TSTP Solution File: SYN070+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN070+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 : n015.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 08:23:18 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 42 unt; 7 typ; 0 def)
% Number of atoms : 641 ( 151 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 831 ( 216 ~; 210 |; 26 &; 363 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 144 ( 0 ^ 140 !; 4 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $o ).
thf(tp_big_g,type,
big_g: $i > $o ).
thf(tp_big_h,type,
big_h: $i > $i > $o ).
thf(tp_big_j,type,
big_j: $i > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_X1,type,
sK2_X1: $i ).
thf(tp_sK3_REN,type,
sK3_REN: $o ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( ( big_f @ X )
& ( big_f @ Y )
& ( big_h @ X @ Y ) )
=> ~ ( big_j @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel46_3) ).
thf(2,axiom,
( ? [X: $i] :
( ( big_f @ X )
& ~ ( big_g @ X ) )
=> ? [X1: $i] :
( ( big_f @ X1 )
& ~ ( big_g @ X1 )
& ! [Y: $i] :
( ( ( big_f @ Y )
& ~ ( big_g @ Y ) )
=> ( big_j @ X1 @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel46_2) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( ( big_f @ X )
& ( ( ( big_f @ Y )
& ( big_h @ Y @ X ) )
=> ( big_g @ Y ) ) )
=> ( big_g @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel46_1) ).
thf(4,conjecture,
! [X: $i] :
( ( big_f @ X )
=> ( big_g @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel46) ).
thf(5,negated_conjecture,
( ( ! [X: $i] :
( ( big_f @ X )
=> ( big_g @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [X: $i] :
( ( big_f @ X )
=> ( big_g @ X ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [X: $i,Y: $i] :
( ( ( big_f @ X )
& ( big_f @ Y )
& ( big_h @ X @ Y ) )
=> ~ ( big_j @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ? [X: $i] :
( ( big_f @ X )
& ~ ( big_g @ X ) )
=> ? [X1: $i] :
( ( big_f @ X1 )
& ~ ( big_g @ X1 )
& ! [Y: $i] :
( ( ( big_f @ Y )
& ~ ( big_g @ Y ) )
=> ( big_j @ X1 @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [X: $i,Y: $i] :
( ( ( big_f @ X )
& ( ( ( big_f @ Y )
& ( big_h @ Y @ X ) )
=> ( big_g @ Y ) ) )
=> ( big_g @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ( big_f @ sK1_X )
=> ( big_g @ sK1_X ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( big_f @ sK1_X )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(12,plain,
( ( big_g @ sK1_X )
= $false ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( big_g @ sK1_X ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X )
| ~ ( big_f @ Y )
| ~ ( big_h @ X @ Y )
| ~ ( big_j @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ( ! [X: $i] :
( ~ ( big_f @ X )
| ( big_g @ X ) )
| sK3_REN )
& ( sK3_REN
=> ( ! [SY8: $i] :
( ~ ( big_f @ SY8 )
| ( big_g @ SY8 )
| ( big_j @ sK2_X1 @ SY8 ) )
& ( big_f @ sK2_X1 )
& ~ ( big_g @ sK2_X1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(16,plain,
( ( ! [X: $i] :
( ! [Y: $i] : ( big_f @ Y )
| ~ ( big_f @ X )
| ( big_g @ X ) )
& ! [X: $i] :
( ! [Y: $i] : ( big_h @ Y @ X )
| ~ ( big_f @ X )
| ( big_g @ X ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( big_g @ Y )
| ~ ( big_f @ X )
| ( big_g @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(17,plain,
( ( ! [X: $i] :
( ! [Y: $i] : ( big_f @ Y )
| ~ ( big_f @ X )
| ( big_g @ X ) )
& ! [X: $i] :
( ! [Y: $i] : ( big_h @ Y @ X )
| ~ ( big_f @ X )
| ( big_g @ X ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( big_g @ Y )
| ~ ( big_f @ X )
| ( big_g @ X ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(18,plain,
( ( ( ! [X: $i] :
( ~ ( big_f @ X )
| ( big_g @ X ) )
| sK3_REN )
& ( sK3_REN
=> ( ! [SY8: $i] :
( ~ ( big_f @ SY8 )
| ( big_g @ SY8 )
| ( big_j @ sK2_X1 @ SY8 ) )
& ( big_f @ sK2_X1 )
& ~ ( big_g @ sK2_X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X )
| ~ ( big_f @ Y )
| ~ ( big_h @ X @ Y )
| ~ ( big_j @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( big_f @ sK1_X )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(21,plain,
( ( ~ ( big_g @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(22,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_h @ SX1 @ SX0 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( big_g @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(23,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| sK3_REN )
| ~ ( ~ sK3_REN
| ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) )
| ~ ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(24,plain,
! [SV1: $i] :
( ( ! [SY9: $i] :
( ~ ( big_f @ SV1 )
| ~ ( big_f @ SY9 )
| ~ ( big_h @ SV1 @ SY9 )
| ~ ( big_j @ SY9 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( big_g @ sK1_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_h @ SX1 @ SX0 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( big_g @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| sK3_REN )
| ~ ( ~ sK3_REN
| ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) )
| ~ ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( big_f @ SV1 )
| ~ ( big_f @ SV2 )
| ~ ( big_h @ SV1 @ SV2 )
| ~ ( big_j @ SV2 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_h @ SX1 @ SX0 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( big_g @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| sK3_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ( ~ sK3_REN
| ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) )
| ~ ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(33,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( big_f @ SV1 )
| ~ ( big_f @ SV2 )
| ~ ( big_h @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( big_j @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_h @ SX1 @ SX0 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( big_g @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| sK3_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(37,plain,
( ( ~ sK3_REN
| ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) )
| ~ ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( big_f @ SV1 )
| ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( big_h @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( big_j @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_h @ SX1 @ SX0 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV3: $i] :
( ( ! [SX1: $i] :
~ ( big_g @ SX1 )
| ~ ( big_f @ SV3 )
| ( big_g @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ( ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $true )
| ( sK3_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
( ( ( ~ sK3_REN )
= $true )
| ( ( ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) )
| ~ ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( big_f @ SV1 ) )
= $true )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( big_h @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( big_j @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( big_h @ SX1 @ SX0 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV3: $i] :
( ( ( ! [SX1: $i] :
~ ( big_g @ SX1 )
| ~ ( big_f @ SV3 ) )
= $true )
| ( ( big_g @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV4: $i] :
( ( ( ~ ( big_f @ SV4 )
| ( big_g @ SV4 ) )
= $true )
| ( sK3_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
( ( sK3_REN = $false )
| ( ( ~ ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) )
| ~ ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV2: $i,SV1: $i] :
( ( ( big_f @ SV1 )
= $false )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( big_h @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( big_j @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(51,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] : ( big_h @ SX1 @ SX0 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV3: $i] :
( ( ( ! [SX1: $i] :
~ ( big_g @ SX1 ) )
= $true )
| ( ( ~ ( big_f @ SV3 ) )
= $true )
| ( ( big_g @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( ~ ( big_f @ SV4 ) )
= $true )
| ( ( big_g @ SV4 )
= $true )
| ( sK3_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(54,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) )
| ~ ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV1: $i,SV2: $i] :
( ( ( big_f @ SV2 )
= $false )
| ( ( big_f @ SV1 )
= $false )
| ( ( ~ ( big_h @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( big_j @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV5: $i] :
( ( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SV5 )
| ( big_g @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV6: $i] :
( ( ! [SY12: $i] : ( big_h @ SY12 @ SV6 )
| ~ ( big_f @ SV6 )
| ( big_g @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( big_g @ SV7 ) )
= $true )
| ( ( ~ ( big_f @ SV3 ) )
= $true )
| ( ( big_g @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV4: $i] :
( ( ( big_f @ SV4 )
= $false )
| ( ( big_g @ SV4 )
= $true )
| ( sK3_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(60,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(61,plain,
( ( ( ~ ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(62,plain,
! [SV2: $i,SV1: $i] :
( ( ( big_h @ SV1 @ SV2 )
= $false )
| ( ( big_f @ SV1 )
= $false )
| ( ( big_f @ SV2 )
= $false )
| ( ( ~ ( big_j @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( ! [SX1: $i] : ( big_f @ SX1 )
| ~ ( big_f @ SV5 ) )
= $true )
| ( ( big_g @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV6: $i] :
( ( ( ! [SY12: $i] : ( big_h @ SY12 @ SV6 )
| ~ ( big_f @ SV6 ) )
= $true )
| ( ( big_g @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV3: $i,SV7: $i] :
( ( ( big_g @ SV7 )
= $false )
| ( ( ~ ( big_f @ SV3 ) )
= $true )
| ( ( big_g @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(66,plain,
( ( ( ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ( big_g @ SX0 )
| ( big_j @ sK2_X1 @ SX0 ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
( ( ( ~ ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV1: $i,SV2: $i] :
( ( ( big_j @ SV2 @ SV1 )
= $false )
| ( ( big_f @ SV2 )
= $false )
| ( ( big_f @ SV1 )
= $false )
| ( ( big_h @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV5: $i] :
( ( ( ! [SX1: $i] : ( big_f @ SX1 ) )
= $true )
| ( ( ~ ( big_f @ SV5 ) )
= $true )
| ( ( big_g @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV6: $i] :
( ( ( ! [SY12: $i] : ( big_h @ SY12 @ SV6 ) )
= $true )
| ( ( ~ ( big_f @ SV6 ) )
= $true )
| ( ( big_g @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV7: $i,SV3: $i] :
( ( ( big_f @ SV3 )
= $false )
| ( ( big_g @ SV7 )
= $false )
| ( ( big_g @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV8: $i] :
( ( ( ~ ( big_f @ SV8 )
| ( big_g @ SV8 )
| ( big_j @ sK2_X1 @ SV8 ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(73,plain,
( ( ( ~ ( big_f @ sK2_X1 )
| ~ ~ ( big_g @ sK2_X1 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV5: $i,SV9: $i] :
( ( ( big_f @ SV9 )
= $true )
| ( ( ~ ( big_f @ SV5 ) )
= $true )
| ( ( big_g @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV6: $i,SV10: $i] :
( ( ( big_h @ SV10 @ SV6 )
= $true )
| ( ( ~ ( big_f @ SV6 ) )
= $true )
| ( ( big_g @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV8: $i] :
( ( ( ~ ( big_f @ SV8 )
| ( big_g @ SV8 ) )
= $true )
| ( ( big_j @ sK2_X1 @ SV8 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(77,plain,
( ( ( ~ ( big_f @ sK2_X1 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(78,plain,
( ( ( ~ ~ ( big_g @ sK2_X1 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(79,plain,
! [SV9: $i,SV5: $i] :
( ( ( big_f @ SV5 )
= $false )
| ( ( big_f @ SV9 )
= $true )
| ( ( big_g @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV10: $i,SV6: $i] :
( ( ( big_f @ SV6 )
= $false )
| ( ( big_h @ SV10 @ SV6 )
= $true )
| ( ( big_g @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV8: $i] :
( ( ( ~ ( big_f @ SV8 ) )
= $true )
| ( ( big_g @ SV8 )
= $true )
| ( ( big_j @ sK2_X1 @ SV8 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
( ( ( big_f @ sK2_X1 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(83,plain,
( ( ( ~ ( big_g @ sK2_X1 ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(84,plain,
! [SV8: $i] :
( ( ( big_f @ SV8 )
= $false )
| ( ( big_g @ SV8 )
= $true )
| ( ( big_j @ sK2_X1 @ SV8 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
( ( ( big_g @ sK2_X1 )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(86,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,85,84,82,80,79,71,68,59,25]) ).
thf(87,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN070+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 20:54:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 3
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.20/0.40
% 0.20/0.40 ********************************
% 0.20/0.40 * All subproblems solved! *
% 0.20/0.40 ********************************
% 0.20/0.40 % SZS status Theorem for /export/starexec/sandbox/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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:86,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.40
% 0.20/0.40 %**** Beginning of derivation protocol ****
% 0.20/0.40 % SZS output start CNFRefutation
% See solution above
% 0.20/0.40
% 0.20/0.40 %**** End of derivation protocol ****
% 0.20/0.40 %**** no. of clauses in derivation: 87 ****
% 0.20/0.40 %**** clause counter: 86 ****
% 0.20/0.40
% 0.20/0.40 % SZS status Theorem for /export/starexec/sandbox/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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:86,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------