SV1 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV2: $i] :
( ( ! [SY5: $i,SY6: $i] :
( ( multiply @ ( multiply @ SV2 @ SY5 ) @ SY6 )
= ( multiply @ SV2 @ ( multiply @ SY5 @ SY6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV3: $i] :
( ( ( multiply @ identity @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY7: $i] :
( ( multiply @ ( multiply @ SV2 @ SV4 ) @ SY7 )
= ( multiply @ SV2 @ ( multiply @ SV4 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( multiply @ ( multiply @ SV2 @ SV4 ) @ SV5 )
= ( multiply @ SV2 @ ( multiply @ SV4 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,28,26,25,23,22]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 06:04:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 5
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.12/0.37
% 0.12/0.37 ********************************
% 0.12/0.37 * All subproblems solved! *
% 0.12/0.37 ********************************
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.37
% 0.12/0.37 %**** Beginning of derivation protocol ****
% 0.12/0.37 % SZS output start CNFRefutation
% See solution above
% 0.12/0.37
% 0.12/0.37 %**** End of derivation protocol ****
% 0.12/0.37 %**** no. of clauses in derivation: 30 ****
% 0.12/0.37 %**** clause counter: 29 ****
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------