TSTP Solution File: BOO025-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : BOO025-1 : TPTP v8.1.0. Released v2.2.0.
% 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 23:43:36 EDT 2022
% Result : Unsatisfiable 0.81s 1.01s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 56 ( 49 unt; 7 typ; 0 def)
% Number of atoms : 127 ( 80 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 263 ( 6 ~; 0 |; 0 &; 257 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 80 ( 0 ^ 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_pixley,type,
pixley: $i > $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( pixley @ X @ Y @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley3) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( pixley @ X @ Y @ Y )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley2) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( pixley @ X @ X @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley1) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( pixley @ X @ Y @ Z )
= ( add @ ( multiply @ X @ ( inverse @ Y ) ) @ ( add @ ( multiply @ X @ Z ) @ ( multiply @ ( inverse @ Y ) @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley_defn) ).
thf(5,axiom,
! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( add @ X @ Y ) @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,negated_conjecture,
( multiply @ b @ ( inverse @ b ) )
!= ( multiply @ a @ ( inverse @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_identity) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ( pixley @ X @ Y @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] :
( ( pixley @ X @ Y @ Y )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ( pixley @ X @ X @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( pixley @ X @ Y @ Z )
= ( add @ ( multiply @ X @ ( inverse @ Y ) ) @ ( add @ ( multiply @ X @ Z ) @ ( multiply @ ( inverse @ Y ) @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( add @ X @ Y ) @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ( ( multiply @ b @ ( inverse @ b ) )
!= ( multiply @ a @ ( inverse @ a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ( ( multiply @ b @ ( inverse @ b ) )
!= ( multiply @ a @ ( inverse @ a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(22,plain,
( ( ( ( multiply @ b @ ( inverse @ b ) )
!= ( multiply @ a @ ( inverse @ a ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( add @ X @ Y ) @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( add @ X @ ( inverse @ X ) )
= n1 ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( pixley @ X @ Y @ Z )
= ( add @ ( multiply @ X @ ( inverse @ Y ) ) @ ( add @ ( multiply @ X @ Z ) @ ( multiply @ ( inverse @ Y ) @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( pixley @ X @ X @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ( pixley @ X @ Y @ Y )
= X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( pixley @ X @ Y @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( ( multiply @ b @ ( inverse @ b ) )
= ( multiply @ a @ ( inverse @ a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(32,plain,
! [SV1: $i] :
( ( ! [SY15: $i] :
( ( multiply @ ( add @ SV1 @ SY15 ) @ SY15 )
= SY15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV2: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( multiply @ SV2 @ ( add @ SY16 @ SY17 ) )
= ( add @ ( multiply @ SY16 @ SV2 ) @ ( multiply @ SY17 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV3: $i] :
( ( ( add @ SV3 @ ( inverse @ SV3 ) )
= n1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
! [SV4: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( pixley @ SV4 @ SY18 @ SY19 )
= ( add @ ( multiply @ SV4 @ ( inverse @ SY18 ) ) @ ( add @ ( multiply @ SV4 @ SY19 ) @ ( multiply @ ( inverse @ SY18 ) @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV5: $i] :
( ( ! [SY20: $i] :
( ( pixley @ SV5 @ SV5 @ SY20 )
= SY20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV6: $i] :
( ( ! [SY21: $i] :
( ( pixley @ SV6 @ SY21 @ SY21 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV7: $i] :
( ( ! [SY22: $i] :
( ( pixley @ SV7 @ SY22 @ SV7 )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV8: $i,SV1: $i] :
( ( ( multiply @ ( add @ SV1 @ SV8 ) @ SV8 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV9: $i,SV2: $i] :
( ( ! [SY23: $i] :
( ( multiply @ SV2 @ ( add @ SV9 @ SY23 ) )
= ( add @ ( multiply @ SV9 @ SV2 ) @ ( multiply @ SY23 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY24: $i] :
( ( pixley @ SV4 @ SV10 @ SY24 )
= ( add @ ( multiply @ SV4 @ ( inverse @ SV10 ) ) @ ( add @ ( multiply @ SV4 @ SY24 ) @ ( multiply @ ( inverse @ SV10 ) @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV11: $i,SV5: $i] :
( ( ( pixley @ SV5 @ SV5 @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV12: $i,SV6: $i] :
( ( ( pixley @ SV6 @ SV12 @ SV12 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV13: $i,SV7: $i] :
( ( ( pixley @ SV7 @ SV13 @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV14: $i,SV9: $i,SV2: $i] :
( ( ( multiply @ SV2 @ ( add @ SV9 @ SV14 ) )
= ( add @ ( multiply @ SV9 @ SV2 ) @ ( multiply @ SV14 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( pixley @ SV4 @ SV10 @ SV15 )
= ( add @ ( multiply @ SV4 @ ( inverse @ SV10 ) ) @ ( add @ ( multiply @ SV4 @ SV15 ) @ ( multiply @ ( inverse @ SV10 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,47,46,45,44,43,40,39,34]) ).
thf(49,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO025-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 16:39:36 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 8
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.81/1.01
% 0.81/1.01 ********************************
% 0.81/1.01 * All subproblems solved! *
% 0.81/1.01 ********************************
% 0.81/1.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.81/1.01
% 0.81/1.01 %**** Beginning of derivation protocol ****
% 0.81/1.01 % SZS output start CNFRefutation
% See solution above
% 0.81/1.01
% 0.81/1.01 %**** End of derivation protocol ****
% 0.81/1.01 %**** no. of clauses in derivation: 49 ****
% 0.81/1.01 %**** clause counter: 48 ****
% 0.81/1.01
% 0.81/1.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------