TSTP Solution File: GRP406-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP406-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n006.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 10:17:54 EDT 2022
% Result : Unsatisfiable 2.37s 2.56s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 19 unt; 4 typ; 0 def)
% Number of atoms : 49 ( 26 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 138 ( 6 ~; 0 |; 0 &; 132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 ^ 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a1,type,
a1: $i ).
thf(tp_b1,type,
b1: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( multiply @ ( inverse @ B ) @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(2,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(3,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,negated_conjecture,
( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
thf(5,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( multiply @ ( inverse @ B ) @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) )
= C ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( multiply @ ( inverse @ B ) @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) )
= C ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY3: $i,SY4: $i] :
( ( multiply @ SV1 @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ SV1 @ SY3 ) ) @ SY4 ) ) @ ( multiply @ ( inverse @ SY3 ) @ ( multiply @ ( inverse @ SY3 ) @ SY3 ) ) ) ) )
= SY4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY5: $i] :
( ( multiply @ SV1 @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ SV1 @ SV2 ) ) @ SY5 ) ) @ ( multiply @ ( inverse @ SV2 ) @ ( multiply @ ( inverse @ SV2 ) @ SV2 ) ) ) ) )
= SY5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( multiply @ SV1 @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ SV1 @ SV2 ) ) @ SV3 ) ) @ ( multiply @ ( inverse @ SV2 ) @ ( multiply @ ( inverse @ SV2 ) @ SV2 ) ) ) ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(18,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,17,15]) ).
thf(19,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP406-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n006.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 : Tue Jun 14 01:46:26 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 2
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:2,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:4,loop_count:0,foatp_calls:0,translation:fof_full)
% 2.37/2.56 ********************************
% 2.37/2.56 * All subproblems solved! *
% 2.37/2.56 ********************************
% 2.37/2.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:18,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.37/2.56
% 2.37/2.56 %**** Beginning of derivation protocol ****
% 2.37/2.56 % SZS output start CNFRefutation
% See solution above
% 2.37/2.56
% 2.37/2.56 %**** End of derivation protocol ****
% 2.37/2.56 %**** no. of clauses in derivation: 19 ****
% 2.37/2.56 %**** clause counter: 18 ****
% 2.37/2.56
% 2.37/2.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:18,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------