TSTP Solution File: LCL186-1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL186-1 : 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 : n009.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 12:21:22 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 50 unt; 6 typ; 0 def)
% Number of atoms : 257 ( 72 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 580 ( 46 ~; 48 |; 0 &; 486 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 119 ( 0 ^ 119 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_axiom,type,
axiom: $i > $o ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_or,type,
or: $i > $i > $i ).
thf(tp_p,type,
p: $i ).
thf(tp_q,type,
q: $i ).
thf(tp_theorem,type,
theorem: $i > $o ).
thf(1,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( theorem @ ( or @ ( not @ X ) @ Z ) )
| ~ ( axiom @ ( or @ ( not @ X ) @ Y ) )
| ~ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( theorem @ X )
| ~ ( axiom @ ( or @ ( not @ Y ) @ X ) )
| ~ ( theorem @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
thf(3,axiom,
! [X: $i] :
( ( theorem @ X )
| ~ ( axiom @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] : ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
thf(6,axiom,
! [A: $i,B: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
thf(7,axiom,
! [A: $i,B: $i] : ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(8,axiom,
! [A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
~ ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( theorem @ ( or @ ( not @ X ) @ Z ) )
| ~ ( axiom @ ( or @ ( not @ X ) @ Y ) )
| ~ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ( theorem @ X )
| ~ ( axiom @ ( or @ ( not @ Y ) @ X ) )
| ~ ( theorem @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( theorem @ X )
| ~ ( axiom @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i] : ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] : ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ~ ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [X: $i,Z: $i] :
( ( theorem @ ( or @ ( not @ X ) @ Z ) )
| ! [Y: $i] :
( ~ ( axiom @ ( or @ ( not @ X ) @ Y ) )
| ~ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( theorem @ X )
| ! [Y: $i] :
( ~ ( axiom @ ( or @ ( not @ Y ) @ X ) )
| ~ ( theorem @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(25,plain,
( ( ~ ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(26,plain,
( ( ! [A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] : ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(29,plain,
( ( ! [A: $i,B: $i,C: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(30,plain,
( ( ! [A: $i,B: $i,C: $i] : ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( theorem @ X )
| ~ ( axiom @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( theorem @ X )
| ! [Y: $i] :
( ~ ( axiom @ ( or @ ( not @ Y ) @ X ) )
| ~ ( theorem @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [X: $i,Z: $i] :
( ( theorem @ ( or @ ( not @ X ) @ Z ) )
| ! [Y: $i] :
( ~ ( axiom @ ( or @ ( not @ X ) @ Y ) )
| ~ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV1: $i] :
( ( axiom @ ( or @ ( not @ ( or @ SV1 @ SV1 ) ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV2: $i] :
( ( ! [SY17: $i] : ( axiom @ ( or @ ( not @ SV2 ) @ ( or @ SY17 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV3: $i] :
( ( ! [SY18: $i] : ( axiom @ ( or @ ( not @ ( or @ SV3 @ SY18 ) ) @ ( or @ SY18 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV4: $i] :
( ( ! [SY19: $i,SY20: $i] : ( axiom @ ( or @ ( not @ ( or @ SV4 @ ( or @ SY19 @ SY20 ) ) ) @ ( or @ SY19 @ ( or @ SV4 @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(40,plain,
! [SV5: $i] :
( ( ! [SY21: $i,SY22: $i] : ( axiom @ ( or @ ( not @ ( or @ ( not @ SV5 ) @ SY21 ) ) @ ( or @ ( not @ ( or @ SY22 @ SV5 ) ) @ ( or @ SY22 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV6: $i] :
( ( ( theorem @ SV6 )
| ~ ( axiom @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV7: $i] :
( ( ( theorem @ SV7 )
| ! [SY23: $i] :
( ~ ( axiom @ ( or @ ( not @ SY23 ) @ SV7 ) )
| ~ ( theorem @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV8: $i] :
( ( ! [SY24: $i] :
( ( theorem @ ( or @ ( not @ SV8 ) @ SY24 ) )
| ! [SY25: $i] :
( ~ ( axiom @ ( or @ ( not @ SV8 ) @ SY25 ) )
| ~ ( theorem @ ( or @ ( not @ SY25 ) @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(45,plain,
! [SV9: $i,SV2: $i] :
( ( axiom @ ( or @ ( not @ SV2 ) @ ( or @ SV9 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV10: $i,SV3: $i] :
( ( axiom @ ( or @ ( not @ ( or @ SV3 @ SV10 ) ) @ ( or @ SV10 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV11: $i,SV4: $i] :
( ( ! [SY26: $i] : ( axiom @ ( or @ ( not @ ( or @ SV4 @ ( or @ SV11 @ SY26 ) ) ) @ ( or @ SV11 @ ( or @ SV4 @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV12: $i,SV5: $i] :
( ( ! [SY27: $i] : ( axiom @ ( or @ ( not @ ( or @ ( not @ SV5 ) @ SV12 ) ) @ ( or @ ( not @ ( or @ SY27 @ SV5 ) ) @ ( or @ SY27 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV6: $i] :
( ( ( theorem @ SV6 )
= $true )
| ( ( ~ ( axiom @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV7: $i] :
( ( ( theorem @ SV7 )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( axiom @ ( or @ ( not @ SY23 ) @ SV7 ) )
| ~ ( theorem @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV13: $i,SV8: $i] :
( ( ( theorem @ ( or @ ( not @ SV8 ) @ SV13 ) )
| ! [SY28: $i] :
( ~ ( axiom @ ( or @ ( not @ SV8 ) @ SY28 ) )
| ~ ( theorem @ ( or @ ( not @ SY28 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV14: $i,SV11: $i,SV4: $i] :
( ( axiom @ ( or @ ( not @ ( or @ SV4 @ ( or @ SV11 @ SV14 ) ) ) @ ( or @ SV11 @ ( or @ SV4 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV15: $i,SV12: $i,SV5: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ SV5 ) @ SV12 ) ) @ ( or @ ( not @ ( or @ SV15 @ SV5 ) ) @ ( or @ SV15 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV6: $i] :
( ( ( axiom @ SV6 )
= $false )
| ( ( theorem @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ( axiom @ ( or @ ( not @ SV16 ) @ SV7 ) )
| ~ ( theorem @ SV16 ) )
= $true )
| ( ( theorem @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV13: $i,SV8: $i] :
( ( ( theorem @ ( or @ ( not @ SV8 ) @ SV13 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( axiom @ ( or @ ( not @ SV8 ) @ SY28 ) )
| ~ ( theorem @ ( or @ ( not @ SY28 ) @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ( axiom @ ( or @ ( not @ SV16 ) @ SV7 ) ) )
= $true )
| ( ( ~ ( theorem @ SV16 ) )
= $true )
| ( ( theorem @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV13: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( axiom @ ( or @ ( not @ SV8 ) @ SV17 ) )
| ~ ( theorem @ ( or @ ( not @ SV17 ) @ SV13 ) ) )
= $true )
| ( ( theorem @ ( or @ ( not @ SV8 ) @ SV13 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV7: $i,SV16: $i] :
( ( ( axiom @ ( or @ ( not @ SV16 ) @ SV7 ) )
= $false )
| ( ( ~ ( theorem @ SV16 ) )
= $true )
| ( ( theorem @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV13: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( axiom @ ( or @ ( not @ SV8 ) @ SV17 ) ) )
= $true )
| ( ( ~ ( theorem @ ( or @ ( not @ SV17 ) @ SV13 ) ) )
= $true )
| ( ( theorem @ ( or @ ( not @ SV8 ) @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV7: $i,SV16: $i] :
( ( ( theorem @ SV16 )
= $false )
| ( ( axiom @ ( or @ ( not @ SV16 ) @ SV7 ) )
= $false )
| ( ( theorem @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV13: $i,SV17: $i,SV8: $i] :
( ( ( axiom @ ( or @ ( not @ SV8 ) @ SV17 ) )
= $false )
| ( ( ~ ( theorem @ ( or @ ( not @ SV17 ) @ SV13 ) ) )
= $true )
| ( ( theorem @ ( or @ ( not @ SV8 ) @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV8: $i,SV13: $i,SV17: $i] :
( ( ( theorem @ ( or @ ( not @ SV17 ) @ SV13 ) )
= $false )
| ( ( axiom @ ( or @ ( not @ SV8 ) @ SV17 ) )
= $false )
| ( ( theorem @ ( or @ ( not @ SV8 ) @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,63,61,54,53,52,46,45,44,36]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL186-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n009.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 : Sun Jul 3 13:50:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 9
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.19/0.40
% 0.19/0.40 ********************************
% 0.19/0.40 * All subproblems solved! *
% 0.19/0.40 ********************************
% 0.19/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:64,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.41
% 0.19/0.41 %**** Beginning of derivation protocol ****
% 0.19/0.41 % SZS output start CNFRefutation
% See solution above
% 0.19/0.41
% 0.19/0.41 %**** End of derivation protocol ****
% 0.19/0.41 %**** no. of clauses in derivation: 65 ****
% 0.19/0.41 %**** clause counter: 64 ****
% 0.19/0.41
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:64,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------