TSTP Solution File: SYN067+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN067+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 : n014.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 08:23:15 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 22
% Syntax : Number of formulae : 298 ( 111 unt; 21 typ; 0 def)
% Number of atoms : 2942 ( 587 equ; 0 cnn)
% Maximal formula atoms : 18 ( 10 avg)
% Number of connectives : 5953 (1871 ~;1332 |; 130 &;2591 @)
% ( 3 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 584 ( 0 ^ 528 !; 56 ?; 584 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_big_p,type,
big_p: $i > $o ).
thf(tp_big_r,type,
big_r: $i > $i > $o ).
thf(tp_sK10_REN,type,
sK10_REN: $o ).
thf(tp_sK11_REN,type,
sK11_REN: $o ).
thf(tp_sK12_X,type,
sK12_X: $i ).
thf(tp_sK13_SY27,type,
sK13_SY27: $i ).
thf(tp_sK14_Z2,type,
sK14_Z2: $i > $i ).
thf(tp_sK15_SY30,type,
sK15_SY30: $i > $i ).
thf(tp_sK16_Z1,type,
sK16_Z1: $i > $i ).
thf(tp_sK17_SY31,type,
sK17_SY31: $i > $i ).
thf(tp_sK18_REN,type,
sK18_REN: $o ).
thf(tp_sK1_X1,type,
sK1_X1: $i ).
thf(tp_sK2_SY24,type,
sK2_SY24: $i ).
thf(tp_sK3_SY21,type,
sK3_SY21: $i ).
thf(tp_sK4_SY18,type,
sK4_SY18: $i ).
thf(tp_sK5_Z,type,
sK5_Z: $i > $i ).
thf(tp_sK6_SY25,type,
sK6_SY25: $i > $i ).
thf(tp_sK7_Z,type,
sK7_Z: $i > $i ).
thf(tp_sK8_SY26,type,
sK8_SY26: $i > $i ).
thf(tp_sK9_REN,type,
sK9_REN: $o ).
thf(1,conjecture,
( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ? [Y: $i] :
( ( big_p @ Y )
& ( big_r @ X @ Y ) ) ) )
=> ? [Z: $i,W: $i] :
( ( big_p @ Z )
& ( big_r @ X @ W )
& ( big_r @ W @ Z ) ) )
<=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ? [Z1: $i,W1: $i] :
( ( big_p @ Z1 )
& ( big_r @ X1 @ W1 )
& ( big_r @ W1 @ Z1 ) ) )
& ( ~ ( big_p @ a )
| ~ ? [Y1: $i] :
( ( big_p @ Y1 )
& ( big_r @ X1 @ Y1 ) )
| ? [Z2: $i,W2: $i] :
( ( big_p @ Z2 )
& ( big_r @ X1 @ W2 )
& ( big_r @ W2 @ Z2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38) ).
thf(2,negated_conjecture,
( ( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ? [Y: $i] :
( ( big_p @ Y )
& ( big_r @ X @ Y ) ) ) )
=> ? [Z: $i,W: $i] :
( ( big_p @ Z )
& ( big_r @ X @ W )
& ( big_r @ W @ Z ) ) )
<=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ? [Z1: $i,W1: $i] :
( ( big_p @ Z1 )
& ( big_r @ X1 @ W1 )
& ( big_r @ W1 @ Z1 ) ) )
& ( ~ ( big_p @ a )
| ~ ? [Y1: $i] :
( ( big_p @ Y1 )
& ( big_r @ X1 @ Y1 ) )
| ? [Z2: $i,W2: $i] :
( ( big_p @ Z2 )
& ( big_r @ X1 @ W2 )
& ( big_r @ W2 @ Z2 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ? [Y: $i] :
( ( big_p @ Y )
& ( big_r @ X @ Y ) ) ) )
=> ? [Z: $i,W: $i] :
( ( big_p @ Z )
& ( big_r @ X @ W )
& ( big_r @ W @ Z ) ) )
<=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ? [Z1: $i,W1: $i] :
( ( big_p @ Z1 )
& ( big_r @ X1 @ W1 )
& ( big_r @ W1 @ Z1 ) ) )
& ( ~ ( big_p @ a )
| ~ ? [Y1: $i] :
( ( big_p @ Y1 )
& ( big_r @ X1 @ Y1 ) )
| ? [Z2: $i,W2: $i] :
( ( big_p @ Z2 )
& ( big_r @ X1 @ W2 )
& ( big_r @ W2 @ Z2 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ? [Y: $i] :
( ( big_p @ Y )
& ( big_r @ X @ Y ) ) ) )
=> ? [Z: $i,W: $i] :
( ( big_p @ Z )
& ( big_r @ X @ W )
& ( big_r @ W @ Z ) ) )
=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ? [Z1: $i,W1: $i] :
( ( big_p @ Z1 )
& ( big_r @ X1 @ W1 )
& ( big_r @ W1 @ Z1 ) ) )
& ( ~ ( big_p @ a )
| ~ ? [Y1: $i] :
( ( big_p @ Y1 )
& ( big_r @ X1 @ Y1 ) )
| ? [Z2: $i,W2: $i] :
( ( big_p @ Z2 )
& ( big_r @ X1 @ W2 )
& ( big_r @ W2 @ Z2 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ? [Z1: $i,W1: $i] :
( ( big_p @ Z1 )
& ( big_r @ X1 @ W1 )
& ( big_r @ W1 @ Z1 ) ) )
& ( ~ ( big_p @ a )
| ~ ? [Y1: $i] :
( ( big_p @ Y1 )
& ( big_r @ X1 @ Y1 ) )
| ? [Z2: $i,W2: $i] :
( ( big_p @ Z2 )
& ( big_r @ X1 @ W2 )
& ( big_r @ W2 @ Z2 ) ) ) )
=> ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ? [Y: $i] :
( ( big_p @ Y )
& ( big_r @ X @ Y ) ) ) )
=> ? [Z: $i,W: $i] :
( ( big_p @ Z )
& ( big_r @ X @ W )
& ( big_r @ W @ Z ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ? [Y: $i] :
( ( big_p @ Y )
& ( big_r @ X @ Y ) ) ) )
=> ? [Z: $i,W: $i] :
( ( big_p @ Z )
& ( big_r @ X @ W )
& ( big_r @ W @ Z ) ) )
=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ? [Z1: $i,W1: $i] :
( ( big_p @ Z1 )
& ( big_r @ X1 @ W1 )
& ( big_r @ W1 @ Z1 ) ) )
& ( ~ ( big_p @ a )
| ~ ? [Y1: $i] :
( ( big_p @ Y1 )
& ( big_r @ X1 @ Y1 ) )
| ? [Z2: $i,W2: $i] :
( ( big_p @ Z2 )
& ( big_r @ X1 @ W2 )
& ( big_r @ W2 @ Z2 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ? [Z1: $i,W1: $i] :
( ( big_p @ Z1 )
& ( big_r @ X1 @ W1 )
& ( big_r @ W1 @ Z1 ) ) )
& ( ~ ( big_p @ a )
| ~ ? [Y1: $i] :
( ( big_p @ Y1 )
& ( big_r @ X1 @ Y1 ) )
| ? [Z2: $i,W2: $i] :
( ( big_p @ Z2 )
& ( big_r @ X1 @ W2 )
& ( big_r @ W2 @ Z2 ) ) ) )
=> ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ? [Y: $i] :
( ( big_p @ Y )
& ( big_r @ X @ Y ) ) ) )
=> ? [Z: $i,W: $i] :
( ( big_p @ Z )
& ( big_r @ X @ W )
& ( big_r @ W @ Z ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [X: $i] :
( ( big_p @ X )
| ~ ( big_p @ a )
| ( ( big_p @ ( sK7_Z @ X ) )
& ( big_r @ X @ ( sK8_SY26 @ X ) )
& ( big_r @ ( sK8_SY26 @ X ) @ ( sK7_Z @ X ) ) ) )
& ! [X: $i] :
( ! [Y: $i] :
( ~ ( big_p @ Y )
| ~ ( big_r @ X @ Y ) )
| ~ ( big_p @ a )
| ( ( big_p @ ( sK5_Z @ X ) )
& ( big_r @ X @ ( sK6_SY25 @ X ) )
& ( big_r @ ( sK6_SY25 @ X ) @ ( sK5_Z @ X ) ) ) )
& ( ! [SY10: $i,SY11: $i] :
( ~ ( big_p @ SY10 )
| ~ ( big_r @ sK1_X1 @ SY11 )
| ~ ( big_r @ SY11 @ SY10 ) )
| ! [SY12: $i,SY13: $i] :
( ~ ( big_p @ SY12 )
| ~ ( big_r @ sK1_X1 @ SY13 )
| ~ ( big_r @ SY13 @ SY12 ) ) )
& ( ! [SY14: $i,SY15: $i] :
( ~ ( big_p @ SY14 )
| ~ ( big_r @ sK1_X1 @ SY15 )
| ~ ( big_r @ SY15 @ SY14 ) )
| ( big_p @ a ) )
& ( ! [SY16: $i,SY17: $i] :
( ~ ( big_p @ SY16 )
| ~ ( big_r @ sK1_X1 @ SY17 )
| ~ ( big_r @ SY17 @ SY16 ) )
| sK11_REN )
& ( sK11_REN
=> ( ( big_p @ sK4_SY18 )
& ( big_r @ sK1_X1 @ sK4_SY18 ) ) )
& ( ( big_p @ a )
| ! [SY19: $i,SY20: $i] :
( ~ ( big_p @ SY19 )
| ~ ( big_r @ sK1_X1 @ SY20 )
| ~ ( big_r @ SY20 @ SY19 ) ) )
& ( ( big_p @ a )
| ( big_p @ a ) )
& ( ( big_p @ a )
| sK10_REN )
& ( sK10_REN
=> ( ( big_p @ sK3_SY21 )
& ( big_r @ sK1_X1 @ sK3_SY21 ) ) )
& ( ~ ( big_p @ sK1_X1 )
| ! [SY22: $i,SY23: $i] :
( ~ ( big_p @ SY22 )
| ~ ( big_r @ sK1_X1 @ SY23 )
| ~ ( big_r @ SY23 @ SY22 ) ) )
& ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
& ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
& ( sK9_REN
=> ( ( big_p @ sK2_SY24 )
& ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(9,plain,
( ( ! [X1: $i] :
( ( ( big_p @ ( sK16_Z1 @ X1 ) )
& ( big_r @ X1 @ ( sK17_SY31 @ X1 ) )
& ( big_r @ ( sK17_SY31 @ X1 ) @ ( sK16_Z1 @ X1 ) ) )
| ~ ( big_p @ a )
| ( big_p @ X1 ) )
& ! [X1: $i] :
( ( ( big_p @ ( sK14_Z2 @ X1 ) )
& ( big_r @ X1 @ ( sK15_SY30 @ X1 ) )
& ( big_r @ ( sK15_SY30 @ X1 ) @ ( sK14_Z2 @ X1 ) ) )
| ~ ( big_p @ a )
| ! [Y1: $i] :
( ~ ( big_p @ Y1 )
| ~ ( big_r @ X1 @ Y1 ) ) )
& ( ~ ( big_p @ sK12_X )
| sK18_REN )
& ( sK18_REN
=> ( ( big_p @ sK13_SY27 )
& ( big_r @ sK12_X @ sK13_SY27 ) ) )
& ( big_p @ a )
& ! [SY28: $i,SY29: $i] :
( ~ ( big_p @ SY28 )
| ~ ( big_r @ sK12_X @ SY29 )
| ~ ( big_r @ SY29 @ SY28 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ! [X: $i] :
( ( big_p @ X )
| ~ ( big_p @ a )
| ( ( big_p @ ( sK7_Z @ X ) )
& ( big_r @ X @ ( sK8_SY26 @ X ) )
& ( big_r @ ( sK8_SY26 @ X ) @ ( sK7_Z @ X ) ) ) )
& ! [X: $i] :
( ! [Y: $i] :
( ~ ( big_p @ Y )
| ~ ( big_r @ X @ Y ) )
| ~ ( big_p @ a )
| ( ( big_p @ ( sK5_Z @ X ) )
& ( big_r @ X @ ( sK6_SY25 @ X ) )
& ( big_r @ ( sK6_SY25 @ X ) @ ( sK5_Z @ X ) ) ) )
& ( ! [SY10: $i,SY11: $i] :
( ~ ( big_p @ SY10 )
| ~ ( big_r @ sK1_X1 @ SY11 )
| ~ ( big_r @ SY11 @ SY10 ) )
| ! [SY12: $i,SY13: $i] :
( ~ ( big_p @ SY12 )
| ~ ( big_r @ sK1_X1 @ SY13 )
| ~ ( big_r @ SY13 @ SY12 ) ) )
& ( ! [SY14: $i,SY15: $i] :
( ~ ( big_p @ SY14 )
| ~ ( big_r @ sK1_X1 @ SY15 )
| ~ ( big_r @ SY15 @ SY14 ) )
| ( big_p @ a ) )
& ( ! [SY16: $i,SY17: $i] :
( ~ ( big_p @ SY16 )
| ~ ( big_r @ sK1_X1 @ SY17 )
| ~ ( big_r @ SY17 @ SY16 ) )
| sK11_REN )
& ( sK11_REN
=> ( ( big_p @ sK4_SY18 )
& ( big_r @ sK1_X1 @ sK4_SY18 ) ) )
& ( ( big_p @ a )
| ! [SY19: $i,SY20: $i] :
( ~ ( big_p @ SY19 )
| ~ ( big_r @ sK1_X1 @ SY20 )
| ~ ( big_r @ SY20 @ SY19 ) ) )
& ( ( big_p @ a )
| ( big_p @ a ) )
& ( ( big_p @ a )
| sK10_REN )
& ( sK10_REN
=> ( ( big_p @ sK3_SY21 )
& ( big_r @ sK1_X1 @ sK3_SY21 ) ) )
& ( ~ ( big_p @ sK1_X1 )
| ! [SY22: $i,SY23: $i] :
( ~ ( big_p @ SY22 )
| ~ ( big_r @ sK1_X1 @ SY23 )
| ~ ( big_r @ SY23 @ SY22 ) ) )
& ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
& ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
& ( sK9_REN
=> ( ( big_p @ sK2_SY24 )
& ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( big_p @ SX0 )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK8_SY26 @ SX0 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SX0 ) @ ( sK7_Z @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK6_SY25 @ SX0 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SX0 ) @ ( sK5_Z @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( big_p @ SX0 )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK8_SY26 @ SX0 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SX0 ) @ ( sK7_Z @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK6_SY25 @ SX0 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SX0 ) @ ( sK5_Z @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( big_p @ SX0 )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK8_SY26 @ SX0 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SX0 ) @ ( sK7_Z @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK6_SY25 @ SX0 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SX0 ) @ ( sK5_Z @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( big_p @ SX0 )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK8_SY26 @ SX0 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SX0 ) @ ( sK7_Z @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK6_SY25 @ SX0 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SX0 ) @ ( sK5_Z @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( ( big_p @ SX0 )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK8_SY26 @ SX0 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SX0 ) @ ( sK7_Z @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK6_SY25 @ SX0 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SX0 ) @ ( sK5_Z @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] :
( ( big_p @ SX0 )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK8_SY26 @ SX0 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SX0 ) @ ( sK7_Z @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK6_SY25 @ SX0 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SX0 ) @ ( sK5_Z @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [SX0: $i] :
( ( big_p @ SX0 )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK8_SY26 @ SX0 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SX0 ) @ ( sK7_Z @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK6_SY25 @ SX0 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SX0 ) @ ( sK5_Z @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i] :
( ( ( big_p @ SV1 )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SV1 ) )
| ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SV1 ) @ ( sK7_Z @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
( ~ ( big_p @ SY32 )
| ~ ( big_r @ SV2 @ SY32 ) )
| ~ ( big_p @ a )
| ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( ( big_p @ SV1 )
| ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SV1 ) )
| ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SV1 ) @ ( sK7_Z @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( ! [SY32: $i] :
( ~ ( big_p @ SY32 )
| ~ ( big_r @ SV2 @ SY32 ) )
| ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(36,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(37,plain,
! [SV1: $i] :
( ( ( big_p @ SV1 )
= $true )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SV1 ) )
| ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SV1 ) @ ( sK7_Z @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( ! [SY32: $i] :
( ~ ( big_p @ SY32 )
| ~ ( big_r @ SV2 @ SY32 ) ) )
= $true )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(42,plain,
( ( ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV1: $i] :
( ( ( big_p @ a )
= $false )
| ( ( big_p @ SV1 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SV1 ) )
| ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SV1 ) @ ( sK7_Z @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( big_p @ SV3 )
| ~ ( big_r @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
( ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
( ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(48,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SV1 ) )
| ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) )
| ~ ( big_r @ ( sK8_SY26 @ SV1 ) @ ( sK7_Z @ SV1 ) ) )
= $false )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( big_p @ SV3 ) )
= $true )
| ( ( ~ ( big_r @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( ! [SY33: $i] :
( ~ ( big_p @ SV4 )
| ~ ( big_r @ sK1_X1 @ SY33 )
| ~ ( big_r @ SY33 @ SV4 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(52,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(53,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(54,plain,
( ( ~ ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(55,plain,
( ( ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(56,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(57,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(58,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( big_p @ ( sK7_Z @ SV1 ) )
| ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) ) )
= $false )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(59,plain,
! [SV1: $i] :
( ( ( ~ ( big_r @ ( sK8_SY26 @ SV1 ) @ ( sK7_Z @ SV1 ) ) )
= $false )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(60,plain,
! [SV2: $i,SV3: $i] :
( ( ( big_p @ SV3 )
= $false )
| ( ( ~ ( big_r @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV5: $i,SV4: $i] :
( ( ( ~ ( big_p @ SV4 )
| ~ ( big_r @ sK1_X1 @ SV5 )
| ~ ( big_r @ SV5 @ SV4 ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| ( big_p @ a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(63,plain,
( ( ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(64,plain,
( ( ( big_p @ a )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(65,plain,
( ( ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(66,plain,
( ( ~ ( big_p @ sK1_X1 )
| ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(67,plain,
( ( ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(68,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( big_p @ ( sK7_Z @ SV1 ) )
| ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) ) )
= $true )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(69,plain,
! [SV1: $i] :
( ( ( big_r @ ( sK8_SY26 @ SV1 ) @ ( sK7_Z @ SV1 ) )
= $true )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(70,plain,
! [SV3: $i,SV2: $i] :
( ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV5: $i,SV4: $i] :
( ( ( ~ ( big_p @ SV4 )
| ~ ( big_r @ sK1_X1 @ SV5 ) )
= $true )
| ( ( ~ ( big_r @ SV5 @ SV4 ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(72,plain,
( ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(73,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
| ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(74,plain,
( ( ( big_p @ a )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(75,plain,
( ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(76,plain,
( ( ( ~ ( big_p @ sK1_X1 ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(77,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV1: $i] :
( ( ( ~ ( big_p @ ( sK7_Z @ SV1 ) )
| ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) )
= $false )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV2: $i,SV3: $i] :
( ( ( big_p @ a )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV5: $i,SV4: $i] :
( ( ( ~ ( big_p @ SV4 ) )
= $true )
| ( ( ~ ( big_r @ sK1_X1 @ SV5 ) )
= $true )
| ( ( ~ ( big_r @ SV5 @ SV4 ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV6: $i] :
( ( ( ! [SY34: $i] :
( ~ ( big_p @ SV6 )
| ~ ( big_r @ sK1_X1 @ SY34 )
| ~ ( big_r @ SY34 @ SV6 ) ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(83,plain,
( ( ~ ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(84,plain,
! [SV7: $i] :
( ( ( ! [SY35: $i] :
( ~ ( big_p @ SV7 )
| ~ ( big_r @ sK1_X1 @ SY35 )
| ~ ( big_r @ SY35 @ SV7 ) ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(85,plain,
( ( ~ ( ( big_p @ a )
| ( big_p @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(86,plain,
( ( ~ ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(87,plain,
( ( ( big_p @ sK1_X1 )
= $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(88,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(89,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(90,plain,
! [SV1: $i] :
( ( ( ~ ( big_p @ ( sK7_Z @ SV1 ) ) )
= $false )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(91,plain,
! [SV1: $i] :
( ( ( ~ ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) ) )
= $false )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(92,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
| ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) )
= $false )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV5: $i,SV4: $i] :
( ( ( big_p @ SV4 )
= $false )
| ( ( ~ ( big_r @ sK1_X1 @ SV5 ) )
= $true )
| ( ( ~ ( big_r @ SV5 @ SV4 ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( big_p @ SV6 )
| ~ ( big_r @ sK1_X1 @ SV8 )
| ~ ( big_r @ SV8 @ SV6 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) )
| sK11_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(96,plain,
( ( ~ sK11_REN
| ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(97,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ( big_p @ SV7 )
| ~ ( big_r @ sK1_X1 @ SV9 )
| ~ ( big_r @ SV9 @ SV7 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(98,plain,
( ( ( big_p @ a )
| ( big_p @ a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(99,plain,
( ( ~ ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(100,plain,
! [SV10: $i] :
( ( ( ! [SY36: $i] :
( ~ ( big_p @ SV10 )
| ~ ( big_r @ sK1_X1 @ SY36 )
| ~ ( big_r @ SY36 @ SV10 ) ) )
= $true )
| ( ( big_p @ sK1_X1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
( ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(102,plain,
( ( ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(103,plain,
! [SV1: $i] :
( ( ( big_p @ ( sK7_Z @ SV1 ) )
= $true )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(104,plain,
! [SV1: $i] :
( ( ( big_r @ SV1 @ ( sK8_SY26 @ SV1 ) )
= $true )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(105,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) ) )
= $false )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(106,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) ) )
= $false )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(107,plain,
! [SV4: $i,SV5: $i] :
( ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( ~ ( big_r @ SV5 @ SV4 ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( big_p @ SV6 )
| ~ ( big_r @ sK1_X1 @ SV8 ) )
= $true )
| ( ( ~ ( big_r @ SV8 @ SV6 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(109,plain,
( ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(110,plain,
( ( ( ~ sK11_REN )
= $true )
| ( ( ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ( big_p @ SV7 )
| ~ ( big_r @ sK1_X1 @ SV9 ) )
= $true )
| ( ( ~ ( big_r @ SV9 @ SV7 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(112,plain,
( ( ( big_p @ a )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(113,plain,
( ( ~ ( ( big_p @ a )
| sK10_REN )
| ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(114,plain,
! [SV11: $i,SV10: $i] :
( ( ( ~ ( big_p @ SV10 )
| ~ ( big_r @ sK1_X1 @ SV11 )
| ~ ( big_r @ SV11 @ SV10 ) )
= $true )
| ( ( big_p @ sK1_X1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(115,plain,
( ( ( ~ ( big_p @ sK1_X1 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(116,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(117,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) ) )
= $true )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(118,plain,
! [SV3: $i,SV2: $i] :
( ( ( big_r @ ( sK6_SY25 @ SV2 ) @ ( sK5_Z @ SV2 ) )
= $true )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(119,plain,
! [SV4: $i,SV5: $i] :
( ( ( big_r @ SV5 @ SV4 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK1_X1 @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( big_p @ SV6 ) )
= $true )
| ( ( ~ ( big_r @ sK1_X1 @ SV8 ) )
= $true )
| ( ( ~ ( big_r @ SV8 @ SV6 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV12: $i] :
( ( ( ! [SY37: $i] :
( ~ ( big_p @ SV12 )
| ~ ( big_r @ sK1_X1 @ SY37 )
| ~ ( big_r @ SY37 @ SV12 ) ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(122,plain,
( ( sK11_REN = $false )
| ( ( ~ ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ( big_p @ SV7 ) )
= $true )
| ( ( ~ ( big_r @ sK1_X1 @ SV9 ) )
= $true )
| ( ( ~ ( big_r @ SV9 @ SV7 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(124,plain,
( ( ~ ( ( big_p @ a )
| sK10_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(125,plain,
( ( ~ ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(126,plain,
! [SV11: $i,SV10: $i] :
( ( ( ~ ( big_p @ SV10 )
| ~ ( big_r @ sK1_X1 @ SV11 ) )
= $true )
| ( ( ~ ( big_r @ SV11 @ SV10 ) )
= $true )
| ( ( big_p @ sK1_X1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(127,plain,
( ( ( big_p @ sK1_X1 )
= $false )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(128,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| sK9_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(129,plain,
( ( ~ ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(130,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( big_p @ ( sK5_Z @ SV2 ) )
| ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
= $false )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV4: $i,SV5: $i,SV13: $i] :
( ( ( ! [SY38: $i] :
( ~ ( big_p @ SV13 )
| ~ ( big_r @ sK1_X1 @ SY38 )
| ~ ( big_r @ SY38 @ SV13 ) ) )
= $true )
| ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( big_r @ SV5 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV8: $i,SV6: $i] :
( ( ( big_p @ SV6 )
= $false )
| ( ( ~ ( big_r @ sK1_X1 @ SV8 ) )
= $true )
| ( ( ~ ( big_r @ SV8 @ SV6 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV14: $i,SV12: $i] :
( ( ( ~ ( big_p @ SV12 )
| ~ ( big_r @ sK1_X1 @ SV14 )
| ~ ( big_r @ SV14 @ SV12 ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(134,plain,
( ( ( ~ ( big_p @ sK4_SY18 )
| ~ ( big_r @ sK1_X1 @ sK4_SY18 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV9: $i,SV7: $i] :
( ( ( big_p @ SV7 )
= $false )
| ( ( ~ ( big_r @ sK1_X1 @ SV9 ) )
= $true )
| ( ( ~ ( big_r @ SV9 @ SV7 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(136,plain,
( ( ( big_p @ a )
| sK10_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(137,plain,
( ( ~ sK10_REN
| ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(138,plain,
! [SV11: $i,SV10: $i] :
( ( ( ~ ( big_p @ SV10 ) )
= $true )
| ( ( ~ ( big_r @ sK1_X1 @ SV11 ) )
= $true )
| ( ( ~ ( big_r @ SV11 @ SV10 ) )
= $true )
| ( ( big_p @ sK1_X1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(139,plain,
( ( ~ ( big_p @ sK1_X1 )
| sK9_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(140,plain,
( ( ~ sK9_REN
| ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(141,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( big_p @ ( sK5_Z @ SV2 ) ) )
= $false )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(142,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) ) )
= $false )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(143,plain,
! [SV4: $i,SV5: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( big_p @ SV13 )
| ~ ( big_r @ sK1_X1 @ SV15 )
| ~ ( big_r @ SV15 @ SV13 ) )
= $true )
| ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( big_r @ SV5 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV6: $i,SV8: $i] :
( ( ( big_r @ sK1_X1 @ SV8 )
= $false )
| ( ( big_p @ SV6 )
= $false )
| ( ( ~ ( big_r @ SV8 @ SV6 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV14: $i,SV12: $i] :
( ( ( ~ ( big_p @ SV12 )
| ~ ( big_r @ sK1_X1 @ SV14 ) )
= $true )
| ( ( ~ ( big_r @ SV14 @ SV12 ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(146,plain,
( ( ( ~ ( big_p @ sK4_SY18 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(147,plain,
( ( ( ~ ( big_r @ sK1_X1 @ sK4_SY18 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(148,plain,
! [SV7: $i,SV9: $i] :
( ( ( big_r @ sK1_X1 @ SV9 )
= $false )
| ( ( big_p @ SV7 )
= $false )
| ( ( ~ ( big_r @ SV9 @ SV7 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(149,plain,
( ( ( big_p @ a )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(150,plain,
( ( ( ~ sK10_REN )
= $true )
| ( ( ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV11: $i,SV10: $i] :
( ( ( big_p @ SV10 )
= $false )
| ( ( ~ ( big_r @ sK1_X1 @ SV11 ) )
= $true )
| ( ( ~ ( big_r @ SV11 @ SV10 ) )
= $true )
| ( ( big_p @ sK1_X1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(152,plain,
( ( ( ~ ( big_p @ sK1_X1 ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(153,plain,
( ( ( ~ sK9_REN )
= $true )
| ( ( ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV3: $i,SV2: $i] :
( ( ( big_p @ ( sK5_Z @ SV2 ) )
= $true )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(155,plain,
! [SV3: $i,SV2: $i] :
( ( ( big_r @ SV2 @ ( sK6_SY25 @ SV2 ) )
= $true )
| ( ( big_r @ SV2 @ SV3 )
= $false )
| ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(156,plain,
! [SV4: $i,SV5: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( big_p @ SV13 )
| ~ ( big_r @ sK1_X1 @ SV15 ) )
= $true )
| ( ( ~ ( big_r @ SV15 @ SV13 ) )
= $true )
| ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( big_r @ SV5 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(157,plain,
! [SV6: $i,SV8: $i] :
( ( ( big_r @ SV8 @ SV6 )
= $false )
| ( ( big_p @ SV6 )
= $false )
| ( ( big_r @ sK1_X1 @ SV8 )
= $false )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV14: $i,SV12: $i] :
( ( ( ~ ( big_p @ SV12 ) )
= $true )
| ( ( ~ ( big_r @ sK1_X1 @ SV14 ) )
= $true )
| ( ( ~ ( big_r @ SV14 @ SV12 ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(159,plain,
( ( ( big_p @ sK4_SY18 )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(160,plain,
( ( ( big_r @ sK1_X1 @ sK4_SY18 )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(161,plain,
! [SV7: $i,SV9: $i] :
( ( ( big_r @ SV9 @ SV7 )
= $false )
| ( ( big_p @ SV7 )
= $false )
| ( ( big_r @ sK1_X1 @ SV9 )
= $false )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(162,plain,
( ( sK10_REN = $false )
| ( ( ~ ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(163,plain,
! [SV10: $i,SV11: $i] :
( ( ( big_r @ sK1_X1 @ SV11 )
= $false )
| ( ( big_p @ SV10 )
= $false )
| ( ( ~ ( big_r @ SV11 @ SV10 ) )
= $true )
| ( ( big_p @ sK1_X1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(164,plain,
( ( ( big_p @ sK1_X1 )
= $false )
| ( sK9_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(165,plain,
( ( sK9_REN = $false )
| ( ( ~ ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(166,plain,
! [SV4: $i,SV5: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( big_p @ SV13 ) )
= $true )
| ( ( ~ ( big_r @ sK1_X1 @ SV15 ) )
= $true )
| ( ( ~ ( big_r @ SV15 @ SV13 ) )
= $true )
| ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( big_r @ SV5 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV14: $i,SV12: $i] :
( ( ( big_p @ SV12 )
= $false )
| ( ( ~ ( big_r @ sK1_X1 @ SV14 ) )
= $true )
| ( ( ~ ( big_r @ SV14 @ SV12 ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(168,plain,
( ( ( ~ ( big_p @ sK3_SY21 )
| ~ ( big_r @ sK1_X1 @ sK3_SY21 ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(169,plain,
! [SV10: $i,SV11: $i] :
( ( ( big_r @ SV11 @ SV10 )
= $false )
| ( ( big_p @ SV10 )
= $false )
| ( ( big_r @ sK1_X1 @ SV11 )
= $false )
| ( ( big_p @ sK1_X1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(170,plain,
( ( ( ~ ( big_p @ sK2_SY24 )
| ~ ( big_r @ sK1_X1 @ sK2_SY24 ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(171,plain,
! [SV4: $i,SV5: $i,SV15: $i,SV13: $i] :
( ( ( big_p @ SV13 )
= $false )
| ( ( ~ ( big_r @ sK1_X1 @ SV15 ) )
= $true )
| ( ( ~ ( big_r @ SV15 @ SV13 ) )
= $true )
| ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( big_r @ SV5 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(172,plain,
! [SV12: $i,SV14: $i] :
( ( ( big_r @ sK1_X1 @ SV14 )
= $false )
| ( ( big_p @ SV12 )
= $false )
| ( ( ~ ( big_r @ SV14 @ SV12 ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(173,plain,
( ( ( ~ ( big_p @ sK3_SY21 ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(174,plain,
( ( ( ~ ( big_r @ sK1_X1 @ sK3_SY21 ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(175,plain,
( ( ( ~ ( big_p @ sK2_SY24 ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(176,plain,
( ( ( ~ ( big_r @ sK1_X1 @ sK2_SY24 ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(177,plain,
! [SV4: $i,SV5: $i,SV13: $i,SV15: $i] :
( ( ( big_r @ sK1_X1 @ SV15 )
= $false )
| ( ( big_p @ SV13 )
= $false )
| ( ( ~ ( big_r @ SV15 @ SV13 ) )
= $true )
| ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( big_r @ SV5 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(178,plain,
! [SV12: $i,SV14: $i] :
( ( ( big_r @ SV14 @ SV12 )
= $false )
| ( ( big_p @ SV12 )
= $false )
| ( ( big_r @ sK1_X1 @ SV14 )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(179,plain,
( ( ( big_p @ sK3_SY21 )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(180,plain,
( ( ( big_r @ sK1_X1 @ sK3_SY21 )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(181,plain,
( ( ( big_p @ sK2_SY24 )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(182,plain,
( ( ( big_r @ sK1_X1 @ sK2_SY24 )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(183,plain,
! [SV4: $i,SV5: $i,SV13: $i,SV15: $i] :
( ( ( big_r @ SV15 @ SV13 )
= $false )
| ( ( big_p @ SV13 )
= $false )
| ( ( big_r @ sK1_X1 @ SV15 )
= $false )
| ( ( big_r @ sK1_X1 @ SV5 )
= $false )
| ( ( big_p @ SV4 )
= $false )
| ( ( big_r @ SV5 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(184,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[69,183,182,181,180,179,178,169,164,161,160,159,157,155,154,149,127,118,112,104,103]) ).
thf(185,plain,
( ( ! [X1: $i] :
( ( ( big_p @ ( sK16_Z1 @ X1 ) )
& ( big_r @ X1 @ ( sK17_SY31 @ X1 ) )
& ( big_r @ ( sK17_SY31 @ X1 ) @ ( sK16_Z1 @ X1 ) ) )
| ~ ( big_p @ a )
| ( big_p @ X1 ) )
& ! [X1: $i] :
( ( ( big_p @ ( sK14_Z2 @ X1 ) )
& ( big_r @ X1 @ ( sK15_SY30 @ X1 ) )
& ( big_r @ ( sK15_SY30 @ X1 ) @ ( sK14_Z2 @ X1 ) ) )
| ~ ( big_p @ a )
| ! [Y1: $i] :
( ~ ( big_p @ Y1 )
| ~ ( big_r @ X1 @ Y1 ) ) )
& ( ~ ( big_p @ sK12_X )
| sK18_REN )
& ( sK18_REN
=> ( ( big_p @ sK13_SY27 )
& ( big_r @ sK12_X @ sK13_SY27 ) ) )
& ( big_p @ a )
& ! [SY28: $i,SY29: $i] :
( ~ ( big_p @ SY28 )
| ~ ( big_r @ sK12_X @ SY29 )
| ~ ( big_r @ SY29 @ SY28 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(186,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK17_SY31 @ SX0 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SX0 ) @ ( sK16_Z1 @ SX0 ) ) )
| ~ ( big_p @ a )
| ( big_p @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK15_SY30 @ SX0 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SX0 ) @ ( sK14_Z2 @ SX0 ) ) )
| ~ ( big_p @ a )
| ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
| ~ ( big_p @ a ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK12_X @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(187,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK17_SY31 @ SX0 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SX0 ) @ ( sK16_Z1 @ SX0 ) ) )
| ~ ( big_p @ a )
| ( big_p @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK15_SY30 @ SX0 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SX0 ) @ ( sK14_Z2 @ SX0 ) ) )
| ~ ( big_p @ a )
| ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
| ~ ( big_p @ a ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK12_X @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(188,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK17_SY31 @ SX0 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SX0 ) @ ( sK16_Z1 @ SX0 ) ) )
| ~ ( big_p @ a )
| ( big_p @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK15_SY30 @ SX0 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SX0 ) @ ( sK14_Z2 @ SX0 ) ) )
| ~ ( big_p @ a )
| ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(189,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
| ~ ( big_p @ a ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK12_X @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(190,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK17_SY31 @ SX0 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SX0 ) @ ( sK16_Z1 @ SX0 ) ) )
| ~ ( big_p @ a )
| ( big_p @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK15_SY30 @ SX0 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SX0 ) @ ( sK14_Z2 @ SX0 ) ) )
| ~ ( big_p @ a )
| ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(191,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
| ~ ( big_p @ a ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK12_X @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(192,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK17_SY31 @ SX0 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SX0 ) @ ( sK16_Z1 @ SX0 ) ) )
| ~ ( big_p @ a )
| ( big_p @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK15_SY30 @ SX0 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SX0 ) @ ( sK14_Z2 @ SX0 ) ) )
| ~ ( big_p @ a )
| ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(193,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
| ~ ( big_p @ a ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK12_X @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(194,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK17_SY31 @ SX0 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SX0 ) @ ( sK16_Z1 @ SX0 ) ) )
| ~ ( big_p @ a )
| ( big_p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(195,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK15_SY30 @ SX0 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SX0 ) @ ( sK14_Z2 @ SX0 ) ) )
| ~ ( big_p @ a )
| ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(196,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
| ~ ( big_p @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(197,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK12_X @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(198,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK17_SY31 @ SX0 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SX0 ) @ ( sK16_Z1 @ SX0 ) ) )
| ~ ( big_p @ a )
| ( big_p @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(199,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SX0 ) )
| ~ ( big_r @ SX0 @ ( sK15_SY30 @ SX0 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SX0 ) @ ( sK14_Z2 @ SX0 ) ) )
| ~ ( big_p @ a )
| ! [SX1: $i] :
( ~ ( big_p @ SX1 )
| ~ ( big_r @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(200,plain,
( ( ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
| ~ ( big_p @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(201,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_r @ sK12_X @ SX1 )
| ~ ( big_r @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(202,plain,
! [SV16: $i] :
( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SV16 ) )
| ~ ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SV16 ) @ ( sK16_Z1 @ SV16 ) ) )
| ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(203,plain,
! [SV17: $i] :
( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SV17 ) )
| ~ ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) ) )
| ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(204,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
| ~ ( big_p @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(205,plain,
! [SV18: $i] :
( ( ! [SY40: $i] :
( ~ ( big_p @ SV18 )
| ~ ( big_r @ sK12_X @ SY40 )
| ~ ( big_r @ SY40 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(206,plain,
! [SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SV16 ) )
| ~ ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SV16 ) @ ( sK16_Z1 @ SV16 ) ) ) )
= $true )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(207,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SV17 ) )
| ~ ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) ) ) )
= $true )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(208,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(209,plain,
( ( ~ ( big_p @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(210,plain,
! [SV19: $i,SV18: $i] :
( ( ~ ( big_p @ SV18 )
| ~ ( big_r @ sK12_X @ SV19 )
| ~ ( big_r @ SV19 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(211,plain,
! [SV16: $i] :
( ( ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SV16 ) )
| ~ ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) ) )
| ~ ( big_r @ ( sK17_SY31 @ SV16 ) @ ( sK16_Z1 @ SV16 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(212,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SV17 ) )
| ~ ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) ) )
| ~ ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(213,plain,
( ( ~ ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(214,plain,
( ( big_p @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(215,plain,
! [SV19: $i,SV18: $i] :
( ( ( ~ ( big_p @ SV18 )
| ~ ( big_r @ sK12_X @ SV19 ) )
= $true )
| ( ( ~ ( big_r @ SV19 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(216,plain,
! [SV16: $i] :
( ( ( ~ ~ ( ~ ( big_p @ ( sK16_Z1 @ SV16 ) )
| ~ ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(217,plain,
! [SV16: $i] :
( ( ( ~ ( big_r @ ( sK17_SY31 @ SV16 ) @ ( sK16_Z1 @ SV16 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(218,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( big_p @ ( sK14_Z2 @ SV17 ) )
| ~ ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(219,plain,
! [SV17: $i] :
( ( ( ~ ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(220,plain,
( ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN )
| ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(221,plain,
! [SV19: $i,SV18: $i] :
( ( ( ~ ( big_p @ SV18 ) )
= $true )
| ( ( ~ ( big_r @ sK12_X @ SV19 ) )
= $true )
| ( ( ~ ( big_r @ SV19 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(222,plain,
! [SV16: $i] :
( ( ( ~ ( ~ ( big_p @ ( sK16_Z1 @ SV16 ) )
| ~ ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) ) ) )
= $true )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(223,plain,
! [SV16: $i] :
( ( ( big_r @ ( sK17_SY31 @ SV16 ) @ ( sK16_Z1 @ SV16 ) )
= $true )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(224,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( big_p @ ( sK14_Z2 @ SV17 ) )
| ~ ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) ) ) )
= $true )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(225,plain,
! [SV17: $i] :
( ( ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) )
= $true )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(226,plain,
( ( ~ ( ~ ( big_p @ sK12_X )
| sK18_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(227,plain,
( ( ~ ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(228,plain,
! [SV19: $i,SV18: $i] :
( ( ( big_p @ SV18 )
= $false )
| ( ( ~ ( big_r @ sK12_X @ SV19 ) )
= $true )
| ( ( ~ ( big_r @ SV19 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(229,plain,
! [SV16: $i] :
( ( ( ~ ( big_p @ ( sK16_Z1 @ SV16 ) )
| ~ ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(230,plain,
! [SV16: $i] :
( ( ( ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ SV16 )
= $true )
| ( ( big_r @ ( sK17_SY31 @ SV16 ) @ ( sK16_Z1 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(231,plain,
! [SV17: $i] :
( ( ( ~ ( big_p @ ( sK14_Z2 @ SV17 ) )
| ~ ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(232,plain,
! [SV17: $i] :
( ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true )
| ( ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(233,plain,
( ( ~ ( big_p @ sK12_X )
| sK18_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(234,plain,
( ( ~ sK18_REN
| ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(235,plain,
! [SV18: $i,SV19: $i] :
( ( ( big_r @ sK12_X @ SV19 )
= $false )
| ( ( big_p @ SV18 )
= $false )
| ( ( ~ ( big_r @ SV19 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(236,plain,
! [SV16: $i] :
( ( ( ~ ( big_p @ ( sK16_Z1 @ SV16 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(237,plain,
! [SV16: $i] :
( ( ( ~ ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(238,plain,
! [SV16: $i] :
( ( ( big_p @ a )
= $false )
| ( ( big_p @ SV16 )
= $true )
| ( ( big_r @ ( sK17_SY31 @ SV16 ) @ ( sK16_Z1 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(239,plain,
! [SV17: $i] :
( ( ( ~ ( big_p @ ( sK14_Z2 @ SV17 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(240,plain,
! [SV17: $i] :
( ( ( ~ ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) ) )
= $false )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(241,plain,
! [SV17: $i] :
( ( ( big_p @ a )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true )
| ( ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(242,plain,
( ( ( ~ ( big_p @ sK12_X ) )
= $true )
| ( sK18_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(243,plain,
( ( ( ~ sK18_REN )
= $true )
| ( ( ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(244,plain,
! [SV18: $i,SV19: $i] :
( ( ( big_r @ SV19 @ SV18 )
= $false )
| ( ( big_p @ SV18 )
= $false )
| ( ( big_r @ sK12_X @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(245,plain,
! [SV16: $i] :
( ( ( big_p @ ( sK16_Z1 @ SV16 ) )
= $true )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(246,plain,
! [SV16: $i] :
( ( ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) )
= $true )
| ( ( ~ ( big_p @ a )
| ( big_p @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(247,plain,
! [SV17: $i] :
( ( ( big_p @ ( sK14_Z2 @ SV17 ) )
= $true )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(248,plain,
! [SV17: $i] :
( ( ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) )
= $true )
| ( ( ~ ( big_p @ a )
| ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(249,plain,
! [SV17: $i,SV20: $i] :
( ( ( ~ ( big_p @ SV20 )
| ~ ( big_r @ SV17 @ SV20 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(250,plain,
( ( ( big_p @ sK12_X )
= $false )
| ( sK18_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(251,plain,
( ( sK18_REN = $false )
| ( ( ~ ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(252,plain,
! [SV16: $i] :
( ( ( ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ SV16 )
= $true )
| ( ( big_p @ ( sK16_Z1 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(253,plain,
! [SV16: $i] :
( ( ( ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ SV16 )
= $true )
| ( ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(254,plain,
! [SV17: $i] :
( ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true )
| ( ( big_p @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(255,plain,
! [SV17: $i] :
( ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true )
| ( ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(256,plain,
! [SV17: $i,SV20: $i] :
( ( ( ~ ( big_p @ SV20 ) )
= $true )
| ( ( ~ ( big_r @ SV17 @ SV20 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(257,plain,
( ( ( ~ ( big_p @ sK13_SY27 )
| ~ ( big_r @ sK12_X @ sK13_SY27 ) )
= $false )
| ( sK18_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(258,plain,
! [SV16: $i] :
( ( ( big_p @ a )
= $false )
| ( ( big_p @ SV16 )
= $true )
| ( ( big_p @ ( sK16_Z1 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(259,plain,
! [SV16: $i] :
( ( ( big_p @ a )
= $false )
| ( ( big_p @ SV16 )
= $true )
| ( ( big_r @ SV16 @ ( sK17_SY31 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(260,plain,
! [SV17: $i] :
( ( ( big_p @ a )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true )
| ( ( big_p @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(261,plain,
! [SV17: $i] :
( ( ( big_p @ a )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( big_p @ SY39 )
| ~ ( big_r @ SV17 @ SY39 ) ) )
= $true )
| ( ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(262,plain,
! [SV17: $i,SV20: $i] :
( ( ( big_p @ SV20 )
= $false )
| ( ( ~ ( big_r @ SV17 @ SV20 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(263,plain,
( ( ( ~ ( big_p @ sK13_SY27 ) )
= $false )
| ( sK18_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(264,plain,
( ( ( ~ ( big_r @ sK12_X @ sK13_SY27 ) )
= $false )
| ( sK18_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(265,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( big_p @ SV21 )
| ~ ( big_r @ SV17 @ SV21 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_p @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(266,plain,
! [SV17: $i,SV22: $i] :
( ( ( ~ ( big_p @ SV22 )
| ~ ( big_r @ SV17 @ SV22 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(267,plain,
! [SV20: $i,SV17: $i] :
( ( ( big_r @ SV17 @ SV20 )
= $false )
| ( ( big_p @ SV20 )
= $false )
| ( ( big_p @ a )
= $false )
| ( ( big_r @ ( sK15_SY30 @ SV17 ) @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(268,plain,
( ( ( big_p @ sK13_SY27 )
= $true )
| ( sK18_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(269,plain,
( ( ( big_r @ sK12_X @ sK13_SY27 )
= $true )
| ( sK18_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(270,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( big_p @ SV21 ) )
= $true )
| ( ( ~ ( big_r @ SV17 @ SV21 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_p @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(271,plain,
! [SV17: $i,SV22: $i] :
( ( ( ~ ( big_p @ SV22 ) )
= $true )
| ( ( ~ ( big_r @ SV17 @ SV22 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(272,plain,
! [SV17: $i,SV21: $i] :
( ( ( big_p @ SV21 )
= $false )
| ( ( ~ ( big_r @ SV17 @ SV21 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_p @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(273,plain,
! [SV17: $i,SV22: $i] :
( ( ( big_p @ SV22 )
= $false )
| ( ( ~ ( big_r @ SV17 @ SV22 ) )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(274,plain,
! [SV21: $i,SV17: $i] :
( ( ( big_r @ SV17 @ SV21 )
= $false )
| ( ( big_p @ SV21 )
= $false )
| ( ( big_p @ a )
= $false )
| ( ( big_p @ ( sK14_Z2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(275,plain,
! [SV22: $i,SV17: $i] :
( ( ( big_r @ SV17 @ SV22 )
= $false )
| ( ( big_p @ SV22 )
= $false )
| ( ( big_p @ a )
= $false )
| ( ( big_r @ SV17 @ ( sK15_SY30 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(276,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[214,275,274,269,268,267,259,258,250,244,238]) ).
thf(277,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[276,184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n014.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 14:49:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (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)..............
% 0.20/0.51
% 0.20/0.51 ********************************
% 0.20/0.51 * All subproblems solved! *
% 0.20/0.51 ********************************
% 0.20/0.51 % 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:276,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.55
% 0.20/0.55 %**** Beginning of derivation protocol ****
% 0.20/0.55 % SZS output start CNFRefutation
% See solution above
% 0.20/0.55
% 0.20/0.55 %**** End of derivation protocol ****
% 0.20/0.55 %**** no. of clauses in derivation: 277 ****
% 0.20/0.55 %**** clause counter: 276 ****
% 0.20/0.55
% 0.20/0.55 % 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:276,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------