TSTP Solution File: GRP715-11 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP715-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n011.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 10:19:44 EDT 2022
% Result : Unsatisfiable 19.32s 19.53s
% Output : CNFRefutation 19.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 71 ( 63 unt; 8 typ; 0 def)
% Number of atoms : 161 ( 104 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 314 ( 6 ~; 0 |; 0 &; 308 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 90 ( 0 ^ 90 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_minus,type,
minus: $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_op_0,type,
op_0: $i ).
thf(tp_op_a,type,
op_a: $i ).
thf(tp_op_b,type,
op_b: $i ).
thf(tp_plus,type,
plus: $i > $i > $i ).
thf(tp_unit,type,
unit: $i ).
thf(tp_x0,type,
x0: $i ).
thf(1,axiom,
( ( mult @ op_b @ op_a )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
thf(2,axiom,
( ( mult @ op_a @ op_b )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
thf(3,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
thf(4,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ B ) )
= ( mult @ ( mult @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( plus @ B @ C ) )
= ( plus @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(8,axiom,
! [A: $i] :
( ( plus @ A @ ( minus @ A ) )
= op_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(9,axiom,
! [A: $i] :
( ( plus @ A @ op_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus @ ( plus @ A @ B ) @ C )
= ( plus @ A @ ( plus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(12,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(13,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,negated_conjecture,
( mult @ ( mult @ x0 @ op_b ) @ op_a )
!= x0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[13]) ).
thf(16,plain,
( ( ( mult @ op_b @ op_a )
= unit )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ( mult @ op_a @ op_b )
= unit )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ B ) )
= ( mult @ ( mult @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( plus @ B @ C ) )
= ( plus @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( plus @ A @ ( minus @ A ) )
= op_0 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( plus @ A @ op_0 )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( plus @ ( plus @ A @ B ) @ C )
= ( plus @ A @ ( plus @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ( ( mult @ ( mult @ x0 @ op_b ) @ op_a )
!= x0 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( ( ( mult @ ( mult @ x0 @ op_b ) @ op_a )
!= x0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(30,plain,
( ( ( ( mult @ ( mult @ x0 @ op_b ) @ op_a )
!= x0 ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( plus @ ( plus @ A @ B ) @ C )
= ( plus @ A @ ( plus @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( plus @ A @ op_0 )
= A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( plus @ A @ ( minus @ A ) )
= op_0 ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(35,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( plus @ B @ C ) )
= ( plus @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(36,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ B ) )
= ( mult @ ( mult @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(40,plain,
( ( ( mult @ op_a @ op_b )
= unit )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(41,plain,
( ( ( mult @ op_b @ op_a )
= unit )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(42,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ( mult @ ( mult @ x0 @ op_b ) @ op_a )
= x0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(44,plain,
! [SV1: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ( plus @ ( plus @ SV1 @ SY17 ) @ SY18 )
= ( plus @ SV1 @ ( plus @ SY17 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(45,plain,
! [SV2: $i] :
( ( ! [SY19: $i] :
( ( plus @ SV2 @ SY19 )
= ( plus @ SY19 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(46,plain,
! [SV3: $i] :
( ( ( plus @ SV3 @ op_0 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(47,plain,
! [SV4: $i] :
( ( ( plus @ SV4 @ ( minus @ SV4 ) )
= op_0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(48,plain,
! [SV5: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ( mult @ SV5 @ ( plus @ SY20 @ SY21 ) )
= ( plus @ ( mult @ SV5 @ SY20 ) @ ( mult @ SV5 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(49,plain,
! [SV6: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ( mult @ ( mult @ ( mult @ SV6 @ SY22 ) @ SY23 ) @ SY22 )
= ( mult @ SV6 @ ( mult @ ( mult @ SY22 @ SY23 ) @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(50,plain,
! [SV7: $i] :
( ( ! [SY24: $i] :
( ( mult @ SV7 @ ( mult @ SY24 @ SY24 ) )
= ( mult @ ( mult @ SV7 @ SY24 ) @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(51,plain,
! [SV8: $i] :
( ( ( mult @ SV8 @ unit )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(52,plain,
! [SV9: $i] :
( ( ( mult @ unit @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(53,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(54,plain,
! [SV10: $i,SV1: $i] :
( ( ! [SY25: $i] :
( ( plus @ ( plus @ SV1 @ SV10 ) @ SY25 )
= ( plus @ SV1 @ ( plus @ SV10 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV11: $i,SV2: $i] :
( ( ( plus @ SV2 @ SV11 )
= ( plus @ SV11 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV12: $i,SV5: $i] :
( ( ! [SY26: $i] :
( ( mult @ SV5 @ ( plus @ SV12 @ SY26 ) )
= ( plus @ ( mult @ SV5 @ SV12 ) @ ( mult @ SV5 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV13: $i,SV6: $i] :
( ( ! [SY27: $i] :
( ( mult @ ( mult @ ( mult @ SV6 @ SV13 ) @ SY27 ) @ SV13 )
= ( mult @ SV6 @ ( mult @ ( mult @ SV13 @ SY27 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV14: $i,SV7: $i] :
( ( ( mult @ SV7 @ ( mult @ SV14 @ SV14 ) )
= ( mult @ ( mult @ SV7 @ SV14 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV15: $i,SV10: $i,SV1: $i] :
( ( ( plus @ ( plus @ SV1 @ SV10 ) @ SV15 )
= ( plus @ SV1 @ ( plus @ SV10 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV16: $i,SV12: $i,SV5: $i] :
( ( ( mult @ SV5 @ ( plus @ SV12 @ SV16 ) )
= ( plus @ ( mult @ SV5 @ SV12 ) @ ( mult @ SV5 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV17: $i,SV13: $i,SV6: $i] :
( ( ( mult @ ( mult @ ( mult @ SV6 @ SV13 ) @ SV17 ) @ SV13 )
= ( mult @ SV6 @ ( mult @ ( mult @ SV13 @ SV17 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(62,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,61,60,59,58,55,53,52,51,47,46,43,41]) ).
thf(63,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP715-11 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n011.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 13:42:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 12
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.36 (rf:0,axioms:12,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:14,loop_count:0,foatp_calls:0,translation:fof_full)...
% 19.32/19.53
% 19.32/19.53 ********************************
% 19.32/19.53 * All subproblems solved! *
% 19.32/19.53 ********************************
% 19.32/19.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:12,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:62,loop_count:0,foatp_calls:1,translation:fof_full)
% 19.32/19.53
% 19.32/19.53 %**** Beginning of derivation protocol ****
% 19.32/19.53 % SZS output start CNFRefutation
% See solution above
% 19.32/19.53
% 19.32/19.53 %**** End of derivation protocol ****
% 19.32/19.53 %**** no. of clauses in derivation: 63 ****
% 19.32/19.53 %**** clause counter: 62 ****
% 19.32/19.53
% 19.32/19.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:12,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:62,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------