TSTP Solution File: SYN082+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN082+1 : TPTP v8.1.0. Released v2.0.0.
% 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 08:23:28 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 34 unt; 5 typ; 0 def)
% Number of atoms : 232 ( 55 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 489 ( 96 ~; 44 |; 16 &; 317 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 ^ 39 !; 8 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY4,type,
sK2_SY4: $i > $i ).
thf(tp_sK3_SY3,type,
sK3_SY3: $i ).
thf(1,conjecture,
! [X: $i] :
( ( big_f @ X @ ( f @ X ) )
<=> ? [Y: $i] :
( ! [Z: $i] :
( ( big_f @ Z @ Y )
=> ( big_f @ Z @ ( f @ X ) ) )
& ( big_f @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel60) ).
thf(2,negated_conjecture,
( ( ! [X: $i] :
( ( big_f @ X @ ( f @ X ) )
<=> ? [Y: $i] :
( ! [Z: $i] :
( ( big_f @ Z @ Y )
=> ( big_f @ Z @ ( f @ X ) ) )
& ( big_f @ X @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: $i] :
( ( big_f @ X @ ( f @ X ) )
<=> ? [Y: $i] :
( ! [Z: $i] :
( ( big_f @ Z @ Y )
=> ( big_f @ Z @ ( f @ X ) ) )
& ( big_f @ X @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( big_f @ sK1_X @ ( f @ sK1_X ) )
<=> ? [SY3: $i] :
( ! [SY4: $i] :
( ( big_f @ SY4 @ SY3 )
=> ( big_f @ SY4 @ ( f @ sK1_X ) ) )
& ( big_f @ sK1_X @ SY3 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( big_f @ sK1_X @ ( f @ sK1_X ) )
=> ? [SY3: $i] :
( ! [SY4: $i] :
( ( big_f @ SY4 @ SY3 )
=> ( big_f @ SY4 @ ( f @ sK1_X ) ) )
& ( big_f @ sK1_X @ SY3 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ? [SY3: $i] :
( ! [SY4: $i] :
( ( big_f @ SY4 @ SY3 )
=> ( big_f @ SY4 @ ( f @ sK1_X ) ) )
& ( big_f @ sK1_X @ SY3 ) )
=> ( big_f @ sK1_X @ ( f @ sK1_X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ( ( big_f @ sK1_X @ ( f @ sK1_X ) )
=> ? [SY3: $i] :
( ! [SY4: $i] :
( ( big_f @ SY4 @ SY3 )
=> ( big_f @ SY4 @ ( f @ sK1_X ) ) )
& ( big_f @ sK1_X @ SY3 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ? [SY3: $i] :
( ! [SY4: $i] :
( ( big_f @ SY4 @ SY3 )
=> ( big_f @ SY4 @ ( f @ sK1_X ) ) )
& ( big_f @ sK1_X @ SY3 ) )
=> ( big_f @ sK1_X @ ( f @ sK1_X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ( big_f @ sK1_X @ ( f @ sK1_X ) )
& ! [SY3: $i] :
( ( ( big_f @ ( sK2_SY4 @ SY3 ) @ SY3 )
& ~ ( big_f @ ( sK2_SY4 @ SY3 ) @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ SY3 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ! [SY5: $i] :
( ~ ( big_f @ SY5 @ sK3_SY3 )
| ( big_f @ SY5 @ ( f @ sK1_X ) ) )
& ( big_f @ sK1_X @ sK3_SY3 )
& ~ ( big_f @ sK1_X @ ( f @ sK1_X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ( big_f @ sK1_X @ ( f @ sK1_X ) )
& ! [SY3: $i] :
( ( ( big_f @ ( sK2_SY4 @ SY3 ) @ SY3 )
& ~ ( big_f @ ( sK2_SY4 @ SY3 ) @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ SY3 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ( big_f @ sK1_X @ ( f @ sK1_X ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( big_f @ ( sK2_SY4 @ SX0 ) @ SX0 )
| ~ ~ ( big_f @ ( sK2_SY4 @ SX0 ) @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ( big_f @ sK1_X @ ( f @ sK1_X ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( big_f @ ( sK2_SY4 @ SX0 ) @ SX0 )
| ~ ~ ( big_f @ ( sK2_SY4 @ SX0 ) @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ( big_f @ sK1_X @ ( f @ sK1_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( big_f @ ( sK2_SY4 @ SX0 ) @ SX0 )
| ~ ~ ( big_f @ ( sK2_SY4 @ SX0 ) @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( big_f @ sK1_X @ ( f @ sK1_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( big_f @ ( sK2_SY4 @ SX0 ) @ SX0 )
| ~ ~ ( big_f @ ( sK2_SY4 @ SX0 ) @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ( ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ SV1 )
| ~ ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ SV1 )
| ~ ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ ( f @ sK1_X ) ) ) )
= $true )
| ( ( ~ ( big_f @ sK1_X @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ SV1 )
| ~ ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ ( f @ sK1_X ) ) )
= $false )
| ( ( ~ ( big_f @ sK1_X @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ~ ( big_f @ sK1_X @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(22,plain,
! [SV1: $i] :
( ( ( ~ ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ ( f @ sK1_X ) ) )
= $false )
| ( ( ~ ( big_f @ sK1_X @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
! [SV1: $i] :
( ( ( big_f @ ( sK2_SY4 @ SV1 ) @ SV1 )
= $true )
| ( ( ~ ( big_f @ sK1_X @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ ( sK2_SY4 @ SV1 ) @ ( f @ sK1_X ) ) )
= $true )
| ( ( ~ ( big_f @ sK1_X @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
! [SV1: $i] :
( ( ( big_f @ sK1_X @ SV1 )
= $false )
| ( ( big_f @ ( sK2_SY4 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( big_f @ ( sK2_SY4 @ SV1 ) @ ( f @ sK1_X ) )
= $false )
| ( ( ~ ( big_f @ sK1_X @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: $i] :
( ( ( big_f @ sK1_X @ SV1 )
= $false )
| ( ( big_f @ ( sK2_SY4 @ SV1 ) @ ( f @ sK1_X ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(28,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,27,25]) ).
thf(29,plain,
( ( ! [SY5: $i] :
( ~ ( big_f @ SY5 @ sK3_SY3 )
| ( big_f @ SY5 @ ( f @ sK1_X ) ) )
& ( big_f @ sK1_X @ sK3_SY3 )
& ~ ( big_f @ sK1_X @ ( f @ sK1_X ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(30,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 @ sK3_SY3 )
| ( big_f @ SX0 @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ sK3_SY3 ) )
| ~ ~ ( big_f @ sK1_X @ ( f @ sK1_X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(31,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 @ sK3_SY3 )
| ( big_f @ SX0 @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ sK3_SY3 ) )
| ~ ~ ( big_f @ sK1_X @ ( f @ sK1_X ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(32,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 @ sK3_SY3 )
| ( big_f @ SX0 @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ sK3_SY3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(33,plain,
( ( ~ ~ ( big_f @ sK1_X @ ( f @ sK1_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 @ sK3_SY3 )
| ( big_f @ SX0 @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ sK3_SY3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ( big_f @ sK1_X @ ( f @ sK1_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 @ sK3_SY3 )
| ( big_f @ SX0 @ ( f @ sK1_X ) ) )
| ~ ( big_f @ sK1_X @ sK3_SY3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
( ( big_f @ sK1_X @ ( f @ sK1_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 @ sK3_SY3 )
| ( big_f @ SX0 @ ( f @ sK1_X ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
( ( ~ ( big_f @ sK1_X @ sK3_SY3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
( ( ! [SX0: $i] :
( ~ ( big_f @ SX0 @ sK3_SY3 )
| ( big_f @ SX0 @ ( f @ sK1_X ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( big_f @ sK1_X @ sK3_SY3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
! [SV2: $i] :
( ( ~ ( big_f @ SV2 @ sK3_SY3 )
| ( big_f @ SV2 @ ( f @ sK1_X ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV2: $i] :
( ( ( ~ ( big_f @ SV2 @ sK3_SY3 ) )
= $true )
| ( ( big_f @ SV2 @ ( f @ sK1_X ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( big_f @ SV2 @ sK3_SY3 )
= $false )
| ( ( big_f @ SV2 @ ( f @ sK1_X ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(45,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,44,41]) ).
thf(46,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[45,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN082+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n028.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 : Mon Jul 11 20:03:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34
% 0.14/0.34 No.of.Axioms: 0
% 0.14/0.34
% 0.14/0.34 Length.of.Defs: 0
% 0.14/0.34
% 0.14/0.34 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:600,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/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:45,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: 46 ****
% 0.20/0.39 %**** clause counter: 45 ****
% 0.20/0.39
% 0.20/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------