TSTP Solution File: KLE169-10 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE169-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:25:13 EDT 2023
% Result : Unsatisfiable 76.40s 19.84s
% Output : Refutation 76.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 35
% Syntax : Number of formulae : 132 ( 74 unt; 13 typ; 0 def)
% Number of atoms : 220 ( 219 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 932 ( 141 ~; 101 |; 0 &; 690 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 152 ( 0 ^; 152 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(star_type,type,
star: $i > $i ).
thf(sigma_type,type,
sigma: $i ).
thf(true_type,type,
true: $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(ifeq2_type,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(ifeq3_type,type,
ifeq3: $i > $i > $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(17,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(56,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(52,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(58,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(59,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[58]) ).
thf(53,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[52]) ).
thf(1,negated_conjecture,
( ( leq @ ( multiplication @ a @ ( multiplication @ b @ a ) ) @ ( multiplication @ ( star @ sigma ) @ ( multiplication @ a @ ( multiplication @ sigma @ a ) ) ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
thf(23,plain,
( ( leq @ ( multiplication @ a @ ( multiplication @ b @ a ) ) @ ( multiplication @ ( star @ sigma ) @ ( multiplication @ a @ ( multiplication @ sigma @ a ) ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(24,plain,
( ( leq @ ( multiplication @ a @ ( multiplication @ b @ a ) ) @ ( multiplication @ ( star @ sigma ) @ ( multiplication @ a @ ( multiplication @ sigma @ a ) ) ) )
!= true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( leq @ ( multiplication @ a @ ( multiplication @ b @ a ) ) @ ( multiplication @ ( star @ sigma ) @ ( multiplication @ a @ ( multiplication @ sigma @ a ) ) ) )
!= true ),
inference(lifteq,[status(thm)],[24]) ).
thf(83,plain,
! [A: $i] :
( ( ( leq @ ( multiplication @ a @ ( multiplication @ b @ a ) ) @ zero )
!= true )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( star @ sigma ) @ ( multiplication @ a @ ( multiplication @ sigma @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,25]) ).
thf(97,plain,
! [A: $i] :
( ( ( leq @ ( multiplication @ a @ ( multiplication @ b @ a ) ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( A
!= ( multiplication @ a @ ( multiplication @ sigma @ a ) ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(99,plain,
( ( ( leq @ ( multiplication @ a @ ( multiplication @ b @ a ) ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero ) ),
inference(simp,[status(thm)],[97]) ).
thf(201,plain,
! [A: $i] :
( ( ( leq @ A @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ a @ ( multiplication @ b @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[59,99]) ).
thf(204,plain,
! [A: $i] :
( ( ( leq @ A @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( A != a )
| ( ( multiplication @ b @ a )
!= one ) ),
inference(simp,[status(thm)],[201]) ).
thf(216,plain,
( ( ( leq @ a @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ b @ a )
!= one ) ),
inference(simp,[status(thm)],[204]) ).
thf(9,axiom,
( sigma
= ( addition @ a @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an) ).
thf(40,plain,
( sigma
= ( addition @ a @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,plain,
( ( addition @ a @ b )
= sigma ),
inference(lifteq,[status(thm)],[40]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ A @ B ) @ C )
= ( addition @ A @ ( addition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ sigma @ C )
= ( addition @ A @ ( addition @ B @ C ) ) )
| ( ( addition @ a @ b )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[41,29]) ).
thf(274,plain,
! [A: $i] :
( ( addition @ sigma @ A )
= ( addition @ a @ ( addition @ b @ A ) ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(319,plain,
! [A: $i] :
( ( addition @ sigma @ A )
= ( addition @ a @ ( addition @ b @ A ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(7,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(36,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[36]) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( ( addition @ a @ ( addition @ b @ A ) )
= B )
| ( ( addition @ sigma @ A )
!= ( addition @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[319,37]) ).
thf(380,plain,
( ( addition @ a @ ( addition @ b @ sigma ) )
= sigma ),
inference(pattern_uni,[status(thm)],[379:[bind(A,$thf( sigma )),bind(B,$thf( sigma ))]]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= sigma )
| ( ( addition @ a @ ( addition @ b @ sigma ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[380,27]) ).
thf(472,plain,
( ( addition @ ( addition @ b @ sigma ) @ a )
= sigma ),
inference(pattern_uni,[status(thm)],[471:[bind(A,$thf( a )),bind(B,$thf( addition @ b @ sigma ))]]) ).
thf(522,plain,
( ( addition @ b @ ( addition @ sigma @ a ) )
= sigma ),
inference(rewrite,[status(thm)],[472,29]) ).
thf(57,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[56]) ).
thf(109,plain,
! [A: $i] :
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ a @ ( multiplication @ b @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,99]) ).
thf(113,plain,
! [A: $i] :
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( A != a )
| ( ( multiplication @ b @ a )
!= zero ) ),
inference(simp,[status(thm)],[109]) ).
thf(117,plain,
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ b @ a )
!= zero ) ),
inference(simp,[status(thm)],[113]) ).
thf(246,plain,
! [A: $i] :
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[53,117]) ).
thf(250,plain,
! [A: $i] :
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( zero != b )
| ( A != a ) ),
inference(simp,[status(thm)],[246]) ).
thf(256,plain,
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( zero != b ) ),
inference(simp,[status(thm)],[250]) ).
thf(6,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(34,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[34]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A ) @ true @ ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_right) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A ) @ true @ ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
thf(46,plain,
! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(45,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(132,plain,
! [A: $i] :
( ( ( leq @ A @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ a @ ( multiplication @ b @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[45,99]) ).
thf(135,plain,
! [A: $i] :
( ( ( leq @ A @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a )
| ( A
!= ( multiplication @ b @ a ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(144,plain,
( ( ( leq @ ( multiplication @ b @ a ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a ) ),
inference(simp,[status(thm)],[135]) ).
thf(262,plain,
! [A: $i] :
( ( ( leq @ A @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a )
| ( ( multiplication @ one @ A )
!= ( multiplication @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[45,144]) ).
thf(266,plain,
! [A: $i] :
( ( ( leq @ A @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a )
| ( one != b )
| ( A != a ) ),
inference(simp,[status(thm)],[262]) ).
thf(270,plain,
( ( ( leq @ a @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a )
| ( one != b ) ),
inference(simp,[status(thm)],[266]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B ) @ true @ ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B ) @ true @ ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[32]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( ( addition @ b @ ( addition @ B @ A ) )
= sigma )
| ( ( addition @ A @ B )
!= ( addition @ sigma @ a ) ) ),
inference(paramod_ordered,[status(thm)],[27,522]) ).
thf(552,plain,
( ( addition @ b @ ( addition @ a @ sigma ) )
= sigma ),
inference(pattern_uni,[status(thm)],[551:[bind(A,$thf( sigma )),bind(B,$thf( a ))]]) ).
thf(706,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= sigma )
| ( ( addition @ b @ ( addition @ a @ sigma ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[552,27]) ).
thf(707,plain,
( ( addition @ ( addition @ a @ sigma ) @ b )
= sigma ),
inference(pattern_uni,[status(thm)],[706:[bind(A,$thf( b )),bind(B,$thf( addition @ a @ sigma ))]]) ).
thf(772,plain,
( ( addition @ a @ ( addition @ sigma @ b ) )
= sigma ),
inference(rewrite,[status(thm)],[707,29]) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= sigma )
| ( ( addition @ a @ ( addition @ sigma @ b ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[772,27]) ).
thf(801,plain,
( ( addition @ ( addition @ sigma @ b ) @ a )
= sigma ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( a )),bind(B,$thf( addition @ sigma @ b ))]]) ).
thf(869,plain,
( ( addition @ sigma @ ( addition @ b @ a ) )
= sigma ),
inference(rewrite,[status(thm)],[801,29]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( ifeq2 @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ifeq2 @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(131,plain,
! [A: $i] :
( ( ( leq @ ( multiplication @ a @ A ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[45,99]) ).
thf(140,plain,
! [A: $i] :
( ( ( leq @ ( multiplication @ a @ A ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != b )
| ( A != a ) ),
inference(simp,[status(thm)],[131]) ).
thf(149,plain,
( ( ( leq @ ( multiplication @ a @ a ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != b ) ),
inference(simp,[status(thm)],[140]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[27,35]) ).
thf(159,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(441,plain,
! [A: $i] :
( ( ( leq @ a @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[57,216]) ).
thf(445,plain,
! [A: $i] :
( ( ( leq @ a @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != zero )
| ( A != b )
| ( zero != a ) ),
inference(simp,[status(thm)],[441]) ).
thf(451,plain,
( ( ( leq @ a @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != zero )
| ( zero != a ) ),
inference(simp,[status(thm)],[445]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[38]) ).
thf(263,plain,
! [A: $i] :
( ( ( leq @ A @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a )
| ( ( multiplication @ A @ one )
!= ( multiplication @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[59,144]) ).
thf(267,plain,
! [A: $i] :
( ( ( leq @ A @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a )
| ( A != b )
| ( one != a ) ),
inference(simp,[status(thm)],[263]) ).
thf(271,plain,
( ( ( leq @ b @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a ) ),
inference(simp,[status(thm)],[267]) ).
thf(546,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= sigma )
| ( ( addition @ b @ ( addition @ sigma @ a ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[522,27]) ).
thf(547,plain,
( ( addition @ ( addition @ sigma @ a ) @ b )
= sigma ),
inference(pattern_uni,[status(thm)],[546:[bind(A,$thf( b )),bind(B,$thf( addition @ sigma @ a ))]]) ).
thf(599,plain,
( ( addition @ sigma @ ( addition @ a @ b ) )
= sigma ),
inference(rewrite,[status(thm)],[547,29]) ).
thf(200,plain,
! [A: $i] :
( ( ( leq @ ( multiplication @ a @ A ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[59,99]) ).
thf(210,plain,
! [A: $i] :
( ( ( leq @ ( multiplication @ a @ A ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( A != b )
| ( one != a ) ),
inference(simp,[status(thm)],[200]) ).
thf(213,plain,
( ( ( leq @ ( multiplication @ a @ b ) @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != a ) ),
inference(simp,[status(thm)],[210]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( ifeq3 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( ifeq3 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= sigma )
| ( ( addition @ a @ b )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[41,27]) ).
thf(155,plain,
( ( addition @ b @ a )
= sigma ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(14,axiom,
! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
thf(50,plain,
! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[30]) ).
thf(440,plain,
! [A: $i] :
( ( ( leq @ a @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[53,216]) ).
thf(444,plain,
! [A: $i] :
( ( ( leq @ a @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != zero )
| ( zero != b )
| ( A != a ) ),
inference(simp,[status(thm)],[440]) ).
thf(450,plain,
( ( ( leq @ a @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( one != zero )
| ( zero != b ) ),
inference(simp,[status(thm)],[444]) ).
thf(111,plain,
! [A: $i] :
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ a @ ( multiplication @ b @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,99]) ).
thf(115,plain,
! [A: $i] :
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( zero != a )
| ( A
!= ( multiplication @ b @ a ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(119,plain,
( ( ( leq @ zero @ zero )
!= true )
| ( ( star @ sigma )
!= zero )
| ( zero != a ) ),
inference(simp,[status(thm)],[115]) ).
thf(111885,plain,
$false,
inference(cvc4,[status(thm)],[56,52,216,522,256,41,35,48,43,62,42,37,25,46,57,29,270,60,380,117,33,28,38,53,869,45,64,149,32,34,44,772,59,27,54,144,159,451,39,271,599,552,213,66,155,50,31,450,99,319,40,26,23,119,58,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE169-10 : TPTP v8.1.2. Released v7.5.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:42:39 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/0.98 % [INFO] Parsing done (127ms).
% 1.27/0.99 % [INFO] Running in sequential loop mode.
% 1.64/1.18 % [INFO] eprover registered as external prover.
% 1.73/1.18 % [INFO] cvc4 registered as external prover.
% 1.73/1.19 % [INFO] Scanning for conjecture ...
% 1.85/1.24 % [INFO] Found a conjecture and 21 axioms. Running axiom selection ...
% 1.88/1.28 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 1.88/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/1.30 % [INFO] Type checking passed.
% 1.88/1.31 % [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 ...
% 76.40/19.84 % External prover 'cvc4' found a proof!
% 76.40/19.84 % [INFO] Killing All external provers ...
% 76.40/19.84 % Time passed: 19313ms (effective reasoning time: 18853ms)
% 76.40/19.84 % 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)>
% 76.40/19.84 % Axioms used in derivation (21): additive_identity, ifeq_axiom_001, ifeq_axiom, star_induction_right, left_annihilation, star_induction_left, right_distributivity, star_unfold_left, order_1, multiplicative_left_identity, ifeq_axiom_002, additive_idempotence, additive_associativity, multiplicative_right_identity, star_unfold_right, order, additive_commutativity, right_annihilation, an, multiplicative_associativity, left_distributivity
% 76.40/19.84 % No. of inferences in proof: 119
% 76.40/19.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19313 ms resp. 18853 ms w/o parsing
% 76.40/19.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 76.40/19.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------