%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE034+2 : 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 : n003.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 07:43:03 AM UTC 2026
% Result : Theorem 126.47s 30.32s
% Output : Refutation 113.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 25
% Syntax : Number of formulae : 208 ( 84 unt; 0 typ; 6 def)
% Number of atoms : 521 ( 280 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1852 ( 245 ~; 158 |; 61 &;1356 @)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 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 : 239 ( 1 ^; 227 !; 5 ?; 239 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% 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(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(addition_decl,type,
addition: $i > $i > $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] :
( ( ( zero @ ( E @ c @ ( B @ ( D @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( E @ test )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( E @ c @ ( B @ ( A @ ( C @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( C @ c @ ( sk1 @ ( B @ multiplication ) @ multiplication ) @ leq ) )
& ( D @ test )
& ( B @ test )
& ( C @ test ) )
=> ( zero @ ( D @ c @ ( A @ ( sk1 @ ( B @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( zero @ ( C @ c @ ( sk2 @ ( B @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( B @ c @ ( sk1 @ ( A @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( A @ test )
& ( B @ test ) )
=> ( zero @ ( C @ c @ ( sk2 @ ( sk1 @ ( A @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( zero @ ( B @ c @ ( sk2 @ ( A @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( A @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( B @ test )
& ( sk3 @ test )
& ( A @ test ) )
=> ( zero @ ( B @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( zero @ ( A @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( A @ test )
& ( sk3 @ test )
& ( sk4 @ test ) )
=> ( zero @ ( A @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[36]) ).
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 @ sk6 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[76]) ).
thf(7,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(41,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)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( zero @ ( E @ c @ ( B @ ( D @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( E @ test )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( E @ c @ ( B @ ( A @ ( C @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( zero @ ( E @ c @ ( B @ ( D @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( E @ test )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( E @ c @ ( B @ ( A @ ( C @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( zero @ ( E @ c @ ( B @ ( D @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( E @ test )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( E @ c @ ( B @ ( A @ ( C @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
( ~ ( zero @ ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( sk5 @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( sk5 @ test )
& ( sk3 @ test )
& ( sk4 @ test ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
sk4 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(1665,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,77]) ).
thf(1666,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1665]) ).
thf(1667,plain,
sk4 @ ( sk4 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1666:[bind(A,$thf( sk4 ))]]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(10,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(50,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)],[10]) ).
thf(51,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)],[50]) ).
thf(52,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)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[52]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(24,plain,
zero @ ( sk5 @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) @ leq ),
inference(cnfConj,[status(thm)],[22]) ).
thf(26,plain,
~ ( zero @ ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(126,plain,
( ( ( zero @ ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk5 @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,26]) ).
thf(127,plain,
( ( zero @ ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk5 @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(131,plain,
( ( zero != zero )
| ( ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) )
!= ( sk5 @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(135,plain,
( ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) )
!= ( sk5 @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(362,plain,
( ( ( sk5 @ c )
!= ( sk5 @ c ) )
| ( ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk2 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(427,plain,
( ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk2 @ ( sk4 @ multiplication ) ) ),
inference(simp,[status(thm)],[362]) ).
thf(434,plain,
( ( sk2 != sk2 )
| ( ( sk1 @ ( sk3 @ multiplication ) )
!= sk4 ) ),
inference(simp,[status(thm)],[427]) ).
thf(470,plain,
( ( sk1 @ ( sk3 @ multiplication ) )
!= sk4 ),
inference(simp,[status(thm)],[434]) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[57,470]) ).
thf(867,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk1 @ complement ) ) ),
inference(pattern_uni,[status(thm)],[866:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(39,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[39]) ).
thf(106,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[40,26]) ).
thf(109,plain,
! [A: $i] :
( ( A
!= ( sk5 @ c ) )
| ( ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(112,plain,
( ( ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(115,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[40,112]) ).
thf(116,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(118,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk1 @ ( sk3 @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(120,plain,
( ( ( sk1 @ ( sk3 @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[118]) ).
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(176,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk5 @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[73,24]) ).
thf(189,plain,
! [A: $i] :
( ( ( sk5 @ c )
!= zero )
| ( A
!= ( sk2 @ ( sk4 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(205,plain,
( ( ( sk5 @ c )
!= zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(185,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[73,26]) ).
thf(195,plain,
! [A: $i] :
( ( ( sk5 @ c )
!= zero )
| ( A
!= ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(201,plain,
( ( ( sk5 @ c )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(1531,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( ( sk5 @ c )
!= zero )
| ~ $true
| ( ( sk5 @ c )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[205,201]) ).
thf(1532,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( ( sk5 @ c )
!= zero ) ),
inference(simp,[status(thm)],[1531]) ).
thf(1533,plain,
( ( sk5 @ c )
!= zero ),
inference(pattern_uni,[status(thm)],[1532:[]]) ).
thf(8,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(44,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)],[8]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(25,plain,
zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ),
inference(cnfConj,[status(thm)],[22]) ).
thf(178,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[73,25]) ).
thf(193,plain,
! [A: $i] :
( ( ( sk4 @ c )
!= zero )
| ( A
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(199,plain,
( ( ( sk4 @ c )
!= zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(170,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[73,120]) ).
thf(171,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(197,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk3 )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(203,plain,
( ( sk1 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(323,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk1 != zero )
| ~ $true
| ( ( sk4 @ c )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[199,203]) ).
thf(324,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk1 != zero )
| ( ( sk4 @ c )
!= zero ) ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
( ( sk1 != zero )
| ( ( sk4 @ c )
!= zero ) ),
inference(pattern_uni,[status(thm)],[324:[]]) ).
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(27,plain,
sk3 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(1662,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,77]) ).
thf(1663,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1662]) ).
thf(1664,plain,
sk3 @ ( sk3 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1663:[bind(A,$thf( sk3 ))]]) ).
thf(28,plain,
sk5 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(1654,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,77]) ).
thf(1655,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1654]) ).
thf(1656,plain,
sk5 @ ( sk5 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1655:[bind(A,$thf( sk5 ))]]) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1656,57]) ).
thf(1681,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1680]) ).
thf(1682,plain,
( ( sk5 @ sk6 @ ( sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1681:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(532,plain,
zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ),
inference(rewrite,[status(thm)],[25,43]) ).
thf(667,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[40,532]) ).
thf(679,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) )
| ( sk3 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[667]) ).
thf(689,plain,
( ( sk3 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(138,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[40,120]) ).
thf(139,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(141,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk3 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(143,plain,
( ( sk3 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(979,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk3 != zero )
| ~ $true
| ( sk3 != zero ) ),
inference(paramod_ordered,[status(thm)],[689,143]) ).
thf(980,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[979]) ).
thf(981,plain,
sk3 != zero,
inference(pattern_uni,[status(thm)],[980:[]]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(cnfConj,[status(thm)],[52]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[60]) ).
thf(534,plain,
~ ( zero @ ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ),
inference(rewrite,[status(thm)],[26,43]) ).
thf(888,plain,
~ ( zero @ ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) ),
inference(rewrite,[status(thm)],[534,43]) ).
thf(892,plain,
( ( ( zero @ ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[532,888]) ).
thf(893,plain,
( ( zero @ ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[892]) ).
thf(928,plain,
( ( zero != zero )
| ( ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[893]) ).
thf(936,plain,
( ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[928]) ).
thf(1250,plain,
( ( ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[936]) ).
thf(1351,plain,
( ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ),
inference(simp,[status(thm)],[1250]) ).
thf(1695,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1664,57]) ).
thf(1696,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1695]) ).
thf(1697,plain,
( ( sk3 @ sk6 @ ( sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1696:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk6 ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(83,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(84,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[84]) ).
thf(1693,plain,
( ( ( sk3 @ ( sk3 @ sk6 @ complement ) )
!= ( sk3 @ ( sk1 @ complement ) ) )
| ( sk4 != zero )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,867]) ).
thf(1694,plain,
( ( ( sk3 @ ( sk3 @ sk6 @ complement ) )
!= ( sk3 @ ( sk1 @ complement ) ) )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[1693]) ).
thf(1707,plain,
( ( sk3 != sk3 )
| ( ( sk3 @ sk6 )
!= sk1 )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[1694]) ).
thf(1708,plain,
( ( ( sk3 @ sk6 )
!= sk1 )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[1707]) ).
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(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(55,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[52]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(1685,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1656,59]) ).
thf(1686,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1685]) ).
thf(1687,plain,
( ( sk5 @ sk6 @ ( sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1686:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(436,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( ( sk2 @ ( sk4 @ multiplication ) )
!= ( sk2 @ ( zero @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,427]) ).
thf(448,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk3 )
| ( sk2 != sk2 )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[436]) ).
thf(461,plain,
( ( sk1 != zero )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[448]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[52]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[58,470]) ).
thf(1027,plain,
( ( sk4 != zero )
| ~ ( sk1 @ ( sk3 @ complement ) ) ),
inference(pattern_uni,[status(thm)],[1026:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(529,plain,
( ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk4 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[135,43]) ).
thf(1187,plain,
( ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk4 @ multiplication ) )
!= ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[529,43]) ).
thf(530,plain,
( ( sk2 @ ( sk4 @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[427,43]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(62,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)],[11]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) )
| ~ ( B @ test )
| ~ ( A @ test ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( B @ test )
| ~ ( A @ test )
| ( ( B @ c @ ( A @ c @ addition ) )
= ( B @ ( A @ multiplication ) @ c ) ) ),
inference(lifteq,[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(9,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(47,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[48]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(86,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)],[18]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(98,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(1688,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1656,58]) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1688]) ).
thf(1690,plain,
( ( sk5 @ ( sk5 @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1689:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(80,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)],[16]) ).
thf(440,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( ( sk2 @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,427]) ).
thf(445,plain,
! [A: $i] :
( ( sk1 != one )
| ( A != sk3 )
| ( sk2 != sk2 )
| ( A != sk4 ) ),
inference(simp,[status(thm)],[440]) ).
thf(473,plain,
( ( sk1 != one )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[445]) ).
thf(531,plain,
zero @ ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk4 @ multiplication ) @ leq ),
inference(rewrite,[status(thm)],[24,43]) ).
thf(580,plain,
( ( ( sk2 @ ( sk1 @ multiplication ) )
!= sk2 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[530]) ).
thf(1355,plain,
( ( ( sk5 @ c @ ( sk2 @ multiplication ) )
!= ( sk4 @ c ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[1351]) ).
thf(1400,plain,
( ( sk5 @ c @ ( sk2 @ multiplication ) )
!= ( sk4 @ c ) ),
inference(simp,[status(thm)],[1355]) ).
thf(19,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(95,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(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(438,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( ( sk2 @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,427]) ).
thf(454,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk3 != one )
| ( sk2 != sk2 )
| ( A != sk4 ) ),
inference(simp,[status(thm)],[438]) ).
thf(465,plain,
( ( sk4 != sk1 )
| ( sk3 != one ) ),
inference(simp,[status(thm)],[454]) ).
thf(364,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( ( sk5 @ c @ ( sk2 @ ( sk4 @ multiplication ) @ multiplication ) )
!= ( sk5 @ c @ ( zero @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,135]) ).
thf(402,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( ( sk5 @ c )
!= ( sk5 @ c ) )
| ( ( sk2 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[364]) ).
thf(422,plain,
( ( sk2 != zero )
| ( ( sk2 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[402]) ).
thf(817,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[73,422]) ).
thf(818,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[817]) ).
thf(828,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[818]) ).
thf(832,plain,
sk2 != zero,
inference(simp,[status(thm)],[828]) ).
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(619,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk4 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[40,531]) ).
thf(621,plain,
! [A: $i] :
( ( A
!= ( sk5 @ c @ ( sk2 @ multiplication ) ) )
| ( sk4 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[619]) ).
thf(635,plain,
( ( sk4 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[621]) ).
thf(156,plain,
( ( ( zero @ ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,26]) ).
thf(157,plain,
( ( zero @ ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(159,plain,
( ( zero != zero )
| ( ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(169,plain,
( ( sk5 @ c @ ( sk2 @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(1093,plain,
( ( sk5 @ c @ ( sk2 @ multiplication ) @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[169,43]) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[37,85]) ).
thf(491,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[490:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(101929,plain,
$false,
inference(e,[status(thm)],[37,77,41,1667,43,867,120,1533,46,325,57,29,1664,1682,981,61,1351,1697,74,85,1708,70,21,28,38,65,1687,461,1656,1027,73,1187,530,888,64,32,34,44,59,27,71,936,49,86,98,1690,80,35,473,531,580,1400,95,50,67,199,470,31,465,203,40,23,58,832,79,635,532,1093,47,68,62,83,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE034+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n003.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 19:17:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.71/0.73 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.98/0.86 % [INFO] Parsing done (123ms).
% 0.98/0.87 % [INFO] Running in sequential loop mode.
% 1.58/1.13 % [INFO] eprover registered as external prover.
% 1.79/1.13 % [INFO] Scanning for conjecture ...
% 1.92/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.09/1.31 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.09/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.09/1.36 % [INFO] Type checking passed.
% 2.09/1.36 % [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 ...
% 126.47/30.31 % External prover 'e' found a proof!
% 126.47/30.31 % [INFO] Killing All external provers ...
% 126.47/30.31 % Time passed: 29823ms (effective reasoning time: 29444ms)
% 126.47/30.31 % 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)>
% 126.47/30.32 % 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
% 126.47/30.32 % No. of inferences in proof: 202
% 126.47/30.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29823 ms resp. 29444 ms w/o parsing
% 113.96/30.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 113.96/30.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------