TSTP Solution File: SYO227^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO227^5 : 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 : n028.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 17:32:51 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 20 unt; 4 typ; 0 def)
% Number of atoms : 289 ( 153 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 267 ( 54 ~; 65 |; 13 &; 125 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 0 ^ 49 !; 5 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_c_less_,type,
c_less_: $i > $i > $o ).
thf(1,conjecture,
( ! [Xx: $i,Xy: $i] :
( ( c_less_ @ Xx @ Xy )
=> ( Xx != Xy ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [A: $i > $o] :
( ~ ( A @ a )
& ( A @ b )
& ~ ( A @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE4_W_AX) ).
thf(2,negated_conjecture,
( ( ! [Xx: $i,Xy: $i] :
( ( c_less_ @ Xx @ Xy )
=> ( Xx != Xy ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [A: $i > $o] :
( ~ ( A @ a )
& ( A @ b )
& ~ ( A @ c ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( c_less_ @ Xx @ Xy )
=> ( Xx != Xy ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [A: $i > $o] :
( ~ ( A @ a )
& ( A @ b )
& ~ ( A @ c ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( c_less_ @ Xx @ Xy )
=> ( Xx != Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( c_less_ @ a @ b )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( c_less_ @ b @ c )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ? [A: $i > $o] :
( ~ ( A @ a )
& ( A @ b )
& ~ ( A @ c ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ? [A: $i > $o] :
( ~ ( A @ a )
& ( A @ b )
& ~ ( A @ c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i > $o] :
( ( A @ a )
| ~ ( A @ b )
| ( A @ c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( c_less_ @ Xx @ Xy )
| ( Xx != Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( c_less_ @ b @ c )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( c_less_ @ a @ b )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( c_less_ @ Xx @ Xy )
| ( Xx != Xy ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ! [A: $i > $o] :
( ( A @ a )
| ~ ( A @ b )
| ( A @ c ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY3: $i] :
( ~ ( c_less_ @ SV1 @ SY3 )
| ( SV1 != SY3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV2: $i > $o] :
( ( ( SV2 @ a )
| ~ ( SV2 @ b )
| ( SV2 @ c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( c_less_ @ SV1 @ SV3 )
| ( SV1 != SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV2: $i > $o] :
( ( ( ( SV2 @ a )
| ~ ( SV2 @ b ) )
= $true )
| ( ( SV2 @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( c_less_ @ SV1 @ SV3 ) )
= $true )
| ( ( ( SV1 != SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV2: $i > $o] :
( ( ( SV2 @ a )
= $true )
| ( ( ~ ( SV2 @ b ) )
= $true )
| ( ( SV2 @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV3: $i,SV1: $i] :
( ( ( c_less_ @ SV1 @ SV3 )
= $false )
| ( ( ( SV1 != SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: $i > $o] :
( ( ( SV2 @ b )
= $false )
| ( ( SV2 @ a )
= $true )
| ( ( SV2 @ c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV3: $i,SV1: $i] :
( ( ( SV1 = SV3 )
= $false )
| ( ( c_less_ @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ( b = b )
= $false )
| ( ( a = b )
= $true )
| ( ( c = b )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[22:[bind(SV2,$thf( ^ [SV4: $i] : ( SV4 = b ) ))]]) ).
thf(25,plain,
( ( ( a = b )
= $true )
| ( ( c = b )
= $true ) ),
inference(sim,[status(thm)],[24]) ).
thf(28,plain,
! [SV6: $i > $o] :
( ( ( ~ ( SV6 @ b ) )
= $false )
| ( ( ~ ( SV6 @ a ) )
= $true )
| ( ( ~ ( SV6 @ c ) )
= $true ) ),
inference(prim_subst,[status(thm)],[22:[bind(SV2,$thf( ^ [SV5: $i] : ~ ( SV6 @ SV5 ) ))]]) ).
thf(30,plain,
( ( ( b = b )
= $false )
| ( ( a = b )
= $true )
| ( ( c = b )
= $true ) ),
inference(prim_subst,[status(thm)],[22:[bind(SV2,$thf( ^ [SV10: $i] : ( SV10 = b ) ))]]) ).
thf(32,plain,
( ( ( c = b )
= $true )
| ( ( ( a = b )
= ( c = b ) )
= $false ) ),
inference(fac_restr,[status(thm)],[25]) ).
thf(33,plain,
! [SV3: $i,SV1: $i] :
( ( ( c_less_ @ SV1 @ SV3 )
= $false )
| ( ( ( SV1 = SV3 )
= ( c_less_ @ SV1 @ SV3 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[23]) ).
thf(34,plain,
( ( ( ~ ( ( a = b )
| ( c = b ) )
| ~ ( ( a != b )
| ( c != b ) ) )
= $false )
| ( ( c = b )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[32]) ).
thf(35,plain,
( ( ( ( a = b )
= ( c = b ) )
= $false )
| ( ( c = b )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( ( SV1 = SV3 )
| ( c_less_ @ SV1 @ SV3 ) )
| ~ ( ( SV1 != SV3 )
| ~ ( c_less_ @ SV1 @ SV3 ) ) )
= $false )
| ( ( c_less_ @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[33]) ).
thf(38,plain,
( ( ( ~ ( ( a = b )
| ( c = b ) ) )
= $false )
| ( ( c = b )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( ( SV1 != SV3 )
| ~ ( c_less_ @ SV1 @ SV3 ) ) )
= $false )
| ( ( c_less_ @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
( ( ( ( a = b )
| ( c = b ) )
= $true )
| ( ( c = b )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(45,plain,
! [SV3: $i,SV1: $i] :
( ( ( ( SV1 != SV3 )
| ~ ( c_less_ @ SV1 @ SV3 ) )
= $true )
| ( ( c_less_ @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( ( a = b )
= $true )
| ( ( c = b )
= $true )
| ( ( c = b )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV3: $i,SV1: $i] :
( ( ( ( SV1 != SV3 ) )
= $true )
| ( ( ~ ( c_less_ @ SV1 @ SV3 ) )
= $true )
| ( ( c_less_ @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV3: $i,SV1: $i] :
( ( ( SV1 = SV3 )
= $false )
| ( ( ~ ( c_less_ @ SV1 @ SV3 ) )
= $true )
| ( ( c_less_ @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV3: $i,SV1: $i] :
( ( ( c_less_ @ SV1 @ SV3 )
= $false )
| ( ( SV1 = SV3 )
= $false )
| ( ( c_less_ @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(54,plain,
( ( ( c = b )
= $true )
| ( ( a = b )
= $false )
| ( ( b = c )
= $false ) ),
inference(extuni,[status(esa)],[35]) ).
thf(55,plain,
( ( ( c = b )
= $true )
| ( ( a = c )
= $false ) ),
inference(extuni,[status(esa)],[35]) ).
thf(56,plain,
! [SV3: $i] :
( ( ( c_less_ @ SV3 @ SV3 )
= $false )
| ( ( c_less_ @ SV3 @ SV3 )
= $false ) ),
inference(extuni,[status(esa)],[53:[bind(SV1,$thf( SV3 ))]]) ).
thf(57,plain,
! [SV3: $i] :
( ( c_less_ @ SV3 @ SV3 )
= $false ),
inference(extuni,[status(esa)],[23:[bind(SV1,$thf( SV3 ))]]) ).
thf(58,plain,
! [SV6: $i > $o] :
( ( ( SV6 @ b )
= $true )
| ( ( ~ ( SV6 @ a ) )
= $true )
| ( ( ~ ( SV6 @ c ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(59,plain,
! [SV6: $i > $o] :
( ( ( SV6 @ a )
= $false )
| ( ( SV6 @ b )
= $true )
| ( ( ~ ( SV6 @ c ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
! [SV6: $i > $o] :
( ( ( SV6 @ c )
= $false )
| ( ( SV6 @ b )
= $true )
| ( ( SV6 @ a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(61,plain,
( ( ( c = b )
= $true )
| ( ( a = b )
= $true ) ),
inference(extuni,[status(esa)],[30]) ).
thf(62,plain,
( ( ( a = b )
= $true )
| ( ( c = b )
= $true ) ),
inference(sim,[status(thm)],[46]) ).
thf(63,plain,
! [SV3: $i] :
( ( c_less_ @ SV3 @ SV3 )
= $false ),
inference(sim,[status(thm)],[56]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,63,62,61,60,57,55,54,25,23,22,12]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO227^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jul 8 18:28:10 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 0
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.37 (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).
% 0.21/0.44
% 0.21/0.44 ********************************
% 0.21/0.44 * All subproblems solved! *
% 0.21/0.44 ********************************
% 0.21/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:64,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.21/0.44
% 0.21/0.44 %**** Beginning of derivation protocol ****
% 0.21/0.44 % SZS output start CNFRefutation
% See solution above
% 0.21/0.44
% 0.21/0.44 %**** End of derivation protocol ****
% 0.21/0.44 %**** no. of clauses in derivation: 52 ****
% 0.21/0.44 %**** clause counter: 64 ****
% 0.21/0.44
% 0.21/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:64,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------