%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL332-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 : Sun Sep 27 07:51:31 AM UTC 2026
% Result : Unsatisfiable 211.22s 56.42s
% Output : Refutation 205.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 10
% Syntax : Number of formulae : 414 ( 199 unt; 0 typ; 0 def)
% Number of atoms : 1006 ( 344 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 5021 ( 491 ~; 308 |; 0 &;4222 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 978 ( 0 ^; 978 !; 0 ?; 978 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(r_decl,type,
r: $i ).
thf(p_decl,type,
p: $i ).
thf(q_decl,type,
q: $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
thf(13,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(20,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[20]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[13,21]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(45,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[40]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
thf(14,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[14,21]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(44,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[37]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[22]) ).
thf(52,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ implies ) @ theorem ) )
| ~ ( D @ theorem )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[44,23]) ).
thf(53,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ implies ) @ theorem ) )
| ~ ( D @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ or ) )),bind(D,$thf( F ))]]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(simp,[status(thm)],[54]) ).
thf(526,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[45,62]) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[526]) ).
thf(528,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[527:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ or ) @ implies ) ))]]) ).
thf(569,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[528]) ).
thf(595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[569,62]) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[595]) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( C @ or ) @ implies ) @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[596:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ ( H @ or ) @ implies ) @ ( E @ or ) ))]]) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( C @ or ) @ implies ) @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[597]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
thf(15,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[15,21]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ or ) @ ( H @ ( I @ or ) @ implies ) ))]]) ).
thf(72,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[67]) ).
thf(1,negated_conjecture,
~ ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
~ ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
~ ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,12]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[156]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ or ) )
= ( B @ ( A @ implies ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ implies ) @ not ) ),
inference(rewrite,[status(thm)],[25,19]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) ),
inference(rewrite,[status(thm)],[171,177]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,12]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[50]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) ) )
| ( B
!= ( q @ ( p @ implies ) @ ( r @ and ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(116,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ ( r @ and ) @ ( A @ or ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ implies ) @ ( r @ and ) @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,116]) ).
thf(119,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ ( r @ and ) @ ( A @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( D )),bind(B,$thf( q @ ( p @ implies ) @ ( r @ and ) )),bind(C,$thf( D @ not ))]]) ).
thf(120,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ ( r @ and ) @ ( A @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(136,plain,
! [A: $i] :
( ( ( r @ ( q @ and ) )
!= ( q @ ( p @ implies ) @ ( r @ and ) ) )
| ( A != p ) ),
inference(simp,[status(thm)],[120]) ).
thf(137,plain,
( ( r @ ( q @ and ) )
!= ( q @ ( p @ implies ) @ ( r @ and ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
( ( ( q @ ( p @ implies ) )
!= r )
| ( q != r ) ),
inference(simp,[status(thm)],[137]) ).
thf(181,plain,
~ ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) @ theorem ),
inference(rewrite,[status(thm)],[12,177]) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[62,181]) ).
thf(539,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[538]) ).
thf(559,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[539]) ).
thf(758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) )
| ~ ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,559]) ).
thf(759,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) )
| ~ ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(781,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) )
| ~ ( A @ theorem ) ),
inference(simp,[status(thm)],[759]) ).
thf(992,plain,
~ ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) )),bind(B,$thf( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ))]]) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[62,992]) ).
thf(1109,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[1108]) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[1109]) ).
thf(1356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) )
| ~ ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,1116]) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) )
| ~ ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[1356:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(1379,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) )
| ~ ( A @ theorem ) ),
inference(simp,[status(thm)],[1357]) ).
thf(1579,plain,
~ ( r @ not @ ( q @ implies ) @ not @ theorem ),
inference(pattern_uni,[status(thm)],[1379:[bind(A,$thf( r @ not @ ( q @ implies ) @ not )),bind(B,$thf( p ))]]) ).
thf(1725,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[62,1579]) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[1725]) ).
thf(1754,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[1726]) ).
thf(1916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[62,1754]) ).
thf(1917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[1916]) ).
thf(1918,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( C @ theorem ) ),
inference(pattern_uni,[status(thm)],[1917:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ or ) ))]]) ).
thf(1950,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( C @ theorem ) ),
inference(simp,[status(thm)],[1918]) ).
thf(1707,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,1579]) ).
thf(1708,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1707]) ).
thf(1750,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1708]) ).
thf(1092,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,992]) ).
thf(1093,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1092]) ).
thf(1129,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1093]) ).
thf(1517,plain,
! [A: $i] :
( ( A
!= ( r @ not @ ( q @ implies ) @ not ) )
| ( ( A @ ( A @ or ) )
!= p ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1520,plain,
( ( r @ not @ ( q @ implies ) @ not @ ( r @ not @ ( q @ implies ) @ not @ or ) )
!= p ),
inference(simp,[status(thm)],[1517]) ).
thf(1522,plain,
( ( r @ not @ ( q @ implies ) @ not @ ( r @ not @ ( q @ implies ) @ implies ) )
!= p ),
inference(rewrite,[status(thm)],[1520,19]) ).
thf(167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( D @ ( C @ or ) @ ( B @ ( A @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,72]) ).
thf(168,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(175,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[168]) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,175]) ).
thf(237,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(242,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[237]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ~ ( B @ ( C @ implies ) @ theorem )
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[45,23]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ ( B @ ( C @ implies ) @ theorem )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( B @ or ) @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ or ) @ implies ) ))]]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( B @ or ) @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[82]) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[242,89]) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[1174]) ).
thf(1176,plain,
! [A: $i] : ( A @ not @ ( A @ not @ or ) @ not @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1175:[bind(A,$thf( N )),bind(B,$thf( N @ not @ ( N @ not @ or ) )),bind(C,$thf( N @ not @ ( N @ not @ or ) @ not @ ( N @ implies ) )),bind(D,$thf( N @ not ))]]) ).
thf(1201,plain,
! [A: $i] : ( A @ not @ ( A @ not @ or ) @ not @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1176]) ).
thf(1254,plain,
! [A: $i] : ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem ),
inference(rewrite,[status(thm)],[1201,19]) ).
thf(1284,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1254,992]) ).
thf(1285,plain,
! [A: $i] :
( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1284]) ).
thf(1290,plain,
! [A: $i] :
( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1285]) ).
thf(3399,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ( A != p ) ),
inference(simp,[status(thm)],[1290]) ).
thf(3400,plain,
( ( r @ not @ ( q @ implies ) @ not )
!= ( p @ not @ ( p @ implies ) @ not ) ),
inference(simp,[status(thm)],[3399]) ).
thf(3401,plain,
( ( r @ not @ ( q @ implies ) )
!= ( p @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[3400]) ).
thf(3402,plain,
( ( ( p @ not )
!= ( r @ not ) )
| ( q != p ) ),
inference(simp,[status(thm)],[3401]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,60]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) ),
inference(rewrite,[status(thm)],[117,177]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( C @ ( B @ ( A @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,45]) ).
thf(84,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(90,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[84]) ).
thf(121,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[90,12]) ).
thf(122,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[121]) ).
thf(132,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(371,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) ),
inference(rewrite,[status(thm)],[132,177]) ).
thf(372,plain,
! [A: $i] :
( ( ( A @ not )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) )
| ( ( A @ not @ ( A @ implies ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[371]) ).
thf(497,plain,
! [A: $i] :
( ( ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) )
!= ( A @ not @ ( A @ implies ) ) )
| ( ( A @ not )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) )
| ( ( A @ not @ ( A @ implies ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[372]) ).
thf(499,plain,
! [A: $i] :
( ( ( r @ not @ ( q @ implies ) @ not )
!= ( A @ not ) )
| ( p != A )
| ( ( A @ not )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) )
| ( ( A @ not @ ( A @ implies ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[497]) ).
thf(502,plain,
( ( ( r @ not @ ( q @ implies ) @ not )
!= ( p @ not ) )
| ( ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not )
!= ( p @ not ) )
| ( ( p @ not @ ( p @ implies ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[499]) ).
thf(698,plain,
( ( ( r @ not @ ( q @ implies ) )
!= p )
| ( ( q @ ( p @ implies ) @ not @ ( r @ implies ) )
!= p )
| ( ( p @ not @ ( p @ implies ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[502]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[16,21]) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ or ) @ ( C @ ( A @ or ) @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ or ) @ ( K @ or ) @ ( N @ ( K @ or ) @ ( M @ or ) @ implies ) ))]]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ or ) @ ( C @ ( A @ or ) @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[141]) ).
thf(1727,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[90,1579]) ).
thf(1728,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1727]) ).
thf(1746,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1728]) ).
thf(182,plain,
( ( r @ not @ ( q @ implies ) @ not )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ),
inference(rewrite,[status(thm)],[137,177]) ).
thf(183,plain,
( ( r @ not @ ( q @ implies ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(184,plain,
( ( ( q @ ( p @ implies ) @ not )
!= ( r @ not ) )
| ( q != r ) ),
inference(simp,[status(thm)],[183]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[19,14]) ).
thf(29,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(31,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(simp,[status(thm)],[29]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[31,21]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(46,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[43]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ implies ) @ theorem ) )
| ~ ( D @ theorem )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[46,23]) ).
thf(96,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ implies ) @ theorem ) )
| ~ ( D @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[95]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ implies ) )),bind(D,$thf( F ))]]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[97]) ).
thf(2125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[1254,105]) ).
thf(2126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[2125]) ).
thf(2127,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ implies ) @ not @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[2126:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ not @ ( I @ implies ) @ not @ ( I @ implies ) ))]]) ).
thf(2269,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ implies ) @ not @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[2127]) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ~ ( C @ ( D @ implies ) @ theorem )
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[44,23]) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ ( C @ ( D @ implies ) @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[55]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ or ) @ ( C @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ or ) @ ( H @ implies ) ))]]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ or ) @ ( C @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[57]) ).
thf(811,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( E @ ( D @ or ) @ ( E @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[175,63]) ).
thf(812,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( E @ ( D @ or ) @ ( E @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[811]) ).
thf(813,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[812:[bind(A,$thf( L @ ( J @ or ) )),bind(B,$thf( L )),bind(C,$thf( L @ not @ ( L @ ( J @ or ) @ or ) )),bind(D,$thf( J )),bind(E,$thf( L ))]]) ).
thf(837,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[813]) ).
thf(865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[837,62]) ).
thf(866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[865]) ).
thf(867,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ or ) @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[866:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ not @ ( I @ ( G @ or ) @ or ) ))]]) ).
thf(875,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ or ) @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[867]) ).
thf(1441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ not @ ( E @ ( D @ or ) @ or ) @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,875]) ).
thf(1442,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ or ) @ or ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1441:[bind(A,$thf( F )),bind(B,$thf( K @ not @ ( K @ ( I @ or ) @ or ) )),bind(C,$thf( F @ not )),bind(D,$thf( I )),bind(E,$thf( K ))]]) ).
thf(1455,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ or ) @ or ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1442]) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[837,992]) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1088]) ).
thf(1132,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ or ) @ or ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1089]) ).
thf(862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( D @ not @ ( B @ ( A @ implies ) @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,837]) ).
thf(863,plain,
! [B: $i,A: $i] : ( A @ not @ ( A @ ( B @ implies ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[862:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(879,plain,
! [B: $i,A: $i] : ( A @ not @ ( A @ ( B @ implies ) @ or ) @ theorem ),
inference(simp,[status(thm)],[863]) ).
thf(1084,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( A @ ( B @ implies ) @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,992]) ).
thf(1085,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( A @ ( B @ implies ) @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1084]) ).
thf(1125,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( A @ ( B @ implies ) @ or ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1085]) ).
thf(2686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ not @ ( C @ ( D @ implies ) @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1125]) ).
thf(2689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( C @ not ) )
| ( ( A @ not )
!= ( C @ ( D @ implies ) ) )
| ( B
!= ( r @ not @ ( q @ implies ) @ not ) )
| ( A != p ) ),
inference(simp,[status(thm)],[2686]) ).
thf(2691,plain,
! [B: $i,A: $i] :
( ( ( r @ not @ ( q @ implies ) @ not )
!= ( A @ not ) )
| ( ( A @ ( B @ implies ) )
!= ( p @ not ) ) ),
inference(simp,[status(thm)],[2689]) ).
thf(901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ ( B @ implies ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[879,62]) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ ( B @ implies ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[901]) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[902:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( I @ not @ ( I @ ( G @ implies ) @ or ) ))]]) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[903]) ).
thf(1493,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ not @ ( E @ ( D @ implies ) @ or ) @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,911]) ).
thf(1494,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1493:[bind(A,$thf( F )),bind(B,$thf( K @ not @ ( K @ ( I @ implies ) @ or ) )),bind(C,$thf( F @ not )),bind(D,$thf( I )),bind(E,$thf( K ))]]) ).
thf(1514,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1494]) ).
thf(1167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[175,89]) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1169,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[1168:[bind(A,$thf( K )),bind(B,$thf( K @ ( K @ or ) )),bind(C,$thf( K @ ( K @ or ) @ not @ ( K @ or ) )),bind(D,$thf( K ))]]) ).
thf(1198,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[1169]) ).
thf(1237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[1198,62]) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[1237]) ).
thf(1239,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[1238:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ ( H @ or ) @ not @ ( H @ or ) ))]]) ).
thf(1251,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[1239]) ).
thf(1551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( D @ or ) @ not @ ( D @ or ) @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,1251]) ).
thf(1552,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1551:[bind(A,$thf( E )),bind(B,$thf( J @ ( J @ or ) @ not @ ( J @ or ) )),bind(C,$thf( E @ not )),bind(D,$thf( J ))]]) ).
thf(1572,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1552]) ).
thf(1911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,1754]) ).
thf(1912,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[1911:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(1946,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( A @ theorem ) ),
inference(simp,[status(thm)],[1912]) ).
thf(179,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(rewrite,[status(thm)],[116,177]) ).
thf(2217,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[105,1579]) ).
thf(2218,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[2217]) ).
thf(2259,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[2218]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ~ ( C @ ( D @ implies ) @ theorem )
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[46,23]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ ( C @ ( D @ implies ) @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[100]) ).
thf(507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[46,62]) ).
thf(508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[507]) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[508:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[509]) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( D @ ( D @ or ) @ implies ) @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,569]) ).
thf(594,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[593:[bind(A,$thf( E )),bind(B,$thf( G @ ( G @ ( G @ or ) @ implies ) )),bind(C,$thf( E @ not )),bind(D,$thf( G ))]]) ).
thf(602,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[594]) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,992]) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1078]) ).
thf(1118,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1079]) ).
thf(1393,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ( B != p ) ),
inference(simp,[status(thm)],[1118]) ).
thf(1394,plain,
! [A: $i] :
( ( p @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1393]) ).
thf(70,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( D @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[19,15]) ).
thf(71,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(74,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[71]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= B )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[32]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( C @ ( D @ implies ) )
!= D )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[44,34]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( C @ ( D @ implies ) )
!= D )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ or ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ or ) @ ( C @ implies ) ) )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ or ) @ ( H @ implies ) ))]]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ or ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ or ) @ ( C @ implies ) ) )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[49]) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[44,62]) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[532]) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[533:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ or ) @ ( H @ implies ) ))]]) ).
thf(571,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[534]) ).
thf(626,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( E @ theorem ) )
| ~ $true
| ( E @ ( D @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[571,62]) ).
thf(627,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( E @ theorem ) )
| ( E @ ( D @ or ) @ theorem ) ),
inference(simp,[status(thm)],[626]) ).
thf(628,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ or ) @ ( D @ implies ) @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[627:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ or ) @ ( K @ implies ) @ ( F @ or ) ))]]) ).
thf(634,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ or ) @ ( D @ implies ) @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[628]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ~ ( B @ ( C @ implies ) @ theorem )
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[90,23]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ ( B @ ( C @ implies ) @ theorem )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ not @ ( I @ not @ ( I @ implies ) @ implies ) ))]]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[128]) ).
thf(75,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,12]) ).
thf(76,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[75]) ).
thf(88,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(266,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) ),
inference(rewrite,[status(thm)],[88,177]) ).
thf(267,plain,
! [A: $i] :
( ( A
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) )
| ( ( A @ ( A @ or ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(270,plain,
( ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ or ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ),
inference(simp,[status(thm)],[267]) ).
thf(655,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( E @ theorem ) )
| ~ $true
| ( E @ ( D @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[574,62]) ).
thf(656,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( E @ theorem ) )
| ( E @ ( D @ or ) @ theorem ) ),
inference(simp,[status(thm)],[655]) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[656:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ or ) ))]]) ).
thf(661,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[657]) ).
thf(1711,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,1579]) ).
thf(1712,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1711]) ).
thf(1736,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1712]) ).
thf(683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( D @ or ) ) )
| ( D @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,602]) ).
thf(684,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[683:[bind(A,$thf( F )),bind(B,$thf( F @ not )),bind(C,$thf( C )),bind(D,$thf( F @ not ))]]) ).
thf(693,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[684]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[32]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( B @ ( C @ implies ) @ theorem ) )
| ~ ( C @ theorem )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[45,23]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( B @ ( C @ implies ) @ theorem ) )
| ~ ( C @ theorem )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
! [A: $i] :
( ~ ( A @ ( A @ or ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ or ) ))]]) ).
thf(92,plain,
! [A: $i] :
( ~ ( A @ ( A @ or ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[79]) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[90,62]) ).
thf(552,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[551]) ).
thf(553,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[552:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ not @ ( I @ not @ ( I @ implies ) @ implies ) ))]]) ).
thf(566,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[553]) ).
thf(653,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,574]) ).
thf(654,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[653:[bind(A,$thf( F )),bind(B,$thf( J @ ( I @ implies ) @ ( J @ implies ) )),bind(C,$thf( F @ not )),bind(D,$thf( I )),bind(E,$thf( J ))]]) ).
thf(665,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[654]) ).
thf(1096,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,992]) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1096]) ).
thf(1128,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1097]) ).
thf(3403,plain,
( ( p != r )
| ( q != p ) ),
inference(simp,[status(thm)],[3402]) ).
thf(697,plain,
( ( ( r @ not @ ( q @ implies ) )
!= p )
| ( ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not )
!= ( p @ not ) )
| ( ( p @ not @ ( p @ implies ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[502]) ).
thf(2090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ( ( C @ ( D @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[62,1946]) ).
thf(2091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ( ( C @ ( D @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[2090]) ).
thf(2092,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( C @ theorem ) ),
inference(pattern_uni,[status(thm)],[2091:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ or ) ))]]) ).
thf(2115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( C @ theorem ) ),
inference(simp,[status(thm)],[2092]) ).
thf(2693,plain,
! [B: $i,A: $i] :
( ( ( r @ not @ ( q @ implies ) )
!= A )
| ( ( A @ ( B @ implies ) )
!= ( p @ not ) ) ),
inference(simp,[status(thm)],[2691]) ).
thf(2694,plain,
! [A: $i] :
( ( r @ not @ ( q @ implies ) @ ( A @ implies ) )
!= ( p @ not ) ),
inference(simp,[status(thm)],[2693]) ).
thf(1693,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[602,1579]) ).
thf(1694,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1693]) ).
thf(1755,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1694]) ).
thf(622,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( D @ or ) @ ( E @ implies ) @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,571]) ).
thf(623,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( F )),bind(B,$thf( J @ ( I @ or ) @ ( J @ implies ) )),bind(C,$thf( F @ not )),bind(D,$thf( I )),bind(E,$thf( J ))]]) ).
thf(637,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[623]) ).
thf(1683,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[637,1579]) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1683]) ).
thf(1739,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1684]) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,1579]) ).
thf(1718,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1717]) ).
thf(1744,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1718]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( B @ ( C @ implies ) )
!= C )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[90,34]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( B @ ( C @ implies ) )
!= C )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[129]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ implies ) )
!= ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) ) )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ not @ ( I @ not @ ( I @ implies ) @ implies ) ))]]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ implies ) )
!= ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) ) )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[131]) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( C @ ( D @ or ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[19,15]) ).
thf(69,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(73,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[69]) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[569,1579]) ).
thf(1704,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1703]) ).
thf(1732,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1704]) ).
thf(1691,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[574,1579]) ).
thf(1692,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1691]) ).
thf(1747,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1692]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) ),
inference(rewrite,[status(thm)],[60,177]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( D @ or ) ) )
| ( E @ ( C @ or ) @ ( D @ or ) @ ( B @ ( A @ implies ) @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[19,16]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ or ) @ ( C @ not @ or ) @ ( A @ ( C @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ not )),bind(E,$thf( B ))]]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ or ) @ ( C @ not @ or ) @ ( A @ ( C @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[147]) ).
thf(3387,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ or ) @ ( C @ implies ) @ ( A @ ( C @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[151,19]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ ( D @ or ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,72]) ).
thf(170,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(176,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[170]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[19,73]) ).
thf(189,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(191,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[189]) ).
thf(1721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[571,1579]) ).
thf(1722,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1721]) ).
thf(1752,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1722]) ).
thf(1695,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( A @ ( B @ implies ) @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,1579]) ).
thf(1696,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( A @ ( B @ implies ) @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1695]) ).
thf(1733,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( A @ ( B @ implies ) @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1696]) ).
thf(144,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( C @ or ) @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( E @ ( D @ or ) @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[19,16]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ not @ or ) @ ( B @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( F )),bind(B,$thf( H @ ( G @ or ) )),bind(C,$thf( G )),bind(D,$thf( F @ not )),bind(E,$thf( H ))]]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ not @ or ) @ ( B @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[145]) ).
thf(457,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[150,19]) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[457,21]) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[458]) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[459:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ or ) @ ( K @ implies ) @ ( N @ ( K @ implies ) @ ( M @ or ) @ implies ) ))]]) ).
thf(466,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[460]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( B @ ( C @ implies ) )
!= C )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[45,34]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( B @ ( C @ implies ) )
!= C )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[85]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ or ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ or ) @ implies ) ) )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ or ) @ implies ) ))]]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ or ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ or ) @ implies ) ) )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[87]) ).
thf(1286,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[1254,62]) ).
thf(1287,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[1286]) ).
thf(1288,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ implies ) @ not @ ( B @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[1287:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ not @ ( I @ implies ) @ not @ ( I @ implies ) ))]]) ).
thf(1293,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ implies ) @ not @ ( B @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[1288]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( B @ ( C @ implies ) @ theorem ) )
| ~ ( C @ theorem )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[90,23]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( B @ ( C @ implies ) @ theorem ) )
| ~ ( C @ theorem )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
! [A: $i] :
( ~ ( A @ not @ ( A @ implies ) @ theorem )
| ( A @ not @ theorem ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( G )),bind(B,$thf( G @ not )),bind(C,$thf( G @ not @ ( G @ implies ) ))]]) ).
thf(135,plain,
! [A: $i] :
( ~ ( A @ not @ ( A @ implies ) @ theorem )
| ( A @ not @ theorem ) ),
inference(simp,[status(thm)],[125]) ).
thf(1397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1128]) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1397:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1398]) ).
thf(142,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( D @ or ) @ ( E @ ( D @ or ) @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[19,16]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ not @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ not )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ not @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[143]) ).
thf(3754,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ implies ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[154,19]) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1579]) ).
thf(1690,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1689]) ).
thf(1753,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1690]) ).
thf(1681,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1254,1579]) ).
thf(1682,plain,
! [A: $i] :
( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1681]) ).
thf(1749,plain,
! [A: $i] :
( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1682]) ).
thf(1110,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[90,992]) ).
thf(1111,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1110]) ).
thf(1133,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1111]) ).
thf(3284,plain,
! [A: $i] :
( ( ( A @ not )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ( ( A @ not @ ( A @ implies ) )
!= p ) ),
inference(simp,[status(thm)],[1133]) ).
thf(1842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ) ),
inference(paramod_ordered,[status(thm)],[19,1736]) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[1842:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(1844,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1843]) ).
thf(1699,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[837,1579]) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1699]) ).
thf(1734,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ or ) @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1700]) ).
thf(2702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( D @ ( C @ or ) @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1132]) ).
thf(2705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( D @ not ) )
| ( ( A @ not )
!= ( D @ ( C @ or ) ) )
| ( B
!= ( r @ not @ ( q @ implies ) @ not ) )
| ( A != p ) ),
inference(simp,[status(thm)],[2702]) ).
thf(2707,plain,
! [B: $i,A: $i] :
( ( ( r @ not @ ( q @ implies ) @ not )
!= ( B @ not ) )
| ( ( B @ ( A @ or ) )
!= ( p @ not ) ) ),
inference(simp,[status(thm)],[2705]) ).
thf(2789,plain,
! [B: $i,A: $i] :
( ( ( r @ not @ ( q @ implies ) )
!= B )
| ( ( B @ ( A @ or ) )
!= ( p @ not ) ) ),
inference(simp,[status(thm)],[2707]) ).
thf(2792,plain,
! [A: $i] :
( ( r @ not @ ( q @ implies ) @ ( A @ or ) )
!= ( p @ not ) ),
inference(simp,[status(thm)],[2789]) ).
thf(1685,plain,
! [A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1198,1579]) ).
thf(1686,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1685]) ).
thf(1745,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1686]) ).
thf(1235,plain,
! [A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1198,992]) ).
thf(1236,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1235]) ).
thf(1244,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[1236]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( C @ ( B @ ( A @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(27,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(30,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[27]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,12]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[93]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( r @ ( q @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( r @ and ) @ implies ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ implies ) ) ),
inference(rewrite,[status(thm)],[104,177]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( C @ ( D @ implies ) )
!= D )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[46,34]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( C @ ( D @ implies ) )
!= D )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) @ ( C @ implies ) ) )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) @ ( C @ implies ) ) )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[103]) ).
thf(696,plain,
( ( ( r @ not @ ( q @ implies ) @ not )
!= ( p @ not ) )
| ( ( q @ ( p @ implies ) @ not @ ( r @ implies ) )
!= p )
| ( ( p @ not @ ( p @ implies ) )
!= ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[502]) ).
thf(540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[72,62]) ).
thf(541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[540]) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( B @ ( C @ or ) @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[541:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ or ) @ ( I @ ( J @ or ) @ implies ) ))]]) ).
thf(575,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( B @ ( C @ or ) @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[542]) ).
thf(178,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ not @ ( r @ implies ) @ not @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not @ ( p @ implies ) ) ),
inference(rewrite,[status(thm)],[120,177]) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ( B != p ) ),
inference(simp,[status(thm)],[1128]) ).
thf(1399,plain,
! [A: $i] :
( ( p @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1396]) ).
thf(2190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[105,1754]) ).
thf(2191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[2190]) ).
thf(2192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( C @ theorem ) ),
inference(pattern_uni,[status(thm)],[2191:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(2270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ or ) )
!= ( r @ not @ ( q @ implies ) @ not ) )
| ~ ( C @ theorem ) ),
inference(simp,[status(thm)],[2192]) ).
thf(1697,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[665,1579]) ).
thf(1698,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( r @ not @ ( q @ implies ) @ not @ theorem ) ),
inference(simp,[status(thm)],[1697]) ).
thf(1737,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( r @ not @ ( q @ implies ) @ not ) ),
inference(simp,[status(thm)],[1698]) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[17,21]) ).
thf(209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[208]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ ( B @ or ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( M )),bind(D,$thf( N @ ( M @ or ) @ ( L @ ( M @ or ) @ implies ) @ ( N @ ( L @ implies ) @ implies ) ))]]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ ( B @ or ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[210]) ).
thf(65980,plain,
$false,
inference(e,[status(thm)],[604,374,138,1950,1750,1522,3402,1290,276,698,153,1746,24,1254,14,184,2269,372,1455,1132,2691,559,1379,1514,20,46,1572,1946,179,2259,106,574,602,1394,74,61,634,89,133,270,661,1736,693,21,33,92,566,665,1128,3403,879,697,2115,2694,1755,1118,1739,637,1744,837,911,13,569,371,134,73,105,266,1732,1251,1754,34,1747,45,180,17,3387,176,191,22,44,1125,1752,875,1733,466,181,91,1293,1198,135,63,18,1400,3754,1753,16,502,1579,31,177,182,72,175,571,1749,11,3284,3400,3401,1844,1734,2792,2707,1745,1244,781,23,1116,1133,30,273,183,19,107,242,696,1129,575,992,15,62,178,1399,2270,90,1737,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL332-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.25/0.50 % Computer : n018.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Fri Sep 25 22:18:20 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.55/1.43 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.03/1.73 % [INFO] Parsing done (303ms).
% 2.03/1.76 % [INFO] Running in sequential loop mode.
% 2.91/2.38 % [INFO] eprover registered as external prover.
% 2.91/2.39 % [INFO] Scanning for conjecture ...
% 3.26/2.52 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.26/2.57 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.43/2.60 % [INFO] Problem is propositional (TPTP CNF).
% 3.43/2.61 % [INFO] Type checking passed.
% 3.43/2.62 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 211.22/56.42 % External prover 'e' found a proof!
% 211.22/56.42 % [INFO] Killing All external provers ...
% 211.22/56.42 % Time passed: 55685ms (effective reasoning time: 54654ms)
% 211.22/56.42 % Axioms used in derivation (9): axiom_1_5, and_defn, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 211.22/56.42 % No. of inferences in proof: 414
% 211.22/56.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 55685 ms resp. 54654 ms w/o parsing
% 205.14/56.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 205.14/56.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------