TSTP Solution File: GRP708-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP708-1 : 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 : n032.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 10:19:41 EDT 2022
% Result : Unsatisfiable 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 56 unt; 7 typ; 0 def)
% Number of atoms : 144 ( 92 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 290 ( 6 ~; 0 |; 0 &; 284 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 0 ^ 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_ld,type,
ld: $i > $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_op_c,type,
op_c: $i ).
thf(tp_rd,type,
rd: $i > $i > $i ).
thf(tp_unit,type,
unit: $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( mult @ ( mult @ op_c @ op_c ) @ ( mult @ A @ B ) )
= ( mult @ ( mult @ ( mult @ op_c @ op_c ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
thf(2,axiom,
! [A: $i] :
( ( mult @ op_c @ A )
= ( mult @ A @ op_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
thf(4,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
thf(5,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
thf(10,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(11,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,negated_conjecture,
( mult @ a @ ( mult @ b @ op_c ) )
!= ( mult @ ( mult @ a @ b ) @ op_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( mult @ op_c @ op_c ) @ ( mult @ A @ B ) )
= ( mult @ ( mult @ ( mult @ op_c @ op_c ) @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [A: $i] :
( ( mult @ op_c @ A )
= ( mult @ A @ op_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ( ( mult @ a @ ( mult @ b @ op_c ) )
!= ( mult @ ( mult @ a @ b ) @ op_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( ( ( mult @ a @ ( mult @ b @ op_c ) )
!= ( mult @ ( mult @ a @ b ) @ op_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(26,plain,
( ( ( ( mult @ a @ ( mult @ b @ op_c ) )
!= ( mult @ ( mult @ a @ b ) @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( mult @ op_c @ A )
= ( mult @ A @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( mult @ op_c @ op_c ) @ ( mult @ A @ B ) )
= ( mult @ ( mult @ ( mult @ op_c @ op_c ) @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(36,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( ( mult @ a @ ( mult @ b @ op_c ) )
= ( mult @ ( mult @ a @ b ) @ op_c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(38,plain,
! [SV1: $i] :
( ( ! [SY16: $i] :
( ( mult @ SV1 @ ( ld @ SV1 @ SY16 ) )
= SY16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(39,plain,
! [SV2: $i] :
( ( ! [SY17: $i] :
( ( ld @ SV2 @ ( mult @ SV2 @ SY17 ) )
= SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(40,plain,
! [SV3: $i] :
( ( ! [SY18: $i] :
( ( mult @ ( rd @ SV3 @ SY18 ) @ SY18 )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(41,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
( ( rd @ ( mult @ SV4 @ SY19 ) @ SY19 )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(42,plain,
! [SV5: $i] :
( ( ( mult @ SV5 @ unit )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV6: $i] :
( ( ( mult @ unit @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
! [SV7: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ( mult @ SV7 @ ( mult @ SY20 @ ( mult @ SV7 @ SY21 ) ) )
= ( mult @ ( mult @ SV7 @ ( mult @ SY20 @ SV7 ) ) @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV8: $i] :
( ( ( mult @ op_c @ SV8 )
= ( mult @ SV8 @ op_c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV9: $i] :
( ( ! [SY22: $i] :
( ( mult @ ( mult @ op_c @ op_c ) @ ( mult @ SV9 @ SY22 ) )
= ( mult @ ( mult @ ( mult @ op_c @ op_c ) @ SV9 ) @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(48,plain,
! [SV10: $i,SV1: $i] :
( ( ( mult @ SV1 @ ( ld @ SV1 @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
! [SV11: $i,SV2: $i] :
( ( ( ld @ SV2 @ ( mult @ SV2 @ SV11 ) )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(50,plain,
! [SV12: $i,SV3: $i] :
( ( ( mult @ ( rd @ SV3 @ SV12 ) @ SV12 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(51,plain,
! [SV13: $i,SV4: $i] :
( ( ( rd @ ( mult @ SV4 @ SV13 ) @ SV13 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(52,plain,
! [SV14: $i,SV7: $i] :
( ( ! [SY23: $i] :
( ( mult @ SV7 @ ( mult @ SV14 @ ( mult @ SV7 @ SY23 ) ) )
= ( mult @ ( mult @ SV7 @ ( mult @ SV14 @ SV7 ) ) @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV15: $i,SV9: $i] :
( ( ( mult @ ( mult @ op_c @ op_c ) @ ( mult @ SV9 @ SV15 ) )
= ( mult @ ( mult @ ( mult @ op_c @ op_c ) @ SV9 ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV16: $i,SV14: $i,SV7: $i] :
( ( ( mult @ SV7 @ ( mult @ SV14 @ ( mult @ SV7 @ SV16 ) ) )
= ( mult @ ( mult @ SV7 @ ( mult @ SV14 @ SV7 ) ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(55,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,54,53,51,50,49,48,47,45,43,42]) ).
thf(56,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP708-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Mon Jun 13 12:21:56 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.15/0.31
% 0.15/0.31 No.of.Axioms: 10
% 0.15/0.31
% 0.15/0.31 Length.of.Defs: 0
% 0.15/0.31
% 0.15/0.31 Contains.Choice.Funs: false
% 0.15/0.32 (rf:0,axioms:10,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:12,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.15/0.52
% 0.15/0.52 ********************************
% 0.15/0.52 * All subproblems solved! *
% 0.15/0.52 ********************************
% 0.15/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:55,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.15/0.52
% 0.15/0.52 %**** Beginning of derivation protocol ****
% 0.15/0.52 % SZS output start CNFRefutation
% See solution above
% 0.15/0.53
% 0.15/0.53 %**** End of derivation protocol ****
% 0.15/0.53 %**** no. of clauses in derivation: 56 ****
% 0.15/0.53 %**** clause counter: 55 ****
% 0.15/0.53
% 0.15/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:55,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------