TSTP Solution File: GRP402-1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.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 10:17:53 EDT 2022
% Result : Unsatisfiable 1.29s 1.49s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 42 unt; 5 typ; 0 def)
% Number of atoms : 154 ( 102 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 288 ( 22 ~; 18 |; 0 &; 248 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 100 ( 0 ^ 100 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_commutator,type,
commutator: $i > $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiply @ ( commutator @ A @ B ) @ C )
= ( multiply @ C @ ( commutator @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nilpotency) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
( commutator @ ( commutator @ a @ b ) @ c )
!= ( commutator @ a @ ( commutator @ b @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiply @ ( commutator @ A @ B ) @ C )
= ( multiply @ C @ ( commutator @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ( ( commutator @ ( commutator @ a @ b ) @ c )
!= ( commutator @ a @ ( commutator @ b @ c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(18,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(19,plain,
( ( ( ( commutator @ ( commutator @ a @ b ) @ c )
!= ( commutator @ a @ ( commutator @ b @ c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(20,plain,
( ( ( ( commutator @ ( commutator @ a @ b ) @ c )
!= ( commutator @ a @ ( commutator @ b @ c ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiply @ ( commutator @ A @ B ) @ C )
= ( multiply @ C @ ( commutator @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(26,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( ( commutator @ ( commutator @ a @ b ) @ c )
= ( commutator @ a @ ( commutator @ b @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV1: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ( multiply @ ( multiply @ SV1 @ SY14 ) @ SY15 )
= ( multiply @ SV1 @ ( multiply @ SY14 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV2: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( ( multiply @ SV2 @ SY16 )
!= ( multiply @ SY17 @ SY16 ) )
| ( SV2 = SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV3: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( ( multiply @ SV3 @ SY18 )
!= ( multiply @ SV3 @ SY19 ) )
| ( SY18 = SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV4: $i] :
( ( ! [SY20: $i] :
( ( multiply @ SV4 @ SY20 )
= ( multiply @ SY20 @ ( multiply @ SV4 @ ( commutator @ SV4 @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV5: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ( multiply @ ( commutator @ SV5 @ SY21 ) @ SY22 )
= ( multiply @ SY22 @ ( commutator @ SV5 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY23: $i] :
( ( multiply @ ( multiply @ SV1 @ SV6 ) @ SY23 )
= ( multiply @ SV1 @ ( multiply @ SV6 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY24: $i] :
( ( ( multiply @ SV2 @ SV7 )
!= ( multiply @ SY24 @ SV7 ) )
| ( SV2 = SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY25: $i] :
( ( ( multiply @ SV3 @ SV8 )
!= ( multiply @ SV3 @ SY25 ) )
| ( SV8 = SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV9: $i,SV4: $i] :
( ( ( multiply @ SV4 @ SV9 )
= ( multiply @ SV9 @ ( multiply @ SV4 @ ( commutator @ SV4 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY26: $i] :
( ( multiply @ ( commutator @ SV5 @ SV10 ) @ SY26 )
= ( multiply @ SY26 @ ( commutator @ SV5 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( multiply @ ( multiply @ SV1 @ SV6 ) @ SV11 )
= ( multiply @ SV1 @ ( multiply @ SV6 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( ( multiply @ SV2 @ SV7 )
!= ( multiply @ SV12 @ SV7 ) )
| ( SV2 = SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ( multiply @ SV3 @ SV8 )
!= ( multiply @ SV3 @ SV13 ) )
| ( SV8 = SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( multiply @ ( commutator @ SV5 @ SV10 ) @ SV14 )
= ( multiply @ SV14 @ ( commutator @ SV5 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( ( ( multiply @ SV2 @ SV7 )
!= ( multiply @ SV12 @ SV7 ) ) )
= $true )
| ( ( SV2 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ( ( multiply @ SV3 @ SV8 )
!= ( multiply @ SV3 @ SV13 ) ) )
= $true )
| ( ( SV8 = SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( ( multiply @ SV2 @ SV7 )
= ( multiply @ SV12 @ SV7 ) )
= $false )
| ( ( SV2 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ( multiply @ SV3 @ SV8 )
= ( multiply @ SV3 @ SV13 ) )
= $false )
| ( ( SV8 = SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,46,45,42,39,37,33]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n008.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 : Mon Jun 13 12:00:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 6
% 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:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full)..
% 1.29/1.49
% 1.29/1.49 ********************************
% 1.29/1.49 * All subproblems solved! *
% 1.29/1.49 ********************************
% 1.29/1.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.29/1.50
% 1.29/1.50 %**** Beginning of derivation protocol ****
% 1.29/1.50 % SZS output start CNFRefutation
% See solution above
% 1.29/1.50
% 1.29/1.50 %**** End of derivation protocol ****
% 1.29/1.50 %**** no. of clauses in derivation: 48 ****
% 1.29/1.50 %**** clause counter: 47 ****
% 1.29/1.50
% 1.29/1.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------