TSTP Solution File: BOO013-4 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n024.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 : Thu Jul 14 23:43:34 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 64 ( 57 unt; 7 typ; 0 def)
% Number of atoms : 145 ( 93 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 223 ( 6 ~; 0 |; 0 &; 217 @)
% ( 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 : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 72 ( 0 ^ 72 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_additive_identity,type,
additive_identity: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiplicative_identity,type,
multiplicative_identity: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(2,axiom,
! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
thf(3,axiom,
! [X: $i] :
( ( multiply @ X @ multiplicative_identity )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
thf(4,axiom,
! [X: $i] :
( ( add @ X @ additive_identity )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( multiply @ Y @ Z ) )
= ( multiply @ ( add @ X @ Y ) @ ( add @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( multiply @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(9,axiom,
( ( multiply @ a @ b )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_an_additive_identity) ).
thf(10,axiom,
( ( add @ a @ b )
= multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_a_multiplicative_identity) ).
thf(11,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(12,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,negated_conjecture,
b
!= ( inverse @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_is_b) ).
thf(14,plain,
$false = $false,
inference(unfold_def,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= multiplicative_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [X: $i] :
( ( multiply @ X @ multiplicative_identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( multiply @ Y @ Z ) )
= ( multiply @ ( add @ X @ Y ) @ ( add @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( multiply @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ( multiply @ a @ b )
= additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ( add @ a @ b )
= multiplicative_identity )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ( b
!= ( inverse @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(26,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(27,plain,
( ( ( b
!= ( inverse @ a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(28,plain,
( ( ( b
!= ( inverse @ a ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(29,plain,
( ( ( add @ a @ b )
= multiplicative_identity )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(30,plain,
( ( ( multiply @ a @ b )
= additive_identity )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( multiply @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( multiply @ Y @ Z ) )
= ( multiply @ ( add @ X @ Y ) @ ( add @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(35,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( multiply @ X @ multiplicative_identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= multiplicative_identity ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(39,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( b
= ( inverse @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(41,plain,
! [SV1: $i] :
( ( ! [SY14: $i] :
( ( add @ SV1 @ SY14 )
= ( add @ SY14 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
( ( multiply @ SV2 @ SY15 )
= ( multiply @ SY15 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV3: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( add @ SV3 @ ( multiply @ SY16 @ SY17 ) )
= ( multiply @ ( add @ SV3 @ SY16 ) @ ( add @ SV3 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
! [SV4: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( multiply @ SV4 @ ( add @ SY18 @ SY19 ) )
= ( add @ ( multiply @ SV4 @ SY18 ) @ ( multiply @ SV4 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(45,plain,
! [SV5: $i] :
( ( ( add @ SV5 @ additive_identity )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(46,plain,
! [SV6: $i] :
( ( ( multiply @ SV6 @ multiplicative_identity )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(47,plain,
! [SV7: $i] :
( ( ( add @ SV7 @ ( inverse @ SV7 ) )
= multiplicative_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(48,plain,
! [SV8: $i] :
( ( ( multiply @ SV8 @ ( inverse @ SV8 ) )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(50,plain,
! [SV9: $i,SV1: $i] :
( ( ( add @ SV1 @ SV9 )
= ( add @ SV9 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV10: $i,SV2: $i] :
( ( ( multiply @ SV2 @ SV10 )
= ( multiply @ SV10 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV11: $i,SV3: $i] :
( ( ! [SY20: $i] :
( ( add @ SV3 @ ( multiply @ SV11 @ SY20 ) )
= ( multiply @ ( add @ SV3 @ SV11 ) @ ( add @ SV3 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV12: $i,SV4: $i] :
( ( ! [SY21: $i] :
( ( multiply @ SV4 @ ( add @ SV12 @ SY21 ) )
= ( add @ ( multiply @ SV4 @ SV12 ) @ ( multiply @ SV4 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV13: $i,SV11: $i,SV3: $i] :
( ( ( add @ SV3 @ ( multiply @ SV11 @ SV13 ) )
= ( multiply @ ( add @ SV3 @ SV11 ) @ ( add @ SV3 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV14: $i,SV12: $i,SV4: $i] :
( ( ( multiply @ SV4 @ ( add @ SV12 @ SV14 ) )
= ( add @ ( multiply @ SV4 @ SV12 ) @ ( multiply @ SV4 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(56,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,55,54,51,50,49,48,47,46,45,40,30]) ).
thf(57,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 16:02:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 11
% 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:11,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:13,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.46
% 0.19/0.46 ********************************
% 0.19/0.46 * All subproblems solved! *
% 0.19/0.46 ********************************
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.46
% 0.19/0.46 %**** Beginning of derivation protocol ****
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
% 0.19/0.46
% 0.19/0.46 %**** End of derivation protocol ****
% 0.19/0.46 %**** no. of clauses in derivation: 57 ****
% 0.19/0.46 %**** clause counter: 56 ****
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------