TSTP Solution File: ALG040+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 17:23:12 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 111 ( 59 unt; 8 typ; 0 def)
% Number of atoms : 654 ( 244 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 1256 ( 212 ~; 178 |; 32 &; 781 @)
% ( 0 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 211 ( 0 ^ 207 !; 4 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_h,type,
h: $i > $i ).
thf(tp_j,type,
j: $i > $i ).
thf(tp_op1,type,
op1: $i > $i > $i ).
thf(tp_op2,type,
op2: $i > $i > $i ).
thf(tp_sK1_V,type,
sK1_V: $i > $i ).
thf(tp_sK2_U,type,
sK2_U: $i ).
thf(tp_sorti1,type,
sorti1: $i > $o ).
thf(tp_sorti2,type,
sorti2: $i > $o ).
thf(1,axiom,
~ ? [U: $i] :
( ( sorti2 @ U )
& ! [V: $i] :
( ( sorti2 @ V )
=> ( ( op2 @ V @ V )
= U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(2,axiom,
? [U: $i] :
( ( sorti1 @ U )
& ! [V: $i] :
( ( sorti1 @ V )
=> ( ( op1 @ V @ V )
= U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(3,axiom,
! [U: $i] :
( ( sorti2 @ U )
=> ! [V: $i] :
( ( sorti2 @ V )
=> ( sorti2 @ ( op2 @ U @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(4,axiom,
! [U: $i] :
( ( sorti1 @ U )
=> ! [V: $i] :
( ( sorti1 @ V )
=> ( sorti1 @ ( op1 @ U @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(5,conjecture,
( ( ! [U: $i] :
( ( sorti1 @ U )
=> ( sorti2 @ ( h @ U ) ) )
& ! [V: $i] :
( ( sorti2 @ V )
=> ( sorti1 @ ( j @ V ) ) ) )
=> ~ ( ! [W: $i] :
( ( sorti1 @ W )
=> ! [X: $i] :
( ( sorti1 @ X )
=> ( ( h @ ( op1 @ W @ X ) )
= ( op2 @ ( h @ W ) @ ( h @ X ) ) ) ) )
& ! [Y: $i] :
( ( sorti2 @ Y )
=> ! [Z: $i] :
( ( sorti2 @ Z )
=> ( ( j @ ( op2 @ Y @ Z ) )
= ( op1 @ ( j @ Y ) @ ( j @ Z ) ) ) ) )
& ! [X1: $i] :
( ( sorti2 @ X1 )
=> ( ( h @ ( j @ X1 ) )
= X1 ) )
& ! [X2: $i] :
( ( sorti1 @ X2 )
=> ( ( j @ ( h @ X2 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(6,negated_conjecture,
( ( ( ! [U: $i] :
( ( sorti1 @ U )
=> ( sorti2 @ ( h @ U ) ) )
& ! [V: $i] :
( ( sorti2 @ V )
=> ( sorti1 @ ( j @ V ) ) ) )
=> ~ ( ! [W: $i] :
( ( sorti1 @ W )
=> ! [X: $i] :
( ( sorti1 @ X )
=> ( ( h @ ( op1 @ W @ X ) )
= ( op2 @ ( h @ W ) @ ( h @ X ) ) ) ) )
& ! [Y: $i] :
( ( sorti2 @ Y )
=> ! [Z: $i] :
( ( sorti2 @ Z )
=> ( ( j @ ( op2 @ Y @ Z ) )
= ( op1 @ ( j @ Y ) @ ( j @ Z ) ) ) ) )
& ! [X1: $i] :
( ( sorti2 @ X1 )
=> ( ( h @ ( j @ X1 ) )
= X1 ) )
& ! [X2: $i] :
( ( sorti1 @ X2 )
=> ( ( j @ ( h @ X2 ) )
= X2 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ( ! [U: $i] :
( ( sorti1 @ U )
=> ( sorti2 @ ( h @ U ) ) )
& ! [V: $i] :
( ( sorti2 @ V )
=> ( sorti1 @ ( j @ V ) ) ) )
=> ~ ( ! [W: $i] :
( ( sorti1 @ W )
=> ! [X: $i] :
( ( sorti1 @ X )
=> ( ( h @ ( op1 @ W @ X ) )
= ( op2 @ ( h @ W ) @ ( h @ X ) ) ) ) )
& ! [Y: $i] :
( ( sorti2 @ Y )
=> ! [Z: $i] :
( ( sorti2 @ Z )
=> ( ( j @ ( op2 @ Y @ Z ) )
= ( op1 @ ( j @ Y ) @ ( j @ Z ) ) ) ) )
& ! [X1: $i] :
( ( sorti2 @ X1 )
=> ( ( h @ ( j @ X1 ) )
= X1 ) )
& ! [X2: $i] :
( ( sorti1 @ X2 )
=> ( ( j @ ( h @ X2 ) )
= X2 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ? [U: $i] :
( ( sorti2 @ U )
& ! [V: $i] :
( ( sorti2 @ V )
=> ( ( op2 @ V @ V )
= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ? [U: $i] :
( ( sorti1 @ U )
& ! [V: $i] :
( ( sorti1 @ V )
=> ( ( op1 @ V @ V )
= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [U: $i] :
( ( sorti2 @ U )
=> ! [V: $i] :
( ( sorti2 @ V )
=> ( sorti2 @ ( op2 @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [U: $i] :
( ( sorti1 @ U )
=> ! [V: $i] :
( ( sorti1 @ V )
=> ( sorti1 @ ( op1 @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [U: $i] :
( ( sorti1 @ U )
=> ( sorti2 @ ( h @ U ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [V: $i] :
( ( sorti2 @ V )
=> ( sorti1 @ ( j @ V ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ ( ! [W: $i] :
( ( sorti1 @ W )
=> ! [X: $i] :
( ( sorti1 @ X )
=> ( ( h @ ( op1 @ W @ X ) )
= ( op2 @ ( h @ W ) @ ( h @ X ) ) ) ) )
& ! [Y: $i] :
( ( sorti2 @ Y )
=> ! [Z: $i] :
( ( sorti2 @ Z )
=> ( ( j @ ( op2 @ Y @ Z ) )
= ( op1 @ ( j @ Y ) @ ( j @ Z ) ) ) ) )
& ! [X1: $i] :
( ( sorti2 @ X1 )
=> ( ( h @ ( j @ X1 ) )
= X1 ) )
& ! [X2: $i] :
( ( sorti1 @ X2 )
=> ( ( j @ ( h @ X2 ) )
= X2 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(15,plain,
( ( ! [W: $i] :
( ( sorti1 @ W )
=> ! [X: $i] :
( ( sorti1 @ X )
=> ( ( h @ ( op1 @ W @ X ) )
= ( op2 @ ( h @ W ) @ ( h @ X ) ) ) ) )
& ! [Y: $i] :
( ( sorti2 @ Y )
=> ! [Z: $i] :
( ( sorti2 @ Z )
=> ( ( j @ ( op2 @ Y @ Z ) )
= ( op1 @ ( j @ Y ) @ ( j @ Z ) ) ) ) )
& ! [X1: $i] :
( ( sorti2 @ X1 )
=> ( ( h @ ( j @ X1 ) )
= X1 ) )
& ! [X2: $i] :
( ( sorti1 @ X2 )
=> ( ( j @ ( h @ X2 ) )
= X2 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [X2: $i] :
( ~ ( sorti1 @ X2 )
| ( ( j @ ( h @ X2 ) )
= X2 ) )
& ! [X1: $i] :
( ~ ( sorti2 @ X1 )
| ( ( h @ ( j @ X1 ) )
= X1 ) )
& ! [W: $i] :
( ~ ( sorti1 @ W )
| ! [X: $i] :
( ~ ( sorti1 @ X )
| ( ( h @ ( op1 @ W @ X ) )
= ( op2 @ ( h @ W ) @ ( h @ X ) ) ) ) )
& ! [Y: $i] :
( ~ ( sorti2 @ Y )
| ! [Z: $i] :
( ~ ( sorti2 @ Z )
| ( ( j @ ( op2 @ Y @ Z ) )
= ( op1 @ ( j @ Y ) @ ( j @ Z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(17,plain,
( ( ! [U: $i] :
( ~ ( sorti1 @ U )
| ( sorti2 @ ( h @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(18,plain,
( ( ! [V: $i] :
( ~ ( sorti2 @ V )
| ( sorti1 @ ( j @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(19,plain,
( ( ! [U: $i] :
( ( ( sorti2 @ ( sK1_V @ U ) )
& ( ( op2 @ ( sK1_V @ U ) @ ( sK1_V @ U ) )
!= U ) )
| ~ ( sorti2 @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(20,plain,
( ( ! [SY16: $i] :
( ~ ( sorti1 @ SY16 )
| ( ( op1 @ SY16 @ SY16 )
= sK2_U ) )
& ( sorti1 @ sK2_U ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(21,plain,
( ( ! [U: $i] :
( ~ ( sorti2 @ U )
| ! [V: $i] :
( ~ ( sorti2 @ V )
| ( sorti2 @ ( op2 @ U @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(22,plain,
( ( ! [U: $i] :
( ~ ( sorti1 @ U )
| ! [V: $i] :
( ~ ( sorti1 @ V )
| ( sorti1 @ ( op1 @ U @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(23,plain,
( ( ! [U: $i] :
( ~ ( sorti1 @ U )
| ! [V: $i] :
( ~ ( sorti1 @ V )
| ( sorti1 @ ( op1 @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [U: $i] :
( ~ ( sorti2 @ U )
| ! [V: $i] :
( ~ ( sorti2 @ V )
| ( sorti2 @ ( op2 @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SY16: $i] :
( ~ ( sorti1 @ SY16 )
| ( ( op1 @ SY16 @ SY16 )
= sK2_U ) )
& ( sorti1 @ sK2_U ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [U: $i] :
( ( ( sorti2 @ ( sK1_V @ U ) )
& ( ( op2 @ ( sK1_V @ U ) @ ( sK1_V @ U ) )
!= U ) )
| ~ ( sorti2 @ U ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ! [V: $i] :
( ~ ( sorti2 @ V )
| ( sorti1 @ ( j @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( ! [U: $i] :
( ~ ( sorti1 @ U )
| ( sorti2 @ ( h @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( ! [X2: $i] :
( ~ ( sorti1 @ X2 )
| ( ( j @ ( h @ X2 ) )
= X2 ) )
& ! [X1: $i] :
( ~ ( sorti2 @ X1 )
| ( ( h @ ( j @ X1 ) )
= X1 ) )
& ! [W: $i] :
( ~ ( sorti1 @ W )
| ! [X: $i] :
( ~ ( sorti1 @ X )
| ( ( h @ ( op1 @ W @ X ) )
= ( op2 @ ( h @ W ) @ ( h @ X ) ) ) ) )
& ! [Y: $i] :
( ~ ( sorti2 @ Y )
| ! [Z: $i] :
( ~ ( sorti2 @ Z )
| ( ( j @ ( op2 @ Y @ Z ) )
= ( op1 @ ( j @ Y ) @ ( j @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(30,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ( ( j @ ( h @ SX0 ) )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ( ( h @ ( j @ SX0 ) )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(31,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( sorti2 @ ( sK1_V @ SX0 ) )
| ~ ( ( ( op2 @ ( sK1_V @ SX0 ) @ ( sK1_V @ SX0 ) )
!= SX0 ) ) )
| ~ ( sorti2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ( ( op1 @ SX0 @ SX0 )
= sK2_U ) )
| ~ ( sorti1 @ sK2_U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(33,plain,
! [SV1: $i] :
( ( ~ ( sorti1 @ SV1 )
| ! [SY17: $i] :
( ~ ( sorti1 @ SY17 )
| ( sorti1 @ ( op1 @ SV1 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(34,plain,
! [SV2: $i] :
( ( ~ ( sorti2 @ SV2 )
| ! [SY18: $i] :
( ~ ( sorti2 @ SY18 )
| ( sorti2 @ ( op2 @ SV2 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(35,plain,
! [SV3: $i] :
( ( ~ ( sorti2 @ SV3 )
| ( sorti1 @ ( j @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
! [SV4: $i] :
( ( ~ ( sorti1 @ SV4 )
| ( sorti2 @ ( h @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ( ( j @ ( h @ SX0 ) )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ( ( h @ ( j @ SX0 ) )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV5: $i] :
( ( ~ ( ~ ( sorti2 @ ( sK1_V @ SV5 ) )
| ~ ( ( ( op2 @ ( sK1_V @ SV5 ) @ ( sK1_V @ SV5 ) )
!= SV5 ) ) )
| ~ ( sorti2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ( ( op1 @ SX0 @ SX0 )
= sK2_U ) )
| ~ ( sorti1 @ sK2_U ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV1: $i] :
( ( ( ~ ( sorti1 @ SV1 ) )
= $true )
| ( ( ! [SY17: $i] :
( ~ ( sorti1 @ SY17 )
| ( sorti1 @ ( op1 @ SV1 @ SY17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( ~ ( sorti2 @ SV2 ) )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( sorti2 @ SY18 )
| ( sorti2 @ ( op2 @ SV2 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV3: $i] :
( ( ( ~ ( sorti2 @ SV3 ) )
= $true )
| ( ( sorti1 @ ( j @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV4: $i] :
( ( ( ~ ( sorti1 @ SV4 ) )
= $true )
| ( ( sorti2 @ ( h @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(44,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ( ( j @ ( h @ SX0 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(45,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ( ( h @ ( j @ SX0 ) )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(46,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( sorti2 @ ( sK1_V @ SV5 ) )
| ~ ( ( ( op2 @ ( sK1_V @ SV5 ) @ ( sK1_V @ SV5 ) )
!= SV5 ) ) ) )
= $true )
| ( ( ~ ( sorti2 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(47,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ( ( op1 @ SX0 @ SX0 )
= sK2_U ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(48,plain,
( ( ~ ( sorti1 @ sK2_U ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(49,plain,
! [SV1: $i] :
( ( ( sorti1 @ SV1 )
= $false )
| ( ( ! [SY17: $i] :
( ~ ( sorti1 @ SY17 )
| ( sorti1 @ ( op1 @ SV1 @ SY17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV2: $i] :
( ( ( sorti2 @ SV2 )
= $false )
| ( ( ! [SY18: $i] :
( ~ ( sorti2 @ SY18 )
| ( sorti2 @ ( op2 @ SV2 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV3: $i] :
( ( ( sorti2 @ SV3 )
= $false )
| ( ( sorti1 @ ( j @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( sorti1 @ SV4 )
= $false )
| ( ( sorti2 @ ( h @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(53,plain,
( ( ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ( ( j @ ( h @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(54,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ( ( h @ ( j @ SX0 ) )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(55,plain,
! [SV5: $i] :
( ( ( ~ ( sorti2 @ ( sK1_V @ SV5 ) )
| ~ ( ( ( op2 @ ( sK1_V @ SV5 ) @ ( sK1_V @ SV5 ) )
!= SV5 ) ) )
= $false )
| ( ( ~ ( sorti2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(56,plain,
( ( ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ( ( op1 @ SX0 @ SX0 )
= sK2_U ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(57,plain,
( ( sorti1 @ sK2_U )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(58,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ( sorti1 @ SV6 )
| ( sorti1 @ ( op1 @ SV1 @ SV6 ) ) )
= $true )
| ( ( sorti1 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( sorti2 @ SV7 )
| ( sorti2 @ ( op2 @ SV2 @ SV7 ) ) )
= $true )
| ( ( sorti2 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV8: $i] :
( ( ~ ( sorti1 @ SV8 )
| ( ( j @ ( h @ SV8 ) )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(61,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ( ( h @ ( j @ SX0 ) )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV5: $i] :
( ( ( ~ ( sorti2 @ ( sK1_V @ SV5 ) ) )
= $false )
| ( ( ~ ( sorti2 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( ~ ( ( ( op2 @ ( sK1_V @ SV5 ) @ ( sK1_V @ SV5 ) )
!= SV5 ) ) )
= $false )
| ( ( ~ ( sorti2 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(64,plain,
! [SV9: $i] :
( ( ~ ( sorti1 @ SV9 )
| ( ( op1 @ SV9 @ SV9 )
= sK2_U ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ( sorti1 @ SV6 ) )
= $true )
| ( ( sorti1 @ ( op1 @ SV1 @ SV6 ) )
= $true )
| ( ( sorti1 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( sorti2 @ SV7 ) )
= $true )
| ( ( sorti2 @ ( op2 @ SV2 @ SV7 ) )
= $true )
| ( ( sorti2 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV8: $i] :
( ( ( ~ ( sorti1 @ SV8 ) )
= $true )
| ( ( ( j @ ( h @ SV8 ) )
= SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(68,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ( ( h @ ( j @ SX0 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(70,plain,
! [SV5: $i] :
( ( ( sorti2 @ ( sK1_V @ SV5 ) )
= $true )
| ( ( ~ ( sorti2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(71,plain,
! [SV5: $i] :
( ( ( ( ( op2 @ ( sK1_V @ SV5 ) @ ( sK1_V @ SV5 ) )
!= SV5 ) )
= $true )
| ( ( ~ ( sorti2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(72,plain,
! [SV9: $i] :
( ( ( ~ ( sorti1 @ SV9 ) )
= $true )
| ( ( ( op1 @ SV9 @ SV9 )
= sK2_U )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV1: $i,SV6: $i] :
( ( ( sorti1 @ SV6 )
= $false )
| ( ( sorti1 @ ( op1 @ SV1 @ SV6 ) )
= $true )
| ( ( sorti1 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV2: $i,SV7: $i] :
( ( ( sorti2 @ SV7 )
= $false )
| ( ( sorti2 @ ( op2 @ SV2 @ SV7 ) )
= $true )
| ( ( sorti2 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV8: $i] :
( ( ( sorti1 @ SV8 )
= $false )
| ( ( ( j @ ( h @ SV8 ) )
= SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ( ( h @ ( j @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(77,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(78,plain,
! [SV5: $i] :
( ( ( sorti2 @ SV5 )
= $false )
| ( ( sorti2 @ ( sK1_V @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV5: $i] :
( ( ( ( op2 @ ( sK1_V @ SV5 ) @ ( sK1_V @ SV5 ) )
= SV5 )
= $false )
| ( ( ~ ( sorti2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV9: $i] :
( ( ( sorti1 @ SV9 )
= $false )
| ( ( ( op1 @ SV9 @ SV9 )
= sK2_U )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV10: $i] :
( ( ~ ( sorti2 @ SV10 )
| ( ( h @ ( j @ SV10 ) )
= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(82,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV5: $i] :
( ( ( sorti2 @ SV5 )
= $false )
| ( ( ( op2 @ ( sK1_V @ SV5 ) @ ( sK1_V @ SV5 ) )
= SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV10: $i] :
( ( ( ~ ( sorti2 @ SV10 ) )
= $true )
| ( ( ( h @ ( j @ SV10 ) )
= SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(85,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(86,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV10: $i] :
( ( ( sorti2 @ SV10 )
= $false )
| ( ( ( h @ ( j @ SV10 ) )
= SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(88,plain,
( ( ! [SX0: $i] :
( ~ ( sorti1 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti1 @ SX1 )
| ( ( h @ ( op1 @ SX0 @ SX1 ) )
= ( op2 @ ( h @ SX0 ) @ ( h @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(89,plain,
( ( ! [SX0: $i] :
( ~ ( sorti2 @ SX0 )
| ! [SX1: $i] :
( ~ ( sorti2 @ SX1 )
| ( ( j @ ( op2 @ SX0 @ SX1 ) )
= ( op1 @ ( j @ SX0 ) @ ( j @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(90,plain,
! [SV11: $i] :
( ( ~ ( sorti1 @ SV11 )
| ! [SY19: $i] :
( ~ ( sorti1 @ SY19 )
| ( ( h @ ( op1 @ SV11 @ SY19 ) )
= ( op2 @ ( h @ SV11 ) @ ( h @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV12: $i] :
( ( ~ ( sorti2 @ SV12 )
| ! [SY20: $i] :
( ~ ( sorti2 @ SY20 )
| ( ( j @ ( op2 @ SV12 @ SY20 ) )
= ( op1 @ ( j @ SV12 ) @ ( j @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV11: $i] :
( ( ( ~ ( sorti1 @ SV11 ) )
= $true )
| ( ( ! [SY19: $i] :
( ~ ( sorti1 @ SY19 )
| ( ( h @ ( op1 @ SV11 @ SY19 ) )
= ( op2 @ ( h @ SV11 ) @ ( h @ SY19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV12: $i] :
( ( ( ~ ( sorti2 @ SV12 ) )
= $true )
| ( ( ! [SY20: $i] :
( ~ ( sorti2 @ SY20 )
| ( ( j @ ( op2 @ SV12 @ SY20 ) )
= ( op1 @ ( j @ SV12 ) @ ( j @ SY20 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV11: $i] :
( ( ( sorti1 @ SV11 )
= $false )
| ( ( ! [SY19: $i] :
( ~ ( sorti1 @ SY19 )
| ( ( h @ ( op1 @ SV11 @ SY19 ) )
= ( op2 @ ( h @ SV11 ) @ ( h @ SY19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV12: $i] :
( ( ( sorti2 @ SV12 )
= $false )
| ( ( ! [SY20: $i] :
( ~ ( sorti2 @ SY20 )
| ( ( j @ ( op2 @ SV12 @ SY20 ) )
= ( op1 @ ( j @ SV12 ) @ ( j @ SY20 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(96,plain,
! [SV11: $i,SV13: $i] :
( ( ( ~ ( sorti1 @ SV13 )
| ( ( h @ ( op1 @ SV11 @ SV13 ) )
= ( op2 @ ( h @ SV11 ) @ ( h @ SV13 ) ) ) )
= $true )
| ( ( sorti1 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV12: $i,SV14: $i] :
( ( ( ~ ( sorti2 @ SV14 )
| ( ( j @ ( op2 @ SV12 @ SV14 ) )
= ( op1 @ ( j @ SV12 ) @ ( j @ SV14 ) ) ) )
= $true )
| ( ( sorti2 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(98,plain,
! [SV11: $i,SV13: $i] :
( ( ( ~ ( sorti1 @ SV13 ) )
= $true )
| ( ( ( h @ ( op1 @ SV11 @ SV13 ) )
= ( op2 @ ( h @ SV11 ) @ ( h @ SV13 ) ) )
= $true )
| ( ( sorti1 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(99,plain,
! [SV12: $i,SV14: $i] :
( ( ( ~ ( sorti2 @ SV14 ) )
= $true )
| ( ( ( j @ ( op2 @ SV12 @ SV14 ) )
= ( op1 @ ( j @ SV12 ) @ ( j @ SV14 ) ) )
= $true )
| ( ( sorti2 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(100,plain,
! [SV11: $i,SV13: $i] :
( ( ( sorti1 @ SV13 )
= $false )
| ( ( ( h @ ( op1 @ SV11 @ SV13 ) )
= ( op2 @ ( h @ SV11 ) @ ( h @ SV13 ) ) )
= $true )
| ( ( sorti1 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(101,plain,
! [SV12: $i,SV14: $i] :
( ( ( sorti2 @ SV14 )
= $false )
| ( ( ( j @ ( op2 @ SV12 @ SV14 ) )
= ( op1 @ ( j @ SV12 ) @ ( j @ SV14 ) ) )
= $true )
| ( ( sorti2 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(102,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,101,100,87,83,80,78,75,74,73,57,52]) ).
thf(103,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n022.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 : Wed Jun 8 01:43:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 4
% 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: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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.18/0.41
% 0.18/0.41 ********************************
% 0.18/0.41 * All subproblems solved! *
% 0.18/0.41 ********************************
% 0.18/0.41 % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:102,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.41
% 0.18/0.41 %**** Beginning of derivation protocol ****
% 0.18/0.41 % SZS output start CNFRefutation
% See solution above
% 0.18/0.41
% 0.18/0.41 %**** End of derivation protocol ****
% 0.18/0.41 %**** no. of clauses in derivation: 103 ****
% 0.18/0.41 %**** clause counter: 102 ****
% 0.18/0.41
% 0.18/0.41 % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:102,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------