TSTP Solution File: SYO317^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO317^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n010.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 17:33:21 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 25 unt; 5 typ; 0 def)
% Number of atoms : 207 ( 61 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 342 ( 53 ~; 41 |; 20 &; 212 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 0 ^ 85 !; 10 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_cEQ,type,
cEQ: $i > $i > $o ).
thf(tp_cP,type,
cP: $i > $o ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_sK1_Xx,type,
sK1_Xx: ( $i > $o ) > $i ).
thf(1,conjecture,
( ( ! [Xx: $i] : ( cEQ @ Xx @ Xx )
& ! [Xx: $i,Xy: $i] :
( ( ( cEQ @ Xx @ Xy )
& ( cP @ Xx ) )
=> ( cP @ Xy ) )
& ( cP @ a )
& ! [Xy: $i,Xz: $i] :
( ( cEQ @ ( f @ Xy ) @ ( f @ Xz ) )
=> ( cEQ @ Xy @ Xz ) ) )
=> ? [A: $i > $o] :
( ! [Xx: $i] :
( ( A @ ( f @ Xx ) )
=> ( cP @ Xx ) )
& ? [Xz: $i] : ( A @ Xz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM304) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: $i] : ( cEQ @ Xx @ Xx )
& ! [Xx: $i,Xy: $i] :
( ( ( cEQ @ Xx @ Xy )
& ( cP @ Xx ) )
=> ( cP @ Xy ) )
& ( cP @ a )
& ! [Xy: $i,Xz: $i] :
( ( cEQ @ ( f @ Xy ) @ ( f @ Xz ) )
=> ( cEQ @ Xy @ Xz ) ) )
=> ? [A: $i > $o] :
( ! [Xx: $i] :
( ( A @ ( f @ Xx ) )
=> ( cP @ Xx ) )
& ? [Xz: $i] : ( A @ Xz ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: $i] : ( cEQ @ Xx @ Xx )
& ! [Xx: $i,Xy: $i] :
( ( ( cEQ @ Xx @ Xy )
& ( cP @ Xx ) )
=> ( cP @ Xy ) )
& ( cP @ a )
& ! [Xy: $i,Xz: $i] :
( ( cEQ @ ( f @ Xy ) @ ( f @ Xz ) )
=> ( cEQ @ Xy @ Xz ) ) )
=> ? [A: $i > $o] :
( ! [Xx: $i] :
( ( A @ ( f @ Xx ) )
=> ( cP @ Xx ) )
& ? [Xz: $i] : ( A @ Xz ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i] : ( cEQ @ Xx @ Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( cEQ @ Xx @ Xy )
& ( cP @ Xx ) )
=> ( cP @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( cP @ a )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xy: $i,Xz: $i] :
( ( cEQ @ ( f @ Xy ) @ ( f @ Xz ) )
=> ( cEQ @ Xy @ Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ? [A: $i > $o] :
( ! [Xx: $i] :
( ( A @ ( f @ Xx ) )
=> ( cP @ Xx ) )
& ? [Xz: $i] : ( A @ Xz ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ? [A: $i > $o] :
( ! [Xx: $i] :
( ( A @ ( f @ Xx ) )
=> ( cP @ Xx ) )
& ? [Xz: $i] : ( A @ Xz ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [A: $i > $o] :
( ( ( A @ ( f @ ( sK1_Xx @ A ) ) )
& ~ ( cP @ ( sK1_Xx @ A ) ) )
| ! [Xz: $i] :
~ ( A @ Xz ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( cEQ @ Xx @ Xy )
| ~ ( cP @ Xx )
| ( cP @ Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [Xy: $i,Xz: $i] :
( ~ ( cEQ @ ( f @ Xy ) @ ( f @ Xz ) )
| ( cEQ @ Xy @ Xz ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(13,plain,
( ( ! [Xy: $i,Xz: $i] :
( ~ ( cEQ @ ( f @ Xy ) @ ( f @ Xz ) )
| ( cEQ @ Xy @ Xz ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( cP @ a )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(15,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( cEQ @ Xx @ Xy )
| ~ ( cP @ Xx )
| ( cP @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [Xx: $i] : ( cEQ @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [A: $i > $o] :
( ( ( A @ ( f @ ( sK1_Xx @ A ) ) )
& ~ ( cP @ ( sK1_Xx @ A ) ) )
| ! [Xz: $i] :
~ ( A @ Xz ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(18,plain,
( ( ! [SX0: $i > $o] :
( ~ ( ~ ( SX0 @ ( f @ ( sK1_Xx @ SX0 ) ) )
| ~ ~ ( cP @ ( sK1_Xx @ SX0 ) ) )
| ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: $i] :
( ( ! [SY8: $i] :
( ~ ( cEQ @ ( f @ SV1 ) @ ( f @ SY8 ) )
| ( cEQ @ SV1 @ SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(20,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ~ ( cEQ @ SV2 @ SY9 )
| ~ ( cP @ SV2 )
| ( cP @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV3: $i] :
( ( cEQ @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV4: $i > $o] :
( ( ~ ( ~ ( SV4 @ ( f @ ( sK1_Xx @ SV4 ) ) )
| ~ ~ ( cP @ ( sK1_Xx @ SV4 ) ) )
| ! [SY10: $i] :
~ ( SV4 @ SY10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( cEQ @ ( f @ SV1 ) @ ( f @ SV5 ) )
| ( cEQ @ SV1 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( cEQ @ SV2 @ SV6 )
| ~ ( cP @ SV2 )
| ( cP @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV4: $i > $o] :
( ( ( ~ ( ~ ( SV4 @ ( f @ ( sK1_Xx @ SV4 ) ) )
| ~ ~ ( cP @ ( sK1_Xx @ SV4 ) ) ) )
= $true )
| ( ( ! [SY10: $i] :
~ ( SV4 @ SY10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV5: $i,SV1: $i] :
( ( ( ~ ( cEQ @ ( f @ SV1 ) @ ( f @ SV5 ) ) )
= $true )
| ( ( cEQ @ SV1 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( cEQ @ SV2 @ SV6 )
| ~ ( cP @ SV2 ) )
= $true )
| ( ( cP @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV4: $i > $o] :
( ( ( ~ ( SV4 @ ( f @ ( sK1_Xx @ SV4 ) ) )
| ~ ~ ( cP @ ( sK1_Xx @ SV4 ) ) )
= $false )
| ( ( ! [SY10: $i] :
~ ( SV4 @ SY10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV5: $i,SV1: $i] :
( ( ( cEQ @ ( f @ SV1 ) @ ( f @ SV5 ) )
= $false )
| ( ( cEQ @ SV1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( cEQ @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( cP @ SV2 ) )
= $true )
| ( ( cP @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV4: $i > $o] :
( ( ( ~ ( SV4 @ ( f @ ( sK1_Xx @ SV4 ) ) ) )
= $false )
| ( ( ! [SY10: $i] :
~ ( SV4 @ SY10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV4: $i > $o] :
( ( ( ~ ~ ( cP @ ( sK1_Xx @ SV4 ) ) )
= $false )
| ( ( ! [SY10: $i] :
~ ( SV4 @ SY10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV6: $i,SV2: $i] :
( ( ( cEQ @ SV2 @ SV6 )
= $false )
| ( ( ~ ( cP @ SV2 ) )
= $true )
| ( ( cP @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV4: $i > $o] :
( ( ( SV4 @ ( f @ ( sK1_Xx @ SV4 ) ) )
= $true )
| ( ( ! [SY10: $i] :
~ ( SV4 @ SY10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV4: $i > $o] :
( ( ( ~ ( cP @ ( sK1_Xx @ SV4 ) ) )
= $true )
| ( ( ! [SY10: $i] :
~ ( SV4 @ SY10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV6: $i,SV2: $i] :
( ( ( cP @ SV2 )
= $false )
| ( ( cEQ @ SV2 @ SV6 )
= $false )
| ( ( cP @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV7: $i,SV4: $i > $o] :
( ( ( ~ ( SV4 @ SV7 ) )
= $true )
| ( ( SV4 @ ( f @ ( sK1_Xx @ SV4 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV4: $i > $o] :
( ( ( cP @ ( sK1_Xx @ SV4 ) )
= $false )
| ( ( ! [SY10: $i] :
~ ( SV4 @ SY10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV7: $i,SV4: $i > $o] :
( ( ( SV4 @ SV7 )
= $false )
| ( ( SV4 @ ( f @ ( sK1_Xx @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV8: $i,SV4: $i > $o] :
( ( ( ~ ( SV4 @ SV8 ) )
= $true )
| ( ( cP @ ( sK1_Xx @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV8: $i,SV4: $i > $o] :
( ( ( SV4 @ SV8 )
= $false )
| ( ( cP @ ( sK1_Xx @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,41,39,36,29,21]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO317^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 9 02:28:46 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (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)..
% 0.20/0.39
% 0.20/0.39 ********************************
% 0.20/0.39 * All subproblems solved! *
% 0.20/0.39 ********************************
% 0.20/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:42,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.39
% 0.20/0.39 %**** Beginning of derivation protocol ****
% 0.20/0.39 % SZS output start CNFRefutation
% See solution above
% 0.20/0.39
% 0.20/0.39 %**** End of derivation protocol ****
% 0.20/0.39 %**** no. of clauses in derivation: 43 ****
% 0.20/0.39 %**** clause counter: 42 ****
% 0.20/0.39
% 0.20/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------