TSTP Solution File: ALG286^5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG286^5 : 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 : n025.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 14 17:25:42 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 33 unt; 8 typ; 0 def)
% Number of atoms : 162 ( 120 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 228 ( 34 ~; 20 |; 14 &; 150 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 0 ^ 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cL,type,
cL: a > a ).
thf(tp_cP,type,
cP: a > a > a ).
thf(tp_cR,type,
cR: a > a ).
thf(tp_cZ,type,
cZ: a ).
thf(tp_u,type,
u: a ).
thf(tp_x,type,
x: a ).
thf(tp_y,type,
y: a ).
thf(1,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx0: a,Xy0: a] :
( ( cL @ ( cP @ Xx0 @ Xy0 ) )
= Xx0 )
& ! [Xx0: a,Xy0: a] :
( ( cR @ ( cP @ Xx0 @ Xy0 ) )
= Xy0 )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPU_PAIR_NOT_ZERO_pme) ).
thf(2,negated_conjecture,
( ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx0: a,Xy0: a] :
( ( cL @ ( cP @ Xx0 @ Xy0 ) )
= Xx0 )
& ! [Xx0: a,Xy0: a] :
( ( cR @ ( cP @ Xx0 @ Xy0 ) )
= Xy0 )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx0: a,Xy0: a] :
( ( cL @ ( cP @ Xx0 @ Xy0 ) )
= Xx0 )
& ! [Xx0: a,Xy0: a] :
( ( cR @ ( cP @ Xx0 @ Xy0 ) )
= Xy0 )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( cL @ cZ )
= cZ )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ( cR @ cZ )
= cZ )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx0: a,Xy0: a] :
( ( cL @ ( cP @ Xx0 @ Xy0 ) )
= Xx0 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx0: a,Xy0: a] :
( ( cR @ ( cP @ Xx0 @ Xy0 ) )
= Xy0 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( u
= ( cP @ x @ y ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ( u != cZ ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ~ ( ( u != cZ ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( u = cZ )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(13,plain,
( ( ! [Xt: a] :
( ( Xt = cZ )
| ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
& ! [Xt: a] :
( ( Xt
!= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) )
| ( Xt != cZ ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( u
= ( cP @ x @ y ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ! [Xt: a] :
( ( Xt = cZ )
| ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
& ! [Xt: a] :
( ( Xt
!= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) )
| ( Xt != cZ ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [Xx0: a,Xy0: a] :
( ( cR @ ( cP @ Xx0 @ Xy0 ) )
= Xy0 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(17,plain,
( ( ! [Xx0: a,Xy0: a] :
( ( cL @ ( cP @ Xx0 @ Xy0 ) )
= Xx0 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(18,plain,
( ( ( cR @ cZ )
= cZ )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(19,plain,
( ( ( cL @ cZ )
= cZ )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(20,plain,
( ( u = cZ )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ~ ( ~ ! [SX0: a] :
( ( SX0 = cZ )
| ( SX0
= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) ) )
| ~ ! [SX0: a] :
( ( SX0
!= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) )
| ( SX0 != cZ ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(22,plain,
! [SV1: a] :
( ( ! [SY5: a] :
( ( cR @ ( cP @ SV1 @ SY5 ) )
= SY5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV2: a] :
( ( ! [SY6: a] :
( ( cL @ ( cP @ SV2 @ SY6 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
( ( ~ ! [SX0: a] :
( ( SX0 = cZ )
| ( SX0
= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) ) )
| ~ ! [SX0: a] :
( ( SX0
!= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) )
| ( SX0 != cZ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: a,SV1: a] :
( ( ( cR @ ( cP @ SV1 @ SV3 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV4: a,SV2: a] :
( ( ( cL @ ( cP @ SV2 @ SV4 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ! [SX0: a] :
( ( SX0 = cZ )
| ( SX0
= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ! [SX0: a] :
( ( SX0
!= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) )
| ( SX0 != cZ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [SX0: a] :
( ( SX0 = cZ )
| ( SX0
= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
( ( ! [SX0: a] :
( ( SX0
!= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) )
| ( SX0 != cZ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV5: a] :
( ( ( SV5 = cZ )
| ( SV5
= ( cP @ ( cL @ SV5 ) @ ( cR @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV6: a] :
( ( ( SV6
!= ( cP @ ( cL @ SV6 ) @ ( cR @ SV6 ) ) )
| ( SV6 != cZ ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV5: a] :
( ( ( SV5 = cZ )
= $true )
| ( ( SV5
= ( cP @ ( cL @ SV5 ) @ ( cR @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV6: a] :
( ( ( ( SV6
!= ( cP @ ( cL @ SV6 ) @ ( cR @ SV6 ) ) ) )
= $true )
| ( ( ( SV6 != cZ ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV6: a] :
( ( ( SV6
= ( cP @ ( cL @ SV6 ) @ ( cR @ SV6 ) ) )
= $false )
| ( ( ( SV6 != cZ ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(36,plain,
! [SV6: a] :
( ( ( SV6 = cZ )
= $false )
| ( ( SV6
= ( cP @ ( cL @ SV6 ) @ ( cR @ SV6 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(37,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,36,33,26,25,20,19,18]) ).
thf(38,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ALG286^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n025.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 : Thu Jun 9 02:48:05 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: 0
% 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).
% 0.12/0.37
% 0.12/0.37 ********************************
% 0.12/0.37 * All subproblems solved! *
% 0.12/0.37 ********************************
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.37
% 0.12/0.37 %**** Beginning of derivation protocol ****
% 0.12/0.37 % SZS output start CNFRefutation
% See solution above
% 0.12/0.37
% 0.12/0.37 %**** End of derivation protocol ****
% 0.12/0.37 %**** no. of clauses in derivation: 38 ****
% 0.12/0.37 %**** clause counter: 37 ****
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------