%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE027+4 : TPTP v9.3.1. Released v4.0.0.
% 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 : n015.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 07:43:02 AM UTC 2026
% Result : Theorem 97.15s 23.61s
% Output : Refutation 93.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 25
% Syntax : Number of formulae : 236 ( 78 unt; 0 typ; 6 def)
% Number of atoms : 705 ( 347 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2680 ( 352 ~; 284 |; 44 &;1965 @)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 311 ( 1 ^; 294 !; 10 ?; 311 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(one_decl,type,
one: $i ).
thf(complement_decl,type,
complement: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ? [D: $i] : ( D @ test )
& ( C @ test ) )
=> ( ( B @ ( C @ c @ multiplication ) @ ( A @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ ( C @ multiplication ) @ addition ) @ ( B @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ leq ) )
& ( B @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ ( B @ ( C @ c @ multiplication ) @ ( A @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ ( C @ multiplication ) @ addition ) @ leq ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ? [C: $i] : ( C @ test )
& ( B @ test ) )
=> ( ( A @ ( B @ c @ multiplication ) @ ( sk2 @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ ( B @ multiplication ) @ addition ) @ ( A @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ leq ) )
& ( A @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ ( A @ ( B @ c @ multiplication ) @ ( sk2 @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ ( B @ multiplication ) @ addition ) @ leq ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ? [B: $i] : ( B @ test )
& ( A @ test ) )
=> ( ( sk3 @ ( A @ c @ multiplication ) @ ( sk2 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ ( A @ multiplication ) @ addition ) @ ( sk3 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ leq ) )
& ( sk3 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ ( sk3 @ ( A @ c @ multiplication ) @ ( sk2 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ ( A @ multiplication ) @ addition ) @ leq ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ test ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
( ( ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) )
& ( sk5 @ test )
& ( sk4 @ test ) ),
inference(cnf,[status(esa)],[22]) ).
thf(25,plain,
sk5 @ test,
inference(cnfConj,[status(thm)],[23]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(45,plain,
! [A: $i] :
( ( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ! [A: $i] :
( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(miniscope,[status(thm)],[45]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ test )
| ~ ( B @ ( C @ complement ) ) )
& ( ( A @ ( A @ sk6 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(1266,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,48]) ).
thf(1267,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1266]) ).
thf(1268,plain,
sk5 @ ( sk5 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1267:[bind(A,$thf( sk5 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
<=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(67,plain,
( ! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(miniscope,[status(thm)],[66]) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ complement ) )
| ( ( D @ ( C @ addition ) )
!= one )
| ( ( C @ ( D @ multiplication ) )
!= zero )
| ( ( D @ ( C @ multiplication ) )
!= zero ) )
& ( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) )
& ( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) )
& ( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[68]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(1993,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1268,73]) ).
thf(1994,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1993]) ).
thf(1995,plain,
( ( sk5 @ sk6 @ ( sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1994:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(84,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(85,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[84]) ).
thf(86,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[85]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[28]) ).
thf(26,plain,
( ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(121,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[29,26]) ).
thf(135,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(161,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(191,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[29,161]) ).
thf(222,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( sk4 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(242,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(319,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[29,242]) ).
thf(345,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk4 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(367,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(374,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[29,367]) ).
thf(375,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[374]) ).
thf(397,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk4 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(414,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[397]) ).
thf(735,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( zero @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[86,414]) ).
thf(749,plain,
! [A: $i] :
( ( sk3 != zero )
| ( A
!= ( sk4 @ c ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( zero @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[735]) ).
thf(761,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( zero @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[749]) ).
thf(18,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(90,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(91,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[90]) ).
thf(92,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[91]) ).
thf(765,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(rewrite,[status(thm)],[761,92]) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[56,92]) ).
thf(967,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[966:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(1052,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ leq ) ) ),
inference(rewrite,[status(thm)],[765,967]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[68]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(58,plain,
! [A: $i] :
( ( A @ test )
=> ( ! [B: $i] :
( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ! [B: $i] :
( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ( A @ c )
= C )
| ~ ( C @ ( A @ complement ) )
| ~ ( A @ test ) )
& ( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
!= B ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(63,plain,
! [A: $i] :
( ( A @ c @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[62]) ).
thf(1360,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,63]) ).
thf(1361,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1360]) ).
thf(1362,plain,
sk5 @ c @ ( sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1361:[bind(A,$thf( sk5 ))]]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(1384,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1362,50]) ).
thf(1385,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1384]) ).
thf(1386,plain,
sk5 @ c @ test,
inference(pattern_uni,[status(thm)],[1385:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(1392,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1386,63]) ).
thf(1393,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1392]) ).
thf(1394,plain,
sk5 @ c @ c @ ( sk5 @ c @ complement ),
inference(pattern_uni,[status(thm)],[1393:[bind(A,$thf( sk5 @ c ))]]) ).
thf(2415,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1394,50]) ).
thf(2416,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[2415]) ).
thf(2417,plain,
sk5 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[2416:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1389,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1386,48]) ).
thf(1390,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1389]) ).
thf(1391,plain,
sk5 @ c @ ( sk5 @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1390:[bind(A,$thf( sk5 @ c ))]]) ).
thf(24,plain,
sk4 @ test,
inference(cnfConj,[status(thm)],[23]) ).
thf(1357,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,63]) ).
thf(1358,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1357]) ).
thf(1359,plain,
sk4 @ c @ ( sk4 @ complement ),
inference(pattern_uni,[status(thm)],[1358:[bind(A,$thf( sk4 ))]]) ).
thf(1263,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,48]) ).
thf(1264,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1265,plain,
sk4 @ ( sk4 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1264:[bind(A,$thf( sk4 ))]]) ).
thf(1965,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1265,73]) ).
thf(1966,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1965]) ).
thf(1967,plain,
( ( sk4 @ sk6 @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1966:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(81,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(82,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[82]) ).
thf(770,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( A @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[83,765]) ).
thf(772,plain,
! [A: $i] :
( ( sk3 != one )
| ( A
!= ( sk4 @ c ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( A @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[770]) ).
thf(778,plain,
( ( sk3 != one )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( sk4 @ c @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[772]) ).
thf(1055,plain,
( ( sk3 != one )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( sk4 @ c @ ( zero @ leq ) ) ),
inference(rewrite,[status(thm)],[778,967]) ).
thf(1962,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1359,73]) ).
thf(1963,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1962]) ).
thf(1964,plain,
( ( sk4 @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1963:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(2062,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk4 @ ( sk4 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[83,1964]) ).
thf(2064,plain,
! [A: $i] :
( ( sk4 != one )
| ( A
!= ( sk4 @ c ) )
| ( A = zero ) ),
inference(simp,[status(thm)],[2062]) ).
thf(2090,plain,
( ( sk4 != one )
| ( ( sk4 @ c )
= zero ) ),
inference(simp,[status(thm)],[2064]) ).
thf(1371,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1359,50]) ).
thf(1372,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1371]) ).
thf(1373,plain,
sk4 @ c @ test,
inference(pattern_uni,[status(thm)],[1372:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(2487,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( zero @ test )
| ( sk4 != one ) ),
inference(paramod_ordered,[status(thm)],[2090,1373]) ).
thf(2488,plain,
( ( zero @ test )
| ( sk4 != one ) ),
inference(pattern_uni,[status(thm)],[2487:[]]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
= B )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(simp,[status(thm)],[64]) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[43]) ).
thf(1053,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ leq ) ) ),
inference(rewrite,[status(thm)],[414,967]) ).
thf(1279,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[44,1053]) ).
thf(1290,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk4 @ c )
!= one )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1279]) ).
thf(1302,plain,
( ( ( sk4 @ c )
!= one )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1290]) ).
thf(1397,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk4 @ c )
!= one )
| ( sk4 != zero )
| ~ ( A @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[44,1302]) ).
thf(1406,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk4 @ c )
!= one )
| ( ( sk4 @ c )
!= one )
| ( sk4 != zero )
| ~ ( A @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1397]) ).
thf(1415,plain,
( ( ( sk4 @ c )
!= one )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1406]) ).
thf(1615,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk4 @ c ) )
| ( B != one )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[65,1415]) ).
thf(1616,plain,
! [A: $i] :
( ( A != one )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ~ ( A @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(pattern_uni,[status(thm)],[1615:[bind(A,$thf( sk4 ))]]) ).
thf(1754,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ~ ( one @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(simp,[status(thm)],[1616]) ).
thf(1863,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ~ ( one @ ( sk4 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1754,24]) ).
thf(1864,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ~ ( one @ ( sk4 @ complement ) ) ),
inference(simp,[status(thm)],[1863]) ).
thf(1873,plain,
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1362,1864]) ).
thf(1874,plain,
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1873]) ).
thf(1892,plain,
( ( ( sk5 @ c )
!= one )
| ( sk5 != sk4 )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1874]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(93,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[68]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(2614,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1362,74]) ).
thf(2615,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2614]) ).
thf(2616,plain,
( ( sk5 @ c @ ( sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2615:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(1379,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1373,63]) ).
thf(1380,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1379]) ).
thf(1381,plain,
sk4 @ c @ c @ ( sk4 @ c @ complement ),
inference(pattern_uni,[status(thm)],[1380:[bind(A,$thf( sk4 @ c ))]]) ).
thf(1809,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1381,50]) ).
thf(1810,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1809]) ).
thf(1811,plain,
sk4 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[1810:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(1282,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( zero @ ( sk3 @ ( sk4 @ c @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[86,1053]) ).
thf(1294,plain,
! [A: $i] :
( ( sk3 != zero )
| ( A
!= ( sk4 @ c ) )
| ( sk4 != zero )
| ~ ( zero @ ( sk3 @ ( sk4 @ c @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[1282]) ).
thf(1306,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( sk3 @ ( sk4 @ c @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[1294]) ).
thf(768,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( A @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[44,765]) ).
thf(775,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk4 @ c )
!= one )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( A @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[768]) ).
thf(781,plain,
( ( ( sk4 @ c )
!= one )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[775]) ).
thf(1057,plain,
( ( ( sk4 @ c )
!= one )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( zero @ leq ) ) ),
inference(rewrite,[status(thm)],[781,967]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(36,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(769,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[86,765]) ).
thf(774,plain,
! [A: $i] :
( ( sk3 != zero )
| ( A
!= ( sk4 @ c ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[769]) ).
thf(780,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ addition ) @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[774]) ).
thf(820,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(rewrite,[status(thm)],[780,92]) ).
thf(1871,plain,
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1265,1864]) ).
thf(1872,plain,
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1871]) ).
thf(1888,plain,
( ( sk4 != one )
| ( ( sk4 @ sk6 )
!= sk4 )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1872]) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1362,73]) ).
thf(1969,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1968]) ).
thf(1970,plain,
( ( sk5 @ ( sk5 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1969:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(3216,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1362,75]) ).
thf(3217,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3216]) ).
thf(3218,plain,
( ( sk5 @ ( sk5 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3217:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[52]) ).
thf(1318,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[83,1306]) ).
thf(1323,plain,
! [A: $i] :
( ( sk3 != one )
| ( A
!= ( sk4 @ c ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1318]) ).
thf(1329,plain,
( ( sk3 != one )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( sk4 @ c @ leq ) ) ),
inference(simp,[status(thm)],[1323]) ).
thf(2611,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1265,74]) ).
thf(2612,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2611]) ).
thf(2613,plain,
( ( sk4 @ ( sk4 @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2612:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(96,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(3213,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1265,75]) ).
thf(3214,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3213]) ).
thf(3215,plain,
( ( sk4 @ sk6 @ ( sk4 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3214:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(1117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
!= ( zero @ ( D @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[41,86]) ).
thf(1118,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(pattern_uni,[status(thm)],[1117:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( zero )),bind(D,$thf( F @ ( E @ addition ) ))]]) ).
thf(1171,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(simp,[status(thm)],[1118]) ).
thf(1194,plain,
( ( zero @ ( zero @ addition ) )
= zero ),
inference(rewrite,[status(thm)],[1171,86]) ).
thf(2024,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ c @ multiplication ) )
!= ( A @ ( one @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1964,44]) ).
thf(2066,plain,
! [A: $i] :
( ( sk4 != A )
| ( ( sk4 @ c )
!= one )
| ( zero = A ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2092,plain,
( ( ( sk4 @ c )
!= one )
| ( sk4 = zero ) ),
inference(simp,[status(thm)],[2066]) ).
thf(2654,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1268,74]) ).
thf(2655,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2654]) ).
thf(2656,plain,
( ( sk5 @ ( sk5 @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2655:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(2478,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( one != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ( sk4 != one ) ),
inference(paramod_ordered,[status(thm)],[2090,1415]) ).
thf(2479,plain,
( ( one != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk3 @ leq ) )
| ( sk4 != one ) ),
inference(pattern_uni,[status(thm)],[2478:[]]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2602,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1359,74]) ).
thf(2603,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2602]) ).
thf(2604,plain,
( ( sk4 @ c @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2603:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(1376,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1373,48]) ).
thf(1377,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1376]) ).
thf(1378,plain,
sk4 @ c @ ( sk4 @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1377:[bind(A,$thf( sk4 @ c ))]]) ).
thf(1316,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[44,1306]) ).
thf(1325,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk4 @ c )
!= one )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1316]) ).
thf(1331,plain,
( ( ( sk4 @ c )
!= one )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1325]) ).
thf(3210,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1359,75]) ).
thf(3211,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3210]) ).
thf(3212,plain,
( ( sk4 @ ( sk4 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3211:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(36774,plain,
$false,
inference(e,[status(thm)],[1995,56,73,35,1052,26,75,2417,42,1391,24,1359,1386,1967,1265,25,1055,2488,1892,93,57,1362,78,29,1415,2616,1302,1811,2090,1373,1864,84,1394,74,1306,1057,38,820,21,33,92,65,1888,1970,3218,53,1329,1964,2613,96,41,3215,32,45,44,27,54,86,1194,81,39,66,1381,48,63,2092,2656,50,1053,2479,87,30,51,2604,36,967,1268,1378,90,1331,83,3212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE027+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.23/0.49 % Computer : n015.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Fri Sep 25 19:18:43 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.45/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.97/1.66 % [INFO] Parsing done (314ms).
% 1.97/1.68 % [INFO] Running in sequential loop mode.
% 3.35/2.30 % [INFO] eprover registered as external prover.
% 3.35/2.31 % [INFO] Scanning for conjecture ...
% 3.59/2.48 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.77/2.59 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.97/2.63 % [INFO] Problem is first-order (TPTP FOF).
% 3.97/2.64 % [INFO] Type checking passed.
% 3.97/2.65 % [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 ...
% 97.15/23.60 % External prover 'e' found a proof!
% 97.15/23.60 % [INFO] Killing All external provers ...
% 97.15/23.61 % Time passed: 22908ms (effective reasoning time: 21914ms)
% 97.15/23.61 % Solved by 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)>
% 97.15/23.61 % Axioms used in derivation (18): test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, test_deMorgan2, additive_identity, additive_idempotence, additive_associativity, order, additive_commutativity, right_annihilation, test_deMorgan1, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 97.15/23.61 % No. of inferences in proof: 230
% 97.15/23.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22908 ms resp. 21914 ms w/o parsing
% 93.00/23.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 93.00/23.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------