TSTP Solution File: BOO017-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% 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 : Thu Jul 14 23:43:36 EDT 2022
% Result : Unsatisfiable 0.17s 0.41s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 90 ( 82 unt; 8 typ; 0 def)
% Number of atoms : 210 ( 138 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 382 ( 6 ~; 0 |; 0 &; 376 @)
% ( 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 : 124 ( 0 ^ 124 !; 0 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_additive_identity,type,
additive_identity: $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(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [X: $i] :
( ( add @ additive_identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id2) ).
thf(2,axiom,
! [X: $i] :
( ( add @ X @ additive_identity )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
thf(3,axiom,
! [X: $i] :
( ( multiply @ multiplicative_identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id2) ).
thf(4,axiom,
! [X: $i] :
( ( multiply @ X @ multiplicative_identity )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
thf(5,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
thf(6,axiom,
! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(7,axiom,
! [X: $i] :
( ( add @ ( inverse @ X ) @ X )
= multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
thf(8,axiom,
! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
thf(9,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',distributivity4) ).
thf(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
thf(11,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',distributivity2) ).
thf(12,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( add @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(13,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( multiply @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
thf(14,axiom,
! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(15,axiom,
( ( add @ x @ y )
= z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_y) ).
thf(16,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(17,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,negated_conjecture,
( multiply @ x @ z )
!= x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sum) ).
thf(19,plain,
$false = $false,
inference(unfold_def,[status(thm)],[17]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( add @ additive_identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( multiply @ multiplicative_identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [X: $i] :
( ( multiply @ X @ multiplicative_identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( add @ ( inverse @ X ) @ X )
= multiplicative_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= multiplicative_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(28,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)],[9]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(30,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)],[11]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( multiply @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(34,plain,
( ( ( add @ x @ y )
= z )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(35,plain,
( ( ( ( multiply @ x @ z )
!= x ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(36,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(37,plain,
( ( ( ( multiply @ x @ z )
!= x ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(38,plain,
( ( ( ( multiply @ x @ z )
!= x ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(39,plain,
( ( ( add @ x @ y )
= z )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( multiply @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( multiply @ Y @ Z ) )
= ( multiply @ ( add @ X @ Y ) @ ( add @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= multiplicative_identity ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( add @ ( inverse @ X ) @ X )
= multiplicative_identity ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(49,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(50,plain,
( ( ! [X: $i] :
( ( multiply @ X @ multiplicative_identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [X: $i] :
( ( multiply @ multiplicative_identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [X: $i] :
( ( add @ additive_identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(54,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(55,plain,
( ( ( multiply @ x @ z )
= x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(56,plain,
! [SV1: $i] :
( ( ! [SY24: $i] :
( ( add @ SV1 @ SY24 )
= ( add @ SY24 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(57,plain,
! [SV2: $i] :
( ( ! [SY25: $i] :
( ( multiply @ SV2 @ SY25 )
= ( multiply @ SY25 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(58,plain,
! [SV3: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ( add @ ( multiply @ SV3 @ SY26 ) @ SY27 )
= ( multiply @ ( add @ SV3 @ SY27 ) @ ( add @ SY26 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(59,plain,
! [SV4: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( add @ SV4 @ ( multiply @ SY28 @ SY29 ) )
= ( multiply @ ( add @ SV4 @ SY28 ) @ ( add @ SV4 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(60,plain,
! [SV5: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ( multiply @ ( add @ SV5 @ SY30 ) @ SY31 )
= ( add @ ( multiply @ SV5 @ SY31 ) @ ( multiply @ SY30 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(61,plain,
! [SV6: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ( multiply @ SV6 @ ( add @ SY32 @ SY33 ) )
= ( add @ ( multiply @ SV6 @ SY32 ) @ ( multiply @ SV6 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(62,plain,
! [SV7: $i] :
( ( ( add @ SV7 @ ( inverse @ SV7 ) )
= multiplicative_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(63,plain,
! [SV8: $i] :
( ( ( add @ ( inverse @ SV8 ) @ SV8 )
= multiplicative_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(64,plain,
! [SV9: $i] :
( ( ( multiply @ SV9 @ ( inverse @ SV9 ) )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(65,plain,
! [SV10: $i] :
( ( ( multiply @ ( inverse @ SV10 ) @ SV10 )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(66,plain,
! [SV11: $i] :
( ( ( multiply @ SV11 @ multiplicative_identity )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(67,plain,
! [SV12: $i] :
( ( ( multiply @ multiplicative_identity @ SV12 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(68,plain,
! [SV13: $i] :
( ( ( add @ SV13 @ additive_identity )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(69,plain,
! [SV14: $i] :
( ( ( add @ additive_identity @ SV14 )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(70,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(71,plain,
! [SV15: $i,SV1: $i] :
( ( ( add @ SV1 @ SV15 )
= ( add @ SV15 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(72,plain,
! [SV16: $i,SV2: $i] :
( ( ( multiply @ SV2 @ SV16 )
= ( multiply @ SV16 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV17: $i,SV3: $i] :
( ( ! [SY34: $i] :
( ( add @ ( multiply @ SV3 @ SV17 ) @ SY34 )
= ( multiply @ ( add @ SV3 @ SY34 ) @ ( add @ SV17 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
! [SV18: $i,SV4: $i] :
( ( ! [SY35: $i] :
( ( add @ SV4 @ ( multiply @ SV18 @ SY35 ) )
= ( multiply @ ( add @ SV4 @ SV18 ) @ ( add @ SV4 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(75,plain,
! [SV19: $i,SV5: $i] :
( ( ! [SY36: $i] :
( ( multiply @ ( add @ SV5 @ SV19 ) @ SY36 )
= ( add @ ( multiply @ SV5 @ SY36 ) @ ( multiply @ SV19 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(76,plain,
! [SV20: $i,SV6: $i] :
( ( ! [SY37: $i] :
( ( multiply @ SV6 @ ( add @ SV20 @ SY37 ) )
= ( add @ ( multiply @ SV6 @ SV20 ) @ ( multiply @ SV6 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(77,plain,
! [SV21: $i,SV17: $i,SV3: $i] :
( ( ( add @ ( multiply @ SV3 @ SV17 ) @ SV21 )
= ( multiply @ ( add @ SV3 @ SV21 ) @ ( add @ SV17 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV22: $i,SV18: $i,SV4: $i] :
( ( ( add @ SV4 @ ( multiply @ SV18 @ SV22 ) )
= ( multiply @ ( add @ SV4 @ SV18 ) @ ( add @ SV4 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV23: $i,SV19: $i,SV5: $i] :
( ( ( multiply @ ( add @ SV5 @ SV19 ) @ SV23 )
= ( add @ ( multiply @ SV5 @ SV23 ) @ ( multiply @ SV19 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV24: $i,SV20: $i,SV6: $i] :
( ( ( multiply @ SV6 @ ( add @ SV20 @ SV24 ) )
= ( add @ ( multiply @ SV6 @ SV20 ) @ ( multiply @ SV6 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(81,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,80,79,78,77,72,71,70,69,68,67,66,65,64,63,62,55]) ).
thf(82,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n025.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 20:35:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 16
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:16,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:18,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.17/0.41
% 0.17/0.41 ********************************
% 0.17/0.41 * All subproblems solved! *
% 0.17/0.41 ********************************
% 0.17/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,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:81,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.17/0.41
% 0.17/0.41 %**** Beginning of derivation protocol ****
% 0.17/0.41 % SZS output start CNFRefutation
% See solution above
% 0.17/0.41
% 0.17/0.41 %**** End of derivation protocol ****
% 0.17/0.41 %**** no. of clauses in derivation: 82 ****
% 0.17/0.41 %**** clause counter: 81 ****
% 0.17/0.41
% 0.17/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,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:81,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------