%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU444+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:27 AM UTC 2026
% Result : Theorem 0.70s 0.43s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 157 ( 122 unt; 0 typ; 0 def)
% Number of atoms : 640 ( 254 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1569 ( 158 ~; 106 |; 11 &;1272 @)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 6 con; 0-4 aty)
% Number of variables : 320 ( 0 ^; 316 !; 4 ?; 320 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_k10_relset_1,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(tp_k1_funct_5,type,
k1_funct_5: $i > $i ).
thf(tp_k1_xboole_0,type,
k1_xboole_0: $i ).
thf(tp_k1_zfmisc_1,type,
k1_zfmisc_1: $i > $i ).
thf(tp_k2_funct_5,type,
k2_funct_5: $i > $i ).
thf(tp_k2_zfmisc_1,type,
k2_zfmisc_1: $i > $i > $i ).
thf(tp_k4_relat_1,type,
k4_relat_1: $i > $i ).
thf(tp_k6_relset_1,type,
k6_relset_1: $i > $i > $i > $i ).
thf(tp_k9_relat_1,type,
k9_relat_1: $i > $i > $i ).
thf(tp_m1_relset_1,type,
m1_relset_1: $i > $i > $i > $o ).
thf(tp_m1_subset_1,type,
m1_subset_1: $i > $i > $o ).
thf(tp_m2_relset_1,type,
m2_relset_1: $i > $i > $i > $o ).
thf(tp_r1_tarski,type,
r1_tarski: $i > $i > $o ).
thf(tp_r2_hidden,type,
r2_hidden: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i ).
thf(tp_sK3_SY20,type,
sK3_SY20: $i ).
thf(tp_sK4_SY32,type,
sK4_SY32: $i > $i > $i ).
thf(tp_sK5_SY46,type,
sK5_SY46: $i > $i > $i ).
thf(tp_v1_relat_1,type,
v1_relat_1: $i > $o ).
thf(tp_v1_xboole_0,type,
v1_xboole_0: $i > $o ).
thf(tp_v3_relat_1,type,
v3_relat_1: $i > $o ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k1_funct_5 @ C )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ A ) )
& ( ( k2_funct_5 @ C )
= ( k10_relset_1 @ B @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relset_2) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ ( k6_relset_1 @ A @ B @ C ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_1) ).
thf(4,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_5) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_5) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k6_relset_1) ).
thf(16,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(17,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(18,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(42,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(45,conjecture,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k1_funct_5 @ C )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ A ) )
& ( ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ ( k2_funct_5 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relset_2) ).
thf(46,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k1_funct_5 @ C )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ A ) )
& ( ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ ( k2_funct_5 @ C ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[45]) ).
thf(47,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k1_funct_5 @ C )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ A ) )
& ( ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ ( k2_funct_5 @ C ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[46]) ).
thf(48,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k1_funct_5 @ C )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ A ) )
& ( ( k2_funct_5 @ C )
= ( k10_relset_1 @ B @ A @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(49,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ ( k6_relset_1 @ A @ B @ C ) @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(50,plain,
$true = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(51,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(52,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
= C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(55,plain,
$true = $true,
inference(unfold_def,[status(thm)],[16]) ).
thf(56,plain,
$true = $true,
inference(unfold_def,[status(thm)],[17]) ).
thf(57,plain,
$true = $true,
inference(unfold_def,[status(thm)],[18]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[42]) ).
thf(61,plain,
( ( ! [SY18: $i,SY19: $i] :
( ( m2_relset_1 @ SY19 @ SY18 @ sK1_A )
=> ( ( ( k1_funct_5 @ SY19 )
= ( k10_relset_1 @ sK1_A @ SY18 @ ( k6_relset_1 @ SY18 @ sK1_A @ SY19 ) @ sK1_A ) )
& ( ( k10_relset_1 @ sK1_A @ SY18 @ ( k6_relset_1 @ SY18 @ sK1_A @ SY19 ) @ ( k10_relset_1 @ SY18 @ sK1_A @ SY19 @ SY18 ) )
= ( k10_relset_1 @ sK1_A @ SY18 @ ( k6_relset_1 @ SY18 @ sK1_A @ SY19 ) @ ( k2_funct_5 @ SY19 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[47]) ).
thf(62,plain,
( ( ! [SY20: $i] :
( ( m2_relset_1 @ SY20 @ sK2_SY18 @ sK1_A )
=> ( ( ( k1_funct_5 @ SY20 )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ SY20 ) @ sK1_A ) )
& ( ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ SY20 ) @ ( k10_relset_1 @ sK2_SY18 @ sK1_A @ SY20 @ sK2_SY18 ) )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ SY20 ) @ ( k2_funct_5 @ SY20 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(63,plain,
( ( ( m2_relset_1 @ sK3_SY20 @ sK2_SY18 @ sK1_A )
=> ( ( ( k1_funct_5 @ sK3_SY20 )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ sK1_A ) )
& ( ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k10_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 @ sK2_SY18 ) )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k2_funct_5 @ sK3_SY20 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(64,plain,
( ( m2_relset_1 @ sK3_SY20 @ sK2_SY18 @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[63]) ).
thf(65,plain,
( ( ( ( k1_funct_5 @ sK3_SY20 )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ sK1_A ) )
& ( ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k10_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 @ sK2_SY18 ) )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k2_funct_5 @ sK3_SY20 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[63]) ).
thf(66,plain,
( ( ( k1_funct_5 @ sK3_SY20 )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[65]) ).
thf(67,plain,
( ( ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k10_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 @ sK2_SY18 ) )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k2_funct_5 @ sK3_SY20 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[65]) ).
thf(68,plain,
( ( ( k1_funct_5 @ sK3_SY20 )
!= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[66]) ).
thf(69,plain,
( ( ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k10_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 @ sK2_SY18 ) )
!= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k2_funct_5 @ sK3_SY20 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[67]) ).
thf(70,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(71,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(72,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(73,plain,
$true = $true,
inference(copy,[status(thm)],[57]) ).
thf(74,plain,
$true = $true,
inference(copy,[status(thm)],[56]) ).
thf(75,plain,
$true = $true,
inference(copy,[status(thm)],[55]) ).
thf(76,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
= C ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(78,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(79,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(80,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(81,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ ( k6_relset_1 @ A @ B @ C ) @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(82,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k1_funct_5 @ C )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ A ) )
& ( ( k2_funct_5 @ C )
= ( k10_relset_1 @ B @ A @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(83,plain,
( ( m2_relset_1 @ sK3_SY20 @ sK2_SY18 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(84,plain,
( ( ( k1_funct_5 @ sK3_SY20 )
!= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m1_relset_1 @ SX2 @ SX0 @ SX1 )
| ( ( k6_relset_1 @ SX0 @ SX1 @ ( k6_relset_1 @ SX0 @ SX1 @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ( m2_relset_1 @ SX2 @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m1_relset_1 @ SX2 @ SX0 @ SX1 )
| ( m2_relset_1 @ ( k6_relset_1 @ SX0 @ SX1 @ SX2 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( m2_relset_1 @ SX2 @ SX0 @ SX1 )
| ( m1_relset_1 @ SX2 @ SX0 @ SX1 ) )
| ~ ( ~ ( m1_relset_1 @ SX2 @ SX0 @ SX1 )
| ( m2_relset_1 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m2_relset_1 @ SX2 @ SX1 @ SX0 )
| ~ ( ( ( k1_funct_5 @ SX2 )
!= ( k10_relset_1 @ SX0 @ SX1 @ ( k6_relset_1 @ SX1 @ SX0 @ SX2 ) @ SX0 ) )
| ( ( k2_funct_5 @ SX2 )
!= ( k10_relset_1 @ SX1 @ SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(90,plain,
( ( ( k1_funct_5 @ sK3_SY20 )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV1: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( m1_relset_1 @ SY22 @ SV1 @ SY21 )
| ( ( k6_relset_1 @ SV1 @ SY21 @ ( k6_relset_1 @ SV1 @ SY21 @ SY22 ) )
= SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV2: $i] :
( ( ! [SY23: $i] :
~ ! [SY24: $i] :
~ ( m2_relset_1 @ SY24 @ SV2 @ SY23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV3: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( m1_relset_1 @ SY26 @ SV3 @ SY25 )
| ( m2_relset_1 @ ( k6_relset_1 @ SV3 @ SY25 @ SY26 ) @ SY25 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV4: $i] :
( ( ! [SY27: $i,SY28: $i] :
~ ( ~ ( ~ ( m2_relset_1 @ SY28 @ SV4 @ SY27 )
| ( m1_relset_1 @ SY28 @ SV4 @ SY27 ) )
| ~ ( ~ ( m1_relset_1 @ SY28 @ SV4 @ SY27 )
| ( m2_relset_1 @ SY28 @ SV4 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV5: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( m2_relset_1 @ SY30 @ SY29 @ SV5 )
| ~ ( ( ( k1_funct_5 @ SY30 )
!= ( k10_relset_1 @ SV5 @ SY29 @ ( k6_relset_1 @ SY29 @ SV5 @ SY30 ) @ SV5 ) )
| ( ( k2_funct_5 @ SY30 )
!= ( k10_relset_1 @ SY29 @ SV5 @ SY30 @ SY29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY31: $i] :
( ~ ( m1_relset_1 @ SY31 @ SV1 @ SV6 )
| ( ( k6_relset_1 @ SV1 @ SV6 @ ( k6_relset_1 @ SV1 @ SV6 @ SY31 ) )
= SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ! [SY32: $i] :
~ ( m2_relset_1 @ SY32 @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY33: $i] :
( ~ ( m1_relset_1 @ SY33 @ SV3 @ SV8 )
| ( m2_relset_1 @ ( k6_relset_1 @ SV3 @ SV8 @ SY33 ) @ SV8 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY34: $i] :
~ ( ~ ( ~ ( m2_relset_1 @ SY34 @ SV4 @ SV9 )
| ( m1_relset_1 @ SY34 @ SV4 @ SV9 ) )
| ~ ( ~ ( m1_relset_1 @ SY34 @ SV4 @ SV9 )
| ( m2_relset_1 @ SY34 @ SV4 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV5: $i,SV10: $i] :
( ( ! [SY35: $i] :
( ~ ( m2_relset_1 @ SY35 @ SV10 @ SV5 )
| ~ ( ( ( k1_funct_5 @ SY35 )
!= ( k10_relset_1 @ SV5 @ SV10 @ ( k6_relset_1 @ SV10 @ SV5 @ SY35 ) @ SV5 ) )
| ( ( k2_funct_5 @ SY35 )
!= ( k10_relset_1 @ SV10 @ SV5 @ SY35 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV6: $i,SV1: $i,SV11: $i] :
( ( ~ ( m1_relset_1 @ SV11 @ SV1 @ SV6 )
| ( ( k6_relset_1 @ SV1 @ SV6 @ ( k6_relset_1 @ SV1 @ SV6 @ SV11 ) )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY32: $i] :
~ ( m2_relset_1 @ SY32 @ SV2 @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ~ ( m1_relset_1 @ SV12 @ SV3 @ SV8 )
| ( m2_relset_1 @ ( k6_relset_1 @ SV3 @ SV8 @ SV12 ) @ SV8 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( m2_relset_1 @ SV13 @ SV4 @ SV9 )
| ( m1_relset_1 @ SV13 @ SV4 @ SV9 ) )
| ~ ( ~ ( m1_relset_1 @ SV13 @ SV4 @ SV9 )
| ( m2_relset_1 @ SV13 @ SV4 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV5: $i,SV10: $i,SV14: $i] :
( ( ~ ( m2_relset_1 @ SV14 @ SV10 @ SV5 )
| ~ ( ( ( k1_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV5 @ SV10 @ ( k6_relset_1 @ SV10 @ SV5 @ SV14 ) @ SV5 ) )
| ( ( k2_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV10 @ SV5 @ SV14 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV6: $i,SV1: $i,SV11: $i] :
( ( ( ~ ( m1_relset_1 @ SV11 @ SV1 @ SV6 ) )
= $true )
| ( ( ( k6_relset_1 @ SV1 @ SV6 @ ( k6_relset_1 @ SV1 @ SV6 @ SV11 ) )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( m2_relset_1 @ ( sK4_SY32 @ SV7 @ SV2 ) @ SV2 @ SV7 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[102]) ).
thf(108,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( m1_relset_1 @ SV12 @ SV3 @ SV8 ) )
= $true )
| ( ( m2_relset_1 @ ( k6_relset_1 @ SV3 @ SV8 @ SV12 ) @ SV8 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ~ ( ~ ( m2_relset_1 @ SV13 @ SV4 @ SV9 )
| ( m1_relset_1 @ SV13 @ SV4 @ SV9 ) )
| ~ ( ~ ( m1_relset_1 @ SV13 @ SV4 @ SV9 )
| ( m2_relset_1 @ SV13 @ SV4 @ SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV5: $i,SV10: $i,SV14: $i] :
( ( ( ~ ( m2_relset_1 @ SV14 @ SV10 @ SV5 ) )
= $true )
| ( ( ~ ( ( ( k1_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV5 @ SV10 @ ( k6_relset_1 @ SV10 @ SV5 @ SV14 ) @ SV5 ) )
| ( ( k2_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV10 @ SV5 @ SV14 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV6: $i,SV1: $i,SV11: $i] :
( ( ( m1_relset_1 @ SV11 @ SV1 @ SV6 )
= $false )
| ( ( ( k6_relset_1 @ SV1 @ SV6 @ ( k6_relset_1 @ SV1 @ SV6 @ SV11 ) )
= SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV2: $i,SV7: $i] :
( ( m2_relset_1 @ ( sK4_SY32 @ SV7 @ SV2 ) @ SV2 @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(113,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( m1_relset_1 @ SV12 @ SV3 @ SV8 )
= $false )
| ( ( m2_relset_1 @ ( k6_relset_1 @ SV3 @ SV8 @ SV12 ) @ SV8 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ~ ( ~ ( m2_relset_1 @ SV13 @ SV4 @ SV9 )
| ( m1_relset_1 @ SV13 @ SV4 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(115,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ~ ( ~ ( m1_relset_1 @ SV13 @ SV4 @ SV9 )
| ( m2_relset_1 @ SV13 @ SV4 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(116,plain,
! [SV5: $i,SV10: $i,SV14: $i] :
( ( ( m2_relset_1 @ SV14 @ SV10 @ SV5 )
= $false )
| ( ( ~ ( ( ( k1_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV5 @ SV10 @ ( k6_relset_1 @ SV10 @ SV5 @ SV14 ) @ SV5 ) )
| ( ( k2_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV10 @ SV5 @ SV14 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(117,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ~ ( m2_relset_1 @ SV13 @ SV4 @ SV9 )
| ( m1_relset_1 @ SV13 @ SV4 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(118,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ~ ( m1_relset_1 @ SV13 @ SV4 @ SV9 )
| ( m2_relset_1 @ SV13 @ SV4 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(119,plain,
! [SV10: $i,SV5: $i,SV14: $i] :
( ( ( ( ( k1_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV5 @ SV10 @ ( k6_relset_1 @ SV10 @ SV5 @ SV14 ) @ SV5 ) )
| ( ( k2_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV10 @ SV5 @ SV14 @ SV10 ) ) )
= $false )
| ( ( m2_relset_1 @ SV14 @ SV10 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(120,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( m2_relset_1 @ SV13 @ SV4 @ SV9 ) )
= $true )
| ( ( m1_relset_1 @ SV13 @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(121,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( m1_relset_1 @ SV13 @ SV4 @ SV9 ) )
= $true )
| ( ( m2_relset_1 @ SV13 @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(122,plain,
! [SV10: $i,SV5: $i,SV14: $i] :
( ( ( ( k1_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV5 @ SV10 @ ( k6_relset_1 @ SV10 @ SV5 @ SV14 ) @ SV5 ) )
= $false )
| ( ( m2_relset_1 @ SV14 @ SV10 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(123,plain,
! [SV5: $i,SV10: $i,SV14: $i] :
( ( ( ( k2_funct_5 @ SV14 )
!= ( k10_relset_1 @ SV10 @ SV5 @ SV14 @ SV10 ) )
= $false )
| ( ( m2_relset_1 @ SV14 @ SV10 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ( m2_relset_1 @ SV13 @ SV4 @ SV9 )
= $false )
| ( ( m1_relset_1 @ SV13 @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV9: $i,SV4: $i,SV13: $i] :
( ( ( m1_relset_1 @ SV13 @ SV4 @ SV9 )
= $false )
| ( ( m2_relset_1 @ SV13 @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV10: $i,SV5: $i,SV14: $i] :
( ( ( ( k1_funct_5 @ SV14 )
= ( k10_relset_1 @ SV5 @ SV10 @ ( k6_relset_1 @ SV10 @ SV5 @ SV14 ) @ SV5 ) )
= $true )
| ( ( m2_relset_1 @ SV14 @ SV10 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(127,plain,
! [SV5: $i,SV10: $i,SV14: $i] :
( ( ( ( k2_funct_5 @ SV14 )
= ( k10_relset_1 @ SV10 @ SV5 @ SV14 @ SV10 ) )
= $true )
| ( ( m2_relset_1 @ SV14 @ SV10 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(128,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,127,126,125,124,113,112,111,90,83,80,79,75,74,73,72,71]) ).
thf(129,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(130,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(131,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(132,plain,
$true = $true,
inference(copy,[status(thm)],[57]) ).
thf(133,plain,
$true = $true,
inference(copy,[status(thm)],[56]) ).
thf(134,plain,
$true = $true,
inference(copy,[status(thm)],[55]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
= C ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(137,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(138,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(139,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(140,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ ( k6_relset_1 @ A @ B @ C ) @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(141,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k1_funct_5 @ C )
= ( k10_relset_1 @ A @ B @ ( k6_relset_1 @ B @ A @ C ) @ A ) )
& ( ( k2_funct_5 @ C )
= ( k10_relset_1 @ B @ A @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(142,plain,
( ( m2_relset_1 @ sK3_SY20 @ sK2_SY18 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(143,plain,
( ( ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k10_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 @ sK2_SY18 ) )
!= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k2_funct_5 @ sK3_SY20 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ( m2_relset_1 @ SX2 @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( m2_relset_1 @ SX2 @ SX0 @ SX1 )
| ( m1_relset_1 @ SX2 @ SX0 @ SX1 ) )
| ~ ( ~ ( m1_relset_1 @ SX2 @ SX0 @ SX1 )
| ( m2_relset_1 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(146,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m1_relset_1 @ SX2 @ SX0 @ SX1 )
| ( ( k6_relset_1 @ SX0 @ SX1 @ ( k6_relset_1 @ SX0 @ SX1 @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m1_relset_1 @ SX2 @ SX0 @ SX1 )
| ( m2_relset_1 @ ( k6_relset_1 @ SX0 @ SX1 @ SX2 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m2_relset_1 @ SX2 @ SX1 @ SX0 )
| ~ ( ( ( k1_funct_5 @ SX2 )
!= ( k10_relset_1 @ SX0 @ SX1 @ ( k6_relset_1 @ SX1 @ SX0 @ SX2 ) @ SX0 ) )
| ( ( k2_funct_5 @ SX2 )
!= ( k10_relset_1 @ SX1 @ SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(149,plain,
( ( ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k10_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 @ sK2_SY18 ) )
= ( k10_relset_1 @ sK1_A @ sK2_SY18 @ ( k6_relset_1 @ sK2_SY18 @ sK1_A @ sK3_SY20 ) @ ( k2_funct_5 @ sK3_SY20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(150,plain,
! [SV15: $i] :
( ( ! [SY36: $i] :
~ ! [SY37: $i] :
~ ( m2_relset_1 @ SY37 @ SV15 @ SY36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(151,plain,
! [SV16: $i] :
( ( ! [SY38: $i,SY39: $i] :
~ ( ~ ( ~ ( m2_relset_1 @ SY39 @ SV16 @ SY38 )
| ( m1_relset_1 @ SY39 @ SV16 @ SY38 ) )
| ~ ( ~ ( m1_relset_1 @ SY39 @ SV16 @ SY38 )
| ( m2_relset_1 @ SY39 @ SV16 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(152,plain,
! [SV17: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ~ ( m1_relset_1 @ SY41 @ SV17 @ SY40 )
| ( ( k6_relset_1 @ SV17 @ SY40 @ ( k6_relset_1 @ SV17 @ SY40 @ SY41 ) )
= SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV18: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ( m1_relset_1 @ SY43 @ SV18 @ SY42 )
| ( m2_relset_1 @ ( k6_relset_1 @ SV18 @ SY42 @ SY43 ) @ SY42 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV19: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( m2_relset_1 @ SY45 @ SY44 @ SV19 )
| ~ ( ( ( k1_funct_5 @ SY45 )
!= ( k10_relset_1 @ SV19 @ SY44 @ ( k6_relset_1 @ SY44 @ SV19 @ SY45 ) @ SV19 ) )
| ( ( k2_funct_5 @ SY45 )
!= ( k10_relset_1 @ SY44 @ SV19 @ SY45 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV20: $i,SV15: $i] :
( ( ~ ! [SY46: $i] :
~ ( m2_relset_1 @ SY46 @ SV15 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(156,plain,
! [SV21: $i,SV16: $i] :
( ( ! [SY47: $i] :
~ ( ~ ( ~ ( m2_relset_1 @ SY47 @ SV16 @ SV21 )
| ( m1_relset_1 @ SY47 @ SV16 @ SV21 ) )
| ~ ( ~ ( m1_relset_1 @ SY47 @ SV16 @ SV21 )
| ( m2_relset_1 @ SY47 @ SV16 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV22: $i,SV17: $i] :
( ( ! [SY48: $i] :
( ~ ( m1_relset_1 @ SY48 @ SV17 @ SV22 )
| ( ( k6_relset_1 @ SV17 @ SV22 @ ( k6_relset_1 @ SV17 @ SV22 @ SY48 ) )
= SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(158,plain,
! [SV23: $i,SV18: $i] :
( ( ! [SY49: $i] :
( ~ ( m1_relset_1 @ SY49 @ SV18 @ SV23 )
| ( m2_relset_1 @ ( k6_relset_1 @ SV18 @ SV23 @ SY49 ) @ SV23 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(159,plain,
! [SV19: $i,SV24: $i] :
( ( ! [SY50: $i] :
( ~ ( m2_relset_1 @ SY50 @ SV24 @ SV19 )
| ~ ( ( ( k1_funct_5 @ SY50 )
!= ( k10_relset_1 @ SV19 @ SV24 @ ( k6_relset_1 @ SV24 @ SV19 @ SY50 ) @ SV19 ) )
| ( ( k2_funct_5 @ SY50 )
!= ( k10_relset_1 @ SV24 @ SV19 @ SY50 @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(160,plain,
! [SV20: $i,SV15: $i] :
( ( ! [SY46: $i] :
~ ( m2_relset_1 @ SY46 @ SV15 @ SV20 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ~ ( ~ ( ~ ( m2_relset_1 @ SV25 @ SV16 @ SV21 )
| ( m1_relset_1 @ SV25 @ SV16 @ SV21 ) )
| ~ ( ~ ( m1_relset_1 @ SV25 @ SV16 @ SV21 )
| ( m2_relset_1 @ SV25 @ SV16 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV22: $i,SV17: $i,SV26: $i] :
( ( ~ ( m1_relset_1 @ SV26 @ SV17 @ SV22 )
| ( ( k6_relset_1 @ SV17 @ SV22 @ ( k6_relset_1 @ SV17 @ SV22 @ SV26 ) )
= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(163,plain,
! [SV23: $i,SV18: $i,SV27: $i] :
( ( ~ ( m1_relset_1 @ SV27 @ SV18 @ SV23 )
| ( m2_relset_1 @ ( k6_relset_1 @ SV18 @ SV23 @ SV27 ) @ SV23 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(164,plain,
! [SV19: $i,SV24: $i,SV28: $i] :
( ( ~ ( m2_relset_1 @ SV28 @ SV24 @ SV19 )
| ~ ( ( ( k1_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV19 @ SV24 @ ( k6_relset_1 @ SV24 @ SV19 @ SV28 ) @ SV19 ) )
| ( ( k2_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV24 @ SV19 @ SV28 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(165,plain,
! [SV15: $i,SV20: $i] :
( ( ~ ( m2_relset_1 @ ( sK5_SY46 @ SV20 @ SV15 ) @ SV15 @ SV20 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[160]) ).
thf(166,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ~ ( ~ ( m2_relset_1 @ SV25 @ SV16 @ SV21 )
| ( m1_relset_1 @ SV25 @ SV16 @ SV21 ) )
| ~ ( ~ ( m1_relset_1 @ SV25 @ SV16 @ SV21 )
| ( m2_relset_1 @ SV25 @ SV16 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(167,plain,
! [SV22: $i,SV17: $i,SV26: $i] :
( ( ( ~ ( m1_relset_1 @ SV26 @ SV17 @ SV22 ) )
= $true )
| ( ( ( k6_relset_1 @ SV17 @ SV22 @ ( k6_relset_1 @ SV17 @ SV22 @ SV26 ) )
= SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(168,plain,
! [SV23: $i,SV18: $i,SV27: $i] :
( ( ( ~ ( m1_relset_1 @ SV27 @ SV18 @ SV23 ) )
= $true )
| ( ( m2_relset_1 @ ( k6_relset_1 @ SV18 @ SV23 @ SV27 ) @ SV23 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(169,plain,
! [SV19: $i,SV24: $i,SV28: $i] :
( ( ( ~ ( m2_relset_1 @ SV28 @ SV24 @ SV19 ) )
= $true )
| ( ( ~ ( ( ( k1_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV19 @ SV24 @ ( k6_relset_1 @ SV24 @ SV19 @ SV28 ) @ SV19 ) )
| ( ( k2_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV24 @ SV19 @ SV28 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(170,plain,
! [SV15: $i,SV20: $i] :
( ( m2_relset_1 @ ( sK5_SY46 @ SV20 @ SV15 ) @ SV15 @ SV20 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(171,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ~ ( ~ ( m2_relset_1 @ SV25 @ SV16 @ SV21 )
| ( m1_relset_1 @ SV25 @ SV16 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(172,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ~ ( ~ ( m1_relset_1 @ SV25 @ SV16 @ SV21 )
| ( m2_relset_1 @ SV25 @ SV16 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(173,plain,
! [SV22: $i,SV17: $i,SV26: $i] :
( ( ( m1_relset_1 @ SV26 @ SV17 @ SV22 )
= $false )
| ( ( ( k6_relset_1 @ SV17 @ SV22 @ ( k6_relset_1 @ SV17 @ SV22 @ SV26 ) )
= SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(174,plain,
! [SV23: $i,SV18: $i,SV27: $i] :
( ( ( m1_relset_1 @ SV27 @ SV18 @ SV23 )
= $false )
| ( ( m2_relset_1 @ ( k6_relset_1 @ SV18 @ SV23 @ SV27 ) @ SV23 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(175,plain,
! [SV19: $i,SV24: $i,SV28: $i] :
( ( ( m2_relset_1 @ SV28 @ SV24 @ SV19 )
= $false )
| ( ( ~ ( ( ( k1_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV19 @ SV24 @ ( k6_relset_1 @ SV24 @ SV19 @ SV28 ) @ SV19 ) )
| ( ( k2_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV24 @ SV19 @ SV28 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(176,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ~ ( m2_relset_1 @ SV25 @ SV16 @ SV21 )
| ( m1_relset_1 @ SV25 @ SV16 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(177,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ~ ( m1_relset_1 @ SV25 @ SV16 @ SV21 )
| ( m2_relset_1 @ SV25 @ SV16 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(178,plain,
! [SV24: $i,SV19: $i,SV28: $i] :
( ( ( ( ( k1_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV19 @ SV24 @ ( k6_relset_1 @ SV24 @ SV19 @ SV28 ) @ SV19 ) )
| ( ( k2_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV24 @ SV19 @ SV28 @ SV24 ) ) )
= $false )
| ( ( m2_relset_1 @ SV28 @ SV24 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(179,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( m2_relset_1 @ SV25 @ SV16 @ SV21 ) )
= $true )
| ( ( m1_relset_1 @ SV25 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( m1_relset_1 @ SV25 @ SV16 @ SV21 ) )
= $true )
| ( ( m2_relset_1 @ SV25 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV24: $i,SV19: $i,SV28: $i] :
( ( ( ( k1_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV19 @ SV24 @ ( k6_relset_1 @ SV24 @ SV19 @ SV28 ) @ SV19 ) )
= $false )
| ( ( m2_relset_1 @ SV28 @ SV24 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(182,plain,
! [SV19: $i,SV24: $i,SV28: $i] :
( ( ( ( k2_funct_5 @ SV28 )
!= ( k10_relset_1 @ SV24 @ SV19 @ SV28 @ SV24 ) )
= $false )
| ( ( m2_relset_1 @ SV28 @ SV24 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(183,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ( m2_relset_1 @ SV25 @ SV16 @ SV21 )
= $false )
| ( ( m1_relset_1 @ SV25 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(184,plain,
! [SV21: $i,SV16: $i,SV25: $i] :
( ( ( m1_relset_1 @ SV25 @ SV16 @ SV21 )
= $false )
| ( ( m2_relset_1 @ SV25 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV24: $i,SV19: $i,SV28: $i] :
( ( ( ( k1_funct_5 @ SV28 )
= ( k10_relset_1 @ SV19 @ SV24 @ ( k6_relset_1 @ SV24 @ SV19 @ SV28 ) @ SV19 ) )
= $true )
| ( ( m2_relset_1 @ SV28 @ SV24 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(186,plain,
! [SV19: $i,SV24: $i,SV28: $i] :
( ( ( ( k2_funct_5 @ SV28 )
= ( k10_relset_1 @ SV24 @ SV19 @ SV28 @ SV24 ) )
= $true )
| ( ( m2_relset_1 @ SV28 @ SV24 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(187,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[129,186,185,184,183,174,173,170,149,142,139,138,134,133,132,131,130]) ).
thf(188,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[187,128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU444+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.22 % Computer : n008.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Oct 6 15:24:39 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.70/0.43
% 0.70/0.43 No.of.Axioms: 13
% 0.70/0.43
% 0.70/0.43 Length.of.Defs: 0
% 0.70/0.43
% 0.70/0.43 Contains.Choice.Funs: false
% 0.70/0.43 .....
% 0.70/0.43
% 0.70/0.43 ********************************
% 0.70/0.43 * All subproblems solved! *
% 0.70/0.43 ********************************
% 0.70/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:14,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:187,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.70/0.43
% 0.70/0.43 %**** Beginning of derivation protocol ****
% 0.70/0.43 % SZS output start CNFRefutation
% See solution above
% 0.70/0.43
% 0.70/0.43 %**** End of derivation protocol ****
% 0.70/0.43 %**** no. of clauses in derivation: 157 ****
% 0.70/0.43 %**** clause counter: 187 ****
% 0.70/0.43
% 0.70/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:14,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:187,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------