TSTP Solution File: LCL096-10 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n019.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 : Sun Jul 17 12:20:35 EDT 2022
% Result : Unsatisfiable 35.09s 35.32s
% Output : CNFRefutation 35.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 47 unt; 7 typ; 0 def)
% Number of atoms : 125 ( 78 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 559 ( 6 ~; 0 |; 0 &; 553 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 136 ( 0 ^ 136 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_equivalent,type,
equivalent: $i > $i > $i ).
thf(tp_ifeq,type,
ifeq: $i > $i > $i > $i > $i ).
thf(tp_is_a_theorem,type,
is_a_theorem: $i > $i ).
thf(tp_true,type,
true: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ Z ) @ U ) @ ( equivalent @ ( equivalent @ ( equivalent @ X @ V ) @ Z ) @ ( equivalent @ ( equivalent @ Y @ V ) @ U ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_4) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ U ) @ ( equivalent @ ( equivalent @ Y @ Z ) @ U ) ) @ V ) @ V ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_3) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i,U: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ ( equivalent @ Y @ Z ) ) @ U ) @ U ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( ifeq @ ( is_a_theorem @ ( equivalent @ X @ Y ) ) @ true @ ( ifeq @ ( is_a_theorem @ X ) @ true @ ( is_a_theorem @ Y ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
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,
( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) )
!= true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ Z ) @ U ) @ ( equivalent @ ( equivalent @ ( equivalent @ X @ V ) @ Z ) @ ( equivalent @ ( equivalent @ Y @ V ) @ U ) ) ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ U ) @ ( equivalent @ ( equivalent @ Y @ Z ) @ U ) ) @ V ) @ V ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ ( equivalent @ Y @ Z ) ) @ U ) @ U ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] :
( ( ifeq @ ( is_a_theorem @ ( equivalent @ X @ Y ) ) @ true @ ( ifeq @ ( is_a_theorem @ X ) @ true @ ( is_a_theorem @ Y ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) )
!= true ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) )
!= true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(18,plain,
( ( ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) )
!= true ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ( ifeq @ ( is_a_theorem @ ( equivalent @ X @ Y ) ) @ true @ ( ifeq @ ( is_a_theorem @ X ) @ true @ ( is_a_theorem @ Y ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ ( equivalent @ Y @ Z ) ) @ U ) @ U ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ U ) @ ( equivalent @ ( equivalent @ Y @ Z ) @ U ) ) @ V ) @ V ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ Z ) @ U ) @ ( equivalent @ ( equivalent @ ( equivalent @ X @ V ) @ Z ) @ ( equivalent @ ( equivalent @ Y @ V ) @ U ) ) ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) )
= true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV1: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( ifeq @ SV1 @ SV1 @ SY19 @ SY20 )
= SY19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV2: $i] :
( ( ! [SY21: $i] :
( ( ifeq @ ( is_a_theorem @ ( equivalent @ SV2 @ SY21 ) ) @ true @ ( ifeq @ ( is_a_theorem @ SV2 ) @ true @ ( is_a_theorem @ SY21 ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV3: $i] :
( ( ! [SY22: $i,SY23: $i,SY24: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SY22 ) @ ( equivalent @ SV3 @ SY23 ) ) @ ( equivalent @ SY22 @ SY23 ) ) @ SY24 ) @ SY24 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV4: $i] :
( ( ! [SY25: $i,SY26: $i,SY27: $i,SY28: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SY25 ) @ ( equivalent @ SV4 @ SY26 ) ) @ SY27 ) @ ( equivalent @ ( equivalent @ SY25 @ SY26 ) @ SY27 ) ) @ SY28 ) @ SY28 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV5: $i] :
( ( ! [SY29: $i,SY30: $i,SY31: $i,SY32: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SY29 ) @ SY30 ) @ SY31 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SY32 ) @ SY30 ) @ ( equivalent @ ( equivalent @ SY29 @ SY32 ) @ SY31 ) ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY33: $i] :
( ( ifeq @ SV1 @ SV1 @ SV6 @ SY33 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV7: $i,SV2: $i] :
( ( ( ifeq @ ( is_a_theorem @ ( equivalent @ SV2 @ SV7 ) ) @ true @ ( ifeq @ ( is_a_theorem @ SV2 ) @ true @ ( is_a_theorem @ SV7 ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SV8 ) @ ( equivalent @ SV3 @ SY34 ) ) @ ( equivalent @ SV8 @ SY34 ) ) @ SY35 ) @ SY35 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY36: $i,SY37: $i,SY38: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV9 ) @ ( equivalent @ SV4 @ SY36 ) ) @ SY37 ) @ ( equivalent @ ( equivalent @ SV9 @ SY36 ) @ SY37 ) ) @ SY38 ) @ SY38 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY39: $i,SY40: $i,SY41: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SV10 ) @ SY39 ) @ SY40 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SY41 ) @ SY39 ) @ ( equivalent @ ( equivalent @ SV10 @ SY41 ) @ SY40 ) ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( ifeq @ SV1 @ SV1 @ SV6 @ SV11 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY42: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SV8 ) @ ( equivalent @ SV3 @ SV12 ) ) @ ( equivalent @ SV8 @ SV12 ) ) @ SY42 ) @ SY42 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV9 ) @ ( equivalent @ SV4 @ SV13 ) ) @ SY43 ) @ ( equivalent @ ( equivalent @ SV9 @ SV13 ) @ SY43 ) ) @ SY44 ) @ SY44 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SV10 ) @ SV14 ) @ SY45 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SY46 ) @ SV14 ) @ ( equivalent @ ( equivalent @ SV10 @ SY46 ) @ SY45 ) ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV15: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SV8 ) @ ( equivalent @ SV3 @ SV12 ) ) @ ( equivalent @ SV8 @ SV12 ) ) @ SV15 ) @ SV15 ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV16: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY47: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV9 ) @ ( equivalent @ SV4 @ SV13 ) ) @ SV16 ) @ ( equivalent @ ( equivalent @ SV9 @ SV13 ) @ SV16 ) ) @ SY47 ) @ SY47 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV17: $i,SV14: $i,SV10: $i,SV5: $i] :
( ( ! [SY48: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SV10 ) @ SV14 ) @ SV17 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SY48 ) @ SV14 ) @ ( equivalent @ ( equivalent @ SV10 @ SY48 ) @ SV17 ) ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV18: $i,SV16: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV9 ) @ ( equivalent @ SV4 @ SV13 ) ) @ SV16 ) @ ( equivalent @ ( equivalent @ SV9 @ SV13 ) @ SV16 ) ) @ SV18 ) @ SV18 ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV19: $i,SV17: $i,SV14: $i,SV10: $i,SV5: $i] :
( ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SV10 ) @ SV14 ) @ SV17 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV5 @ SV19 ) @ SV14 ) @ ( equivalent @ ( equivalent @ SV10 @ SV19 ) @ SV17 ) ) ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,45,44,41,37,33,31]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jul 4 05:11:23 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33
% 0.11/0.33 No.of.Axioms: 6
% 0.11/0.33
% 0.11/0.33 Length.of.Defs: 0
% 0.11/0.33
% 0.11/0.33 Contains.Choice.Funs: false
% 0.11/0.34 (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)...
% 35.09/35.32
% 35.09/35.32 ********************************
% 35.09/35.32 * All subproblems solved! *
% 35.09/35.32 ********************************
% 35.09/35.32 % 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:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 35.09/35.32
% 35.09/35.32 %**** Beginning of derivation protocol ****
% 35.09/35.32 % SZS output start CNFRefutation
% See solution above
% 35.09/35.32
% 35.09/35.32 %**** End of derivation protocol ****
% 35.09/35.32 %**** no. of clauses in derivation: 47 ****
% 35.09/35.32 %**** clause counter: 46 ****
% 35.09/35.32
% 35.09/35.32 % 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:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------