TSTP Solution File: GRP703-10 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP703-10 : 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 : n025.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 10:19:38 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 86 ( 76 unt; 10 typ; 0 def)
% Number of atoms : 196 ( 128 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 430 ( 6 ~; 0 |; 0 &; 424 @)
% ( 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 : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 120 ( 0 ^ 120 !; 0 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
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_op_d,type,
op_d: $i ).
thf(tp_op_e,type,
op_e: $i ).
thf(tp_op_f,type,
op_f: $i ).
thf(tp_rd,type,
rd: $i > $i > $i ).
thf(tp_unit,type,
unit: $i ).
thf(tp_x2,type,
x2: $i ).
thf(tp_x3,type,
x3: $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( op_f
= ( mult @ A @ ( mult @ B @ ( ld @ ( mult @ A @ B ) @ op_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f13) ).
thf(2,axiom,
! [A: $i,B: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ A @ B ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f12) ).
thf(3,axiom,
! [A: $i] :
( op_d
= ( ld @ A @ ( mult @ op_c @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ op_c @ B ) )
= ( mult @ ( mult @ A @ op_c ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ op_c ) )
= ( mult @ ( mult @ A @ B ) @ op_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( mult @ op_c @ ( mult @ A @ B ) )
= ( mult @ ( mult @ op_c @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(8,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(9,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(14,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(15,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,negated_conjecture,
( mult @ op_e @ ( mult @ x2 @ x3 ) )
!= ( mult @ ( mult @ op_e @ x2 ) @ x3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(17,plain,
$false = $false,
inference(unfold_def,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( op_f
= ( mult @ A @ ( mult @ B @ ( ld @ ( mult @ A @ B ) @ op_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ A @ B ) ) @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
( ( ! [A: $i] :
( op_d
= ( ld @ A @ ( mult @ op_c @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ op_c @ B ) )
= ( mult @ ( mult @ A @ op_c ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ op_c ) )
= ( mult @ ( mult @ A @ B ) @ op_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ op_c @ ( mult @ A @ B ) )
= ( mult @ ( mult @ op_c @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ( ( mult @ op_e @ ( mult @ x2 @ x3 ) )
!= ( mult @ ( mult @ op_e @ x2 ) @ x3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(32,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(33,plain,
( ( ( ( mult @ op_e @ ( mult @ x2 @ x3 ) )
!= ( mult @ ( mult @ op_e @ x2 ) @ x3 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(34,plain,
( ( ( ( mult @ op_e @ ( mult @ x2 @ x3 ) )
!= ( mult @ ( mult @ op_e @ x2 ) @ x3 ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ op_c @ ( mult @ A @ B ) )
= ( mult @ ( mult @ op_c @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ op_c ) )
= ( mult @ ( mult @ A @ B ) @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ op_c @ B ) )
= ( mult @ ( mult @ A @ op_c ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(45,plain,
( ( ! [A: $i] :
( op_d
= ( ld @ A @ ( mult @ op_c @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ A @ B ) ) @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( op_f
= ( mult @ A @ ( mult @ B @ ( ld @ ( mult @ A @ B ) @ op_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(48,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(49,plain,
( ( ( mult @ op_e @ ( mult @ x2 @ x3 ) )
= ( mult @ ( mult @ op_e @ x2 ) @ x3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(50,plain,
! [SV1: $i] :
( ( ! [SY24: $i] :
( ( mult @ SV1 @ ( ld @ SV1 @ SY24 ) )
= SY24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(51,plain,
! [SV2: $i] :
( ( ! [SY25: $i] :
( ( ld @ SV2 @ ( mult @ SV2 @ SY25 ) )
= SY25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(52,plain,
! [SV3: $i] :
( ( ! [SY26: $i] :
( ( mult @ ( rd @ SV3 @ SY26 ) @ SY26 )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(53,plain,
! [SV4: $i] :
( ( ! [SY27: $i] :
( ( rd @ ( mult @ SV4 @ SY27 ) @ SY27 )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(54,plain,
! [SV5: $i] :
( ( ( mult @ SV5 @ unit )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV6: $i] :
( ( ( mult @ unit @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV7: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( mult @ SV7 @ ( mult @ SY28 @ ( mult @ SY28 @ SY29 ) ) )
= ( mult @ ( mult @ ( mult @ SV7 @ SY28 ) @ SY28 ) @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(57,plain,
! [SV8: $i] :
( ( ! [SY30: $i] :
( ( mult @ op_c @ ( mult @ SV8 @ SY30 ) )
= ( mult @ ( mult @ op_c @ SV8 ) @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(58,plain,
! [SV9: $i] :
( ( ! [SY31: $i] :
( ( mult @ SV9 @ ( mult @ SY31 @ op_c ) )
= ( mult @ ( mult @ SV9 @ SY31 ) @ op_c ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
! [SV10: $i] :
( ( ! [SY32: $i] :
( ( mult @ SV10 @ ( mult @ op_c @ SY32 ) )
= ( mult @ ( mult @ SV10 @ op_c ) @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(60,plain,
! [SV11: $i] :
( ( op_d
= ( ld @ SV11 @ ( mult @ op_c @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(61,plain,
! [SV12: $i] :
( ( ! [SY33: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ SV12 @ SY33 ) ) @ SY33 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(62,plain,
! [SV13: $i] :
( ( ! [SY34: $i] :
( op_f
= ( mult @ SV13 @ ( mult @ SY34 @ ( ld @ ( mult @ SV13 @ SY34 ) @ op_c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(63,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(64,plain,
! [SV14: $i,SV1: $i] :
( ( ( mult @ SV1 @ ( ld @ SV1 @ SV14 ) )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(65,plain,
! [SV15: $i,SV2: $i] :
( ( ( ld @ SV2 @ ( mult @ SV2 @ SV15 ) )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(66,plain,
! [SV16: $i,SV3: $i] :
( ( ( mult @ ( rd @ SV3 @ SV16 ) @ SV16 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(67,plain,
! [SV17: $i,SV4: $i] :
( ( ( rd @ ( mult @ SV4 @ SV17 ) @ SV17 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(68,plain,
! [SV18: $i,SV7: $i] :
( ( ! [SY35: $i] :
( ( mult @ SV7 @ ( mult @ SV18 @ ( mult @ SV18 @ SY35 ) ) )
= ( mult @ ( mult @ ( mult @ SV7 @ SV18 ) @ SV18 ) @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(69,plain,
! [SV19: $i,SV8: $i] :
( ( ( mult @ op_c @ ( mult @ SV8 @ SV19 ) )
= ( mult @ ( mult @ op_c @ SV8 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(70,plain,
! [SV20: $i,SV9: $i] :
( ( ( mult @ SV9 @ ( mult @ SV20 @ op_c ) )
= ( mult @ ( mult @ SV9 @ SV20 ) @ op_c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(71,plain,
! [SV21: $i,SV10: $i] :
( ( ( mult @ SV10 @ ( mult @ op_c @ SV21 ) )
= ( mult @ ( mult @ SV10 @ op_c ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(72,plain,
! [SV22: $i,SV12: $i] :
( ( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ SV12 @ SV22 ) ) @ SV22 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(73,plain,
! [SV23: $i,SV13: $i] :
( ( op_f
= ( mult @ SV13 @ ( mult @ SV23 @ ( ld @ ( mult @ SV13 @ SV23 ) @ op_c ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(74,plain,
! [SV24: $i,SV18: $i,SV7: $i] :
( ( ( mult @ SV7 @ ( mult @ SV18 @ ( mult @ SV18 @ SV24 ) ) )
= ( mult @ ( mult @ ( mult @ SV7 @ SV18 ) @ SV18 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[49,74,73,72,71,70,69,67,66,65,64,63,60,55,54]) ).
thf(76,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP703-10 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 11:04:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 14
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:14,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:16,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.19/0.41
% 0.19/0.41 ********************************
% 0.19/0.41 * All subproblems solved! *
% 0.19/0.41 ********************************
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,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:75,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.41
% 0.19/0.41 %**** Beginning of derivation protocol ****
% 0.19/0.41 % SZS output start CNFRefutation
% See solution above
% 0.19/0.41
% 0.19/0.41 %**** End of derivation protocol ****
% 0.19/0.41 %**** no. of clauses in derivation: 76 ****
% 0.19/0.41 %**** clause counter: 75 ****
% 0.19/0.41
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,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:75,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------