TSTP Solution File: SEU581^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU581^2 : 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 : n032.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 : Tue Jul 19 12:13:03 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 42 ( 24 unt; 13 typ; 2 def)
% Number of atoms : 116 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 188 ( 8 ~; 8 |; 0 &; 163 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 20 ^ 54 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY11,type,
sK2_SY11: $i > $o ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i > $i > $o ) > $i ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(1,conjecture,
( powersetE1
=> ( sepInPowerset
=> ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(2,negated_conjecture,
( ( powersetE1
=> ( sepInPowerset
=> ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) )
=> ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,powersetE1,sepInPowerset]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ( subset
@ ( dsetconstr @ sK1_A
@ ^ [SY13: $i] : ( sK2_SY11 @ SY13 ) )
@ sK1_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( subset
@ ( dsetconstr @ sK1_A
@ ^ [SY13: $i] : ( sK2_SY11 @ SY13 ) )
@ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY14: $i > $o] :
( in
@ ( dsetconstr @ SV1
@ ^ [Xx: $i] : ( SY14 @ Xx ) )
@ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
( ~ ( in @ SY16 @ ( powerset @ SV2 ) )
| ( subset @ SY16 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( subset
@ ( dsetconstr @ sK1_A
@ ^ [SY13: $i] : ( sK2_SY11 @ SY13 ) )
@ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV3: $i > $o,SV1: $i] :
( ( in
@ ( dsetconstr @ SV1
@ ^ [SY17: $i] : ( SV3 @ SY17 ) )
@ ( powerset @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ ( powerset @ SV2 ) )
| ( subset @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( subset @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV2: $i,SV4: $i] :
( ( ( in @ SV4 @ ( powerset @ SV2 ) )
= $false )
| ( ( subset @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV5: $i > $o,SV6: $i] :
( ( in
@ ( dsetconstr @ SV6
@ ^ [SX0: $i] : ( SV5 @ SX0 ) )
@ ( powerset @ SV6 ) )
= $true ),
inference(rename,[status(thm)],[16]) ).
thf(22,plain,
! [SV7: $i,SV8: $i] :
( ( ( in @ SV8 @ ( powerset @ SV7 ) )
= $false )
| ( ( subset @ SV8 @ SV7 )
= $true ) ),
inference(rename,[status(thm)],[19]) ).
thf(25,plain,
! [SV7: $i,SV8: $i,SV5: $i > $o,SV6: $i] :
( ( ( ( in @ SV8 @ ( powerset @ SV7 ) )
= ( in
@ ( dsetconstr @ SV6
@ ^ [SX0: $i] : ( SV5 @ SX0 ) )
@ ( powerset @ SV6 ) ) )
= $false )
| ( ( subset @ SV8 @ SV7 )
= $true ) ),
inference(res,[status(thm)],[22,20]) ).
thf(28,plain,
! [SV5: $i > $o,SV6: $i] :
( ( subset
@ ( dsetconstr @ SV6
@ ^ [SX0: $i] : ( SV5 @ SX0 ) )
@ SV6 )
= $true ),
inference(extuni,[status(esa)],[25:[bind(SV7,$thf( SV6 )),bind(SV8,$thf( dsetconstr @ SV6 @ ^ [SX0: $i] : ( SV5 @ SX0 ) ))]]) ).
thf(36,plain,
! [SV9: $i > $o,SV10: $i] :
( ( subset
@ ( dsetconstr @ SV10
@ ^ [SX0: $i] : ( SV9 @ SX0 ) )
@ SV10 )
= $true ),
inference(rename,[status(thm)],[28]) ).
thf(39,plain,
! [SV9: $i > $o,SV10: $i] :
( ( ( subset
@ ( dsetconstr @ SV10
@ ^ [SX0: $i] : ( SV9 @ SX0 ) )
@ SV10 )
= ( subset
@ ( dsetconstr @ sK1_A
@ ^ [SY13: $i] : ( sK2_SY11 @ SY13 ) )
@ sK1_A ) )
= $false ),
inference(res,[status(thm)],[36,15]) ).
thf(51,plain,
$false = $true,
inference(extuni,[status(esa)],[39:[bind(SV9,$thf( ^ [SX0: $i] : ( sK2_SY11 @ SX0 ) )),bind(SV10,$thf( sK1_A ))]]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.08 % Problem : SEU581^2 : TPTP v8.1.0. Released v3.7.0.
% 0.08/0.09 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Mon Jun 20 11:40:34 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.09/0.28
% 0.09/0.28 No.of.Axioms: 0
% 0.09/0.28
% 0.09/0.28 Length.of.Defs: 376
% 0.09/0.28
% 0.09/0.28 Contains.Choice.Funs: false
% 0.09/0.28 (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)..
% 0.13/0.37
% 0.13/0.37 ********************************
% 0.13/0.37 * All subproblems solved! *
% 0.13/0.37 ********************************
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:51,loop_count:5,foatp_calls:1,translation:fof_full)
% 0.13/0.37
% 0.13/0.37 %**** Beginning of derivation protocol ****
% 0.13/0.37 % SZS output start CNFRefutation
% See solution above
% 0.13/0.37
% 0.13/0.37 %**** End of derivation protocol ****
% 0.13/0.37 %**** no. of clauses in derivation: 27 ****
% 0.13/0.37 %**** clause counter: 51 ****
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:51,loop_count:5,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------