TSTP Solution File: SYO005^1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO005^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.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 21 17:31:19 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 25 unt; 6 typ; 2 def)
% Number of atoms : 83 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 126 ( 18 ~; 8 |; 2 &; 82 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 4 ^ 31 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_leibeq1,type,
leibeq1: $i > $i > $o ).
thf(tp_leibeq2,type,
leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i > $i ).
thf(tp_sK3_SY19,type,
sK3_SY19: $i ).
thf(tp_sK4_SY21,type,
sK4_SY21: $i > $o ).
thf(leibeq1,definition,
( leibeq1
= ( ^ [U: $i,V: $i] :
! [Q: $i > $o] :
( ( Q @ U )
=> ( Q @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq1) ).
thf(leibeq2,definition,
( leibeq2
= ( ^ [X: $i > $i,Y: $i > $i] :
! [P: ( $i > $i ) > $o] :
( ( P @ X )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq2) ).
thf(1,conjecture,
! [F: $i > $i,G: $i > $i] :
( ( leibeq2 @ F @ G )
=> ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ! [F: $i > $i,G: $i > $i] :
( ( leibeq2 @ F @ G )
=> ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i,SY1: $i > $i] :
( ! [SY4: ( $i > $i ) > $o] :
( ( SY4 @ SY0 )
=> ( SY4 @ SY1 ) )
=> ! [SY5: $i,SY8: $i > $o] :
( ( SY8 @ ( SY0 @ SY5 ) )
=> ( SY8 @ ( SY1 @ SY5 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,leibeq1,leibeq2]) ).
thf(4,plain,
( ( ! [SY14: $i > $i] :
( ! [SY15: ( $i > $i ) > $o] :
( ( SY15 @ sK1_SY0 )
=> ( SY15 @ SY14 ) )
=> ! [SY16: $i,SY17: $i > $o] :
( ( SY17 @ ( sK1_SY0 @ SY16 ) )
=> ( SY17 @ ( SY14 @ SY16 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY18: ( $i > $i ) > $o] :
( ( SY18 @ sK1_SY0 )
=> ( SY18 @ sK2_SY14 ) )
=> ! [SY19: $i,SY20: $i > $o] :
( ( SY20 @ ( sK1_SY0 @ SY19 ) )
=> ( SY20 @ ( sK2_SY14 @ SY19 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY18: ( $i > $i ) > $o] :
( ( SY18 @ sK1_SY0 )
=> ( SY18 @ sK2_SY14 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY19: $i,SY20: $i > $o] :
( ( SY20 @ ( sK1_SY0 @ SY19 ) )
=> ( SY20 @ ( sK2_SY14 @ SY19 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY19: $i,SY20: $i > $o] :
( ( SY20 @ ( sK1_SY0 @ SY19 ) )
=> ( SY20 @ ( sK2_SY14 @ SY19 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( sK4_SY21 @ ( sK1_SY0 @ sK3_SY19 ) )
& ~ ( sK4_SY21 @ ( sK2_SY14 @ sK3_SY19 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [SY18: ( $i > $i ) > $o] :
( ~ ( SY18 @ sK1_SY0 )
| ( SY18 @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(11,plain,
( ( ! [SY18: ( $i > $i ) > $o] :
( ~ ( SY18 @ sK1_SY0 )
| ( SY18 @ sK2_SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ( sK4_SY21 @ ( sK1_SY0 @ sK3_SY19 ) )
& ~ ( sK4_SY21 @ ( sK2_SY14 @ sK3_SY19 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( ~ ( sK4_SY21 @ ( sK1_SY0 @ sK3_SY19 ) )
| ~ ~ ( sK4_SY21 @ ( sK2_SY14 @ sK3_SY19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,leibeq1,leibeq2]) ).
thf(14,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ~ ( SV1 @ sK1_SY0 )
| ( SV1 @ sK2_SY14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ( sK4_SY21 @ ( sK1_SY0 @ sK3_SY19 ) )
| ~ ~ ( sK4_SY21 @ ( sK2_SY14 @ sK3_SY19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( ~ ( SV1 @ sK1_SY0 ) )
= $true )
| ( ( SV1 @ sK2_SY14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( sK4_SY21 @ ( sK1_SY0 @ sK3_SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( sK4_SY21 @ ( sK2_SY14 @ sK3_SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( SV1 @ sK1_SY0 )
= $false )
| ( ( SV1 @ sK2_SY14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( sK4_SY21 @ ( sK1_SY0 @ sK3_SY19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( sK4_SY21 @ ( sK2_SY14 @ sK3_SY19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( sK4_SY21 @ ( sK2_SY14 @ sK3_SY19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(23,plain,
( ( ( sK1_SY0 = sK1_SY0 )
= $false )
| ( ( sK2_SY14 = sK1_SY0 )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[19:[bind(SV1,$thf( ^ [SV2: $i > $i] : ( SV2 = sK1_SY0 ) ))]]) ).
thf(24,plain,
( ( sK2_SY14 = sK1_SY0 )
= $true ),
inference(sim,[status(thm)],[23]) ).
thf(25,plain,
! [SV3: $i] :
( ( ( sK2_SY14 @ SV3 )
= ( sK1_SY0 @ SV3 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,25,24,22]) ).
thf(27,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO005^1 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n018.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 : Sat Jul 9 10:59:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 321
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.12/0.38
% 0.12/0.38 ********************************
% 0.12/0.38 * All subproblems solved! *
% 0.12/0.38 ********************************
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:26,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.12/0.38
% 0.12/0.38 %**** Beginning of derivation protocol ****
% 0.12/0.38 % SZS output start CNFRefutation
% See solution above
% 0.12/0.38
% 0.12/0.38 %**** End of derivation protocol ****
% 0.12/0.38 %**** no. of clauses in derivation: 27 ****
% 0.12/0.38 %**** clause counter: 26 ****
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:26,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------