%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE017+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 07:42:59 AM UTC 2026
% Result : Theorem 129.33s 39.00s
% Output : Refutation 129.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 232 ( 93 unt; 0 typ; 4 def)
% Number of atoms : 661 ( 314 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 1692 ( 258 ~; 229 |; 55 &;1111 @)
% ( 6 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 313 ( 1 ^; 303 !; 5 ?; 313 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(one_decl,type,
one: $i ).
thf(complement_decl,type,
complement: $i > $i > $o ).
thf(c_decl,type,
c: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $o ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test )
& ( A @ test ) )
=> ( ( ( ( B @ ( C @ leq ) )
& ( A @ ( C @ leq ) ) )
=> ( B @ ( A @ multiplication ) @ ( C @ leq ) ) )
& ( ( B @ ( A @ multiplication ) @ ( C @ leq ) )
=> ( ( B @ ( C @ leq ) )
& ( A @ ( C @ leq ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ test )
& ( A @ test )
& ( sk1 @ test ) )
=> ( ( ( ( A @ ( B @ leq ) )
& ( sk1 @ ( B @ leq ) ) )
=> ( A @ ( sk1 @ multiplication ) @ ( B @ leq ) ) )
& ( ( A @ ( sk1 @ multiplication ) @ ( B @ leq ) )
=> ( ( A @ ( B @ leq ) )
& ( sk1 @ ( B @ leq ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ test )
& ( sk2 @ test )
& ( sk1 @ test ) )
=> ( ( ( ( sk2 @ ( A @ leq ) )
& ( sk1 @ ( A @ leq ) ) )
=> ( sk2 @ ( sk1 @ multiplication ) @ ( A @ leq ) ) )
& ( ( sk2 @ ( sk1 @ multiplication ) @ ( A @ leq ) )
=> ( ( sk2 @ ( A @ leq ) )
& ( sk1 @ ( A @ leq ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[51]) ).
thf(14,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(71,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(72,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[71]) ).
thf(73,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[72]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ ( C @ leq ) )
<=> ( ( B @ ( C @ leq ) )
& ( A @ ( C @ leq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ ( C @ leq ) )
<=> ( ( B @ ( C @ leq ) )
& ( A @ ( C @ leq ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test )
& ( A @ test ) )
=> ( ( ( ( B @ ( C @ leq ) )
& ( A @ ( C @ leq ) ) )
=> ( B @ ( A @ multiplication ) @ ( C @ leq ) ) )
& ( ( B @ ( A @ multiplication ) @ ( C @ leq ) )
=> ( ( B @ ( C @ leq ) )
& ( A @ ( C @ leq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
( ( ~ ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) )
| sk4 )
& ( ( sk2 @ ( sk3 @ leq ) )
| sk4 )
& ( ( sk1 @ ( sk3 @ leq ) )
| sk4 )
& ( ~ sk4
| ~ ( sk2 @ ( sk3 @ leq ) )
| ~ ( sk1 @ ( sk3 @ leq ) ) )
& ( ~ sk4
| ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) ) )
& ( sk3 @ test )
& ( sk2 @ test )
& ( sk1 @ test ) ),
inference(cnf,[status(esa)],[19]) ).
thf(28,plain,
( ( sk2 @ ( sk3 @ leq ) )
| sk4 ),
inference(cnfConj,[status(thm)],[20]) ).
thf(27,plain,
( ~ ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) )
| sk4 ),
inference(cnfConj,[status(thm)],[20]) ).
thf(135,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) )
!= ( sk2 @ ( sk3 @ leq ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[28,27]) ).
thf(136,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) )
!= ( sk2 @ ( sk3 @ leq ) ) )
| sk4 ),
inference(simp,[status(thm)],[135]) ).
thf(143,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) )
!= sk2 )
| ( sk3 != sk3 )
| sk4 ),
inference(simp,[status(thm)],[136]) ).
thf(147,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) )
!= sk2 )
| sk4 ),
inference(simp,[status(thm)],[143]) ).
thf(343,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) ) )
| ( sk2 != zero )
| sk4 ),
inference(paramod_ordered,[status(thm)],[73,147]) ).
thf(348,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk1 )
| ( sk2 != zero )
| sk4 ),
inference(simp,[status(thm)],[343]) ).
thf(353,plain,
( ( sk2 != zero )
| sk4 ),
inference(simp,[status(thm)],[348]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(74,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)],[15]) ).
thf(75,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ! [A: $i] :
( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(miniscope,[status(thm)],[74]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ test )
| ~ ( B @ ( C @ complement ) ) )
& ( ( A @ ( A @ sk5 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[76]) ).
thf(24,plain,
sk3 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(1215,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,77]) ).
thf(1216,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[1215]) ).
thf(1217,plain,
sk3 @ ( sk3 @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1216:[bind(A,$thf( sk3 ))]]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
<=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
thf(53,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)],[11]) ).
thf(54,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)],[53]) ).
thf(55,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)],[54]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(1239,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1217,60]) ).
thf(1240,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1239]) ).
thf(1241,plain,
( ( sk3 @ sk5 @ ( sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1240:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(1233,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1217,62]) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1233]) ).
thf(1235,plain,
( ( sk3 @ sk5 @ ( sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1234:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ sk5 @ ( sk3 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1235,40]) ).
thf(1282,plain,
( ( sk3 @ ( sk3 @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1281:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(23,plain,
( ~ sk4
| ~ ( sk2 @ ( sk3 @ leq ) )
| ~ ( sk1 @ ( sk3 @ leq ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(100,plain,
( ~ $true
| ( ( sk2 @ ( sk3 @ leq ) )
!= ( sk1 @ ( sk3 @ leq ) ) )
| ~ sk4
| ~ ( sk1 @ ( sk3 @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(102,plain,
( ( sk2 != sk1 )
| ( sk3 != sk3 )
| ~ sk4
| ~ ( sk1 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(103,plain,
( ( sk2 != sk1 )
| ~ sk4
| ~ ( sk1 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(26,plain,
( ( sk1 @ ( sk3 @ leq ) )
| sk4 ),
inference(cnfConj,[status(thm)],[20]) ).
thf(140,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) )
!= ( sk1 @ ( sk3 @ leq ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(141,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) )
!= ( sk1 @ ( sk3 @ leq ) ) )
| sk4 ),
inference(simp,[status(thm)],[140]) ).
thf(144,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) )
!= sk1 )
| ( sk3 != sk3 )
| sk4 ),
inference(simp,[status(thm)],[141]) ).
thf(145,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) )
!= sk1 )
| sk4 ),
inference(simp,[status(thm)],[144]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[42]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[76]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(13,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(68,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(69,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[69]) ).
thf(213,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) ) )
| ( A != sk1 )
| sk4 ),
inference(paramod_ordered,[status(thm)],[70,145]) ).
thf(219,plain,
( ( sk2 != one )
| ( sk1 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[213]) ).
thf(222,plain,
( ( sk2 != one )
| sk4 ),
inference(simp,[status(thm)],[219]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(80,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)],[16]) ).
thf(81,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)],[80]) ).
thf(82,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)],[81]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[82]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
!= B ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(86,plain,
! [A: $i] :
( ( A @ c @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[85]) ).
thf(1706,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,86]) ).
thf(1707,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1706]) ).
thf(1708,plain,
sk3 @ c @ ( sk3 @ complement ),
inference(pattern_uni,[status(thm)],[1707:[bind(A,$thf( sk3 ))]]) ).
thf(1727,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1708,79]) ).
thf(1728,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1727]) ).
thf(1729,plain,
sk3 @ c @ test,
inference(pattern_uni,[status(thm)],[1728:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 ))]]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
= B )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[82]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(simp,[status(thm)],[87]) ).
thf(342,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) ) )
| ( A != sk2 )
| sk4 ),
inference(paramod_ordered,[status(thm)],[52,147]) ).
thf(347,plain,
( ( sk2 != sk2 )
| ( sk1 != one )
| sk4 ),
inference(simp,[status(thm)],[342]) ).
thf(352,plain,
( ( sk1 != one )
| sk4 ),
inference(simp,[status(thm)],[347]) ).
thf(5,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(35,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[36]) ).
thf(25,plain,
sk2 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(1218,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,77]) ).
thf(1219,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[1218]) ).
thf(1220,plain,
sk2 @ ( sk2 @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1219:[bind(A,$thf( sk2 ))]]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(1245,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1220,61]) ).
thf(1246,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1245]) ).
thf(1247,plain,
( ( sk2 @ ( sk2 @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1246:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk5 ))]]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(44,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)],[8]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(22,plain,
( ~ sk4
| ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(119,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) )
!= ( sk1 @ ( sk3 @ leq ) ) )
| ( sk2 != sk1 )
| ~ sk4
| ~ $true
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[22,103]) ).
thf(120,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ leq ) )
!= ( sk1 @ ( sk3 @ leq ) ) )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[119]) ).
thf(126,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) )
!= sk1 )
| ( sk3 != sk3 )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[120]) ).
thf(132,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) )
!= sk1 )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[126]) ).
thf(199,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) ) )
| ( A != sk1 )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[70,132]) ).
thf(205,plain,
( ( sk2 != one )
| ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[199]) ).
thf(209,plain,
( ( sk2 != one )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[205]) ).
thf(414,plain,
( ( sk4 != sk4 )
| ( sk2 != one )
| ( sk2 != sk1 )
| ~ $true
| ( sk2 != one ) ),
inference(paramod_ordered,[status(thm)],[222,209]) ).
thf(415,plain,
( ( sk4 != sk4 )
| ( sk2 != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[414]) ).
thf(416,plain,
( ( sk2 != sk1 )
| ( sk2 != one ) ),
inference(pattern_uni,[status(thm)],[415:[]]) ).
thf(21,plain,
sk1 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(1718,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,86]) ).
thf(1719,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1718]) ).
thf(1720,plain,
sk1 @ c @ ( sk1 @ complement ),
inference(pattern_uni,[status(thm)],[1719:[bind(A,$thf( sk1 ))]]) ).
thf(1771,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1720,79]) ).
thf(1772,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1771]) ).
thf(1773,plain,
sk1 @ c @ test,
inference(pattern_uni,[status(thm)],[1772:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(29,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)],[3]) ).
thf(212,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) ) )
| ( sk1 != zero )
| sk4 ),
inference(paramod_ordered,[status(thm)],[43,145]) ).
thf(217,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 != zero )
| ( sk1 != zero )
| sk4 ),
inference(simp,[status(thm)],[212]) ).
thf(221,plain,
( ( sk1 != zero )
| sk4 ),
inference(simp,[status(thm)],[217]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(89,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)],[17]) ).
thf(437,plain,
( ( sk4 != sk4 )
| ( sk2 != sk1 )
| ~ $true
| ~ ( sk1 @ ( sk3 @ leq ) )
| ( sk2 != zero ) ),
inference(paramod_ordered,[status(thm)],[353,103]) ).
thf(438,plain,
( ( sk4 != sk4 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk3 @ leq ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[437]) ).
thf(439,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( sk3 @ leq ) )
| ( sk2 != zero ) ),
inference(pattern_uni,[status(thm)],[438:[]]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[40,37]) ).
thf(270,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(1709,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,86]) ).
thf(1710,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1709]) ).
thf(1711,plain,
sk2 @ c @ ( sk2 @ complement ),
inference(pattern_uni,[status(thm)],[1710:[bind(A,$thf( sk2 ))]]) ).
thf(1749,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1711,79]) ).
thf(1750,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1749]) ).
thf(1751,plain,
sk2 @ c @ test,
inference(pattern_uni,[status(thm)],[1750:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 ))]]) ).
thf(1236,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1217,61]) ).
thf(1237,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1236]) ).
thf(1238,plain,
( ( sk3 @ ( sk3 @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1237:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(92,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)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(65,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(198,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) ) )
| ( sk1 != zero )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[43,132]) ).
thf(203,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 != zero )
| ( sk1 != zero )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[198]) ).
thf(208,plain,
( ( sk1 != zero )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[203]) ).
thf(322,plain,
( ( sk4 != sk4 )
| ( sk1 != zero )
| ( sk2 != sk1 )
| ~ $true
| ( sk1 != zero ) ),
inference(paramod_ordered,[status(thm)],[221,208]) ).
thf(323,plain,
( ( sk4 != sk4 )
| ( sk2 != sk1 )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[322]) ).
thf(324,plain,
( ( sk2 != sk1 )
| ( sk1 != zero ) ),
inference(pattern_uni,[status(thm)],[323:[]]) ).
thf(1227,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,77]) ).
thf(1228,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[1227]) ).
thf(1229,plain,
sk1 @ ( sk1 @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1228:[bind(A,$thf( sk1 ))]]) ).
thf(1257,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1229,60]) ).
thf(1258,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1257]) ).
thf(1259,plain,
( ( sk1 @ sk5 @ ( sk1 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1258:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk5 ))]]) ).
thf(196,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) ) )
| ( A != sk1 )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[52,132]) ).
thf(201,plain,
( ( sk2 != sk1 )
| ( sk1 != one )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[196]) ).
thf(206,plain,
( ( sk1 != one )
| ( sk2 != sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[201]) ).
thf(428,plain,
( ( sk4 != sk4 )
| ( sk1 != one )
| ( sk2 != sk1 )
| ~ $true
| ( sk1 != one ) ),
inference(paramod_ordered,[status(thm)],[352,206]) ).
thf(429,plain,
( ( sk4 != sk4 )
| ( sk2 != sk1 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[428]) ).
thf(430,plain,
( ( sk2 != sk1 )
| ( sk1 != one ) ),
inference(pattern_uni,[status(thm)],[429:[]]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[63]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[33]) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1229,61]) ).
thf(1255,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1254]) ).
thf(1256,plain,
( ( sk1 @ ( sk1 @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1255:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk5 ))]]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(47,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)],[9]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1220,60]) ).
thf(1249,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1248]) ).
thf(1250,plain,
( ( sk2 @ sk5 @ ( sk2 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1249:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk5 ))]]) ).
thf(66,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(1251,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1229,62]) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1251]) ).
thf(1253,plain,
( ( sk1 @ sk5 @ ( sk1 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1252:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk5 ))]]) ).
thf(1242,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1220,62]) ).
thf(1243,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1242]) ).
thf(1244,plain,
( ( sk2 @ sk5 @ ( sk2 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1243:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk5 ))]]) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ multiplication ) ) )
| ( ( zero @ ( D @ ( B @ multiplication ) @ addition ) )
= ( D @ ( C @ ( B @ addition ) @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,49]) ).
thf(459,plain,
! [B: $i,A: $i] :
( ( zero @ ( zero @ ( B @ multiplication ) @ addition ) )
= ( zero @ ( A @ ( B @ addition ) @ multiplication ) ) ),
inference(pattern_uni,[status(thm)],[458:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( zero ))]]) ).
thf(517,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[459,37,73]) ).
thf(526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( B @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( zero @ addition ) )
= ( D @ ( C @ ( B @ addition ) @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[517,49]) ).
thf(527,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ addition ) )
= ( zero @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(pattern_uni,[status(thm)],[526:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( zero ))]]) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ addition ) )
= ( zero @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(simp,[status(thm)],[527]) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ multiplication ) ) )
| ( ( zero @ ( D @ ( B @ multiplication ) @ addition ) )
= ( D @ ( C @ ( B @ addition ) @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[517,49]) ).
thf(525,plain,
! [B: $i,A: $i] :
( ( zero @ ( zero @ ( B @ multiplication ) @ addition ) )
= ( zero @ ( A @ ( B @ addition ) @ multiplication ) ) ),
inference(pattern_uni,[status(thm)],[524:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( zero ))]]) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( zero @ ( zero @ ( B @ multiplication ) @ addition ) )
= ( zero @ ( A @ ( B @ addition ) @ multiplication ) ) ),
inference(simp,[status(thm)],[525]) ).
thf(460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( B @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( zero @ addition ) )
= ( D @ ( C @ ( B @ addition ) @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,49]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ addition ) )
= ( zero @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(pattern_uni,[status(thm)],[460:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( zero ))]]) ).
thf(505,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ addition ) )
= ( zero @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(simp,[status(thm)],[461]) ).
thf(537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ ( B @ multiplication ) @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[517,46]) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( F @ ( E @ multiplication ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(564,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[538]) ).
thf(566,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[564,517]) ).
thf(664,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[505,566,270]) ).
thf(684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ ( B @ multiplication ) @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[664,46]) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[684:[bind(A,$thf( F @ ( E @ multiplication ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(713,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[685]) ).
thf(719,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[713,664]) ).
thf(829,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[561,37,719]) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ ( B @ multiplication ) @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[829,46]) ).
thf(850,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[849:[bind(A,$thf( F @ ( E @ multiplication ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[850]) ).
thf(926,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[888,829]) ).
thf(1064,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[562,270,926]) ).
thf(1084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ ( B @ multiplication ) @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1064,46]) ).
thf(1085,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1084:[bind(A,$thf( F @ ( E @ multiplication ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[1085]) ).
thf(1133,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[1129,1064]) ).
thf(86164,plain,
$false,
inference(e,[status(thm)],[52,353,77,1241,1282,103,145,43,79,222,1729,88,352,24,37,25,1247,46,416,1773,29,147,61,221,132,89,74,60,439,270,1708,1217,1751,70,21,1238,28,38,92,65,324,1259,53,1720,41,430,64,32,34,22,44,1256,27,71,49,86,1250,80,35,67,1235,1220,31,1711,50,1253,40,26,1244,23,1133,1229,19,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/5.53 % Computer : n004.cluster.edu
% 0.14/5.53 % Model : x86_64 x86_64
% 0.14/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.53 % Memory : 8046.5625MB
% 0.14/5.53 % OS : Linux 6.8.0-71-generic
% 0.14/5.53 % CPULimit : 300
% 0.14/5.53 % WCLimit : 300
% 0.14/5.53 % DateTime : Fri Sep 25 19:13:59 UTC 2026
% 0.14/5.54 % CPUTime :
% 0.14/5.54 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.92/6.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/6.48 % [INFO] Parsing done (172ms).
% 1.18/6.50 % [INFO] Running in sequential loop mode.
% 1.75/6.87 % [INFO] eprover registered as external prover.
% 1.75/6.88 % [INFO] Scanning for conjecture ...
% 1.94/7.03 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.15/7.13 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.29/7.18 % [INFO] Problem is first-order (TPTP FOF).
% 2.29/7.19 % [INFO] Type checking passed.
% 2.29/7.19 % [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 ...
% 129.33/39.00 % External prover 'e' found a proof!
% 129.33/39.00 % [INFO] Killing All external provers ...
% 129.33/39.00 % Time passed: 33183ms (effective reasoning time: 32499ms)
% 129.33/39.00 % 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)>
% 129.33/39.00 % Axioms used in derivation (16): additive_identity, test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, right_annihilation, additive_idempotence, additive_associativity, order, additive_commutativity, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 129.33/39.00 % No. of inferences in proof: 228
% 129.33/39.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 33183 ms resp. 32499 ms w/o parsing
% 129.85/39.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 129.85/39.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------