%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE147+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 : Fri Sep 25 01:51:44 PM UTC 2026
% Result : Theorem 119.49s 31.26s
% Output : Proof 119.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 19
% Syntax : Number of formulae : 340 ( 327 unt; 0 def)
% Number of atoms : 357 ( 333 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 12 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 585 ( 38 sgn 97 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f8_nnf,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t19,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t36,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t19]) ).
fof(f17,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f17_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t16,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t28,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t16]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f0_nnf,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t8,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t44,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t48,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t28,t44]) ).
cnf(t3139,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t48]) ).
fof(f12,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction1) ).
fof(f12_nnf,plain,
! [A,B,C] :
( leq(multiplication(star(A),B),C)
| ~ leq(addition(multiplication(A,C),B),C) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,C,B] :
( leq(multiplication(star(A),B),C)
| ~ leq(addition(multiplication(A,C),B),C) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t22,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t100,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t102,plain,
true = ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true),
inference(cp,[status(thm)],[t100,t36]) ).
cnf(t70188,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t102]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t15,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t78,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t15]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t14,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t49,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
fof(f3_nnf,plain,
! [A] : addition(A,A) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : addition(A,A) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t0,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t25,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t52,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t49,t25]) ).
cnf(t146,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t52]) ).
cnf(t155,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t78,t146]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t199035,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t155,t27]) ).
cnf(t169,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t199035]) ).
cnf(t174,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t169,t44]) ).
cnf(t180,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t174]) ).
fof(f10,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
fof(f10_nnf,plain,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t11,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t67,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t184,plain,
true = leq(multiplication(X1,star(X1)),star(X1)),
inference(cp,[status(thm)],[t180,t67]) ).
cnf(t346,plain,
leq(multiplication(X1,star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t184]) ).
cnf(t348,plain,
star(X1) = ifeq(true,true,addition(multiplication(X1,star(X1)),star(X1)),star(X1)),
inference(cp,[status(thm)],[t28,t346]) ).
cnf(t199096,plain,
star(X1) = addition(multiplication(X1,star(X1)),star(X1)),
inference(step,[status(thm)],[t348,t27]) ).
cnf(t199097,plain,
star(X1) = addition(star(X1),multiplication(X1,star(X1))),
inference(step,[status(thm)],[t199096,t44]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f6_nnf,plain,
! [A] : multiplication(one,A) = A,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : multiplication(one,A) = A,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t6,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t24,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t38,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t36,t24]) ).
cnf(t230,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t38]) ).
cnf(t199098,plain,
star(X1) = multiplication(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t199097,t230]) ).
cnf(t1727,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t199098]) ).
cnf(t1757,plain,
star(X1) = multiplication(addition(X1,one),star(X1)),
inference(cp,[status(thm)],[t1727,t44]) ).
cnf(t1774,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(orient,[status(thm)],[t1757]) ).
cnf(t70203,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t70188,t1774]) ).
cnf(hi18,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(hi3,axiom,
addition(X0,X0) = X0,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t3,plain,
leq(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi3]) ).
cnf(t77,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t199736,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(step,[status(thm)],[t70203,t77]) ).
cnf(t199737,plain,
true = leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),
inference(step,[status(thm)],[t199736,t27]) ).
cnf(t199738,plain,
true = leq(multiplication(star(X1),star(X1)),star(X1)),
inference(step,[status(thm)],[t199737,t24]) ).
cnf(t70536,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t199738]) ).
cnf(t70548,plain,
star(X1) = ifeq(true,true,addition(star(X1),multiplication(star(X1),star(X1))),star(X1)),
inference(cp,[status(thm)],[t3139,t70536]) ).
cnf(t199739,plain,
star(X1) = addition(star(X1),multiplication(star(X1),star(X1))),
inference(step,[status(thm)],[t70548,t27]) ).
cnf(t199740,plain,
star(X1) = multiplication(addition(one,star(X1)),star(X1)),
inference(step,[status(thm)],[t199739,t230]) ).
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f7_nnf,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t18,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t32,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t5,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t23,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t33,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t32,t23]) ).
cnf(t218,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t33]) ).
cnf(t231,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(cp,[status(thm)],[t230,t218]) ).
cnf(t265,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(orient,[status(thm)],[t231]) ).
cnf(t199741,plain,
star(X1) = multiplication(star(X1),addition(one,star(X1))),
inference(step,[status(thm)],[t199740,t265]) ).
fof(f11,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).
fof(f11_nnf,plain,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t73,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t149,plain,
addition(one,multiplication(star(X1),X1)) = addition(one,star(X1)),
inference(cp,[status(thm)],[t146,t73]) ).
cnf(t199031,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t149,t73]) ).
cnf(t159,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t199031]) ).
cnf(t199742,plain,
star(X1) = multiplication(star(X1),star(X1)),
inference(step,[status(thm)],[t199741,t159]) ).
cnf(t70550,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t199742]) ).
cnf(t70559,plain,
multiplication(addition(star(X1),X2),star(X1)) = addition(star(X1),multiplication(X2,star(X1))),
inference(cp,[status(thm)],[t36,t70550]) ).
cnf(t199765,plain,
multiplication(addition(star(X1),X2),star(X1)) = multiplication(addition(one,X2),star(X1)),
inference(step,[status(thm)],[t70559,t230]) ).
cnf(t70998,plain,
multiplication(addition(star(X1),X2),star(X1)) = multiplication(addition(one,X2),star(X1)),
inference(orient,[status(thm)],[t199765]) ).
cnf(t153,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t146,t44]) ).
cnf(t197,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t153]) ).
cnf(t71018,plain,
multiplication(addition(one,addition(X1,star(X2))),star(X2)) = multiplication(addition(star(X2),X1),star(X2)),
inference(cp,[status(thm)],[t70998,t197]) ).
cnf(t185,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t180,t49]) ).
cnf(t352,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t185]) ).
cnf(t354,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t352,t44]) ).
cnf(t199040,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t354,t49]) ).
cnf(t429,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t199040]) ).
cnf(t435,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t429,t159]) ).
cnf(t453,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t435]) ).
cnf(t456,plain,
addition(X1,star(X2)) = ifeq(true,true,addition(one,addition(X1,star(X2))),addition(X1,star(X2))),
inference(cp,[status(thm)],[t28,t453]) ).
cnf(t199047,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t456,t27]) ).
cnf(t585,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t199047]) ).
cnf(t199781,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(star(X2),X1),star(X2)),
inference(step,[status(thm)],[t71018,t585]) ).
cnf(t199782,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(one,X1),star(X2)),
inference(step,[status(thm)],[t199781,t70998]) ).
cnf(t71748,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(one,X1),star(X2)),
inference(orient,[status(thm)],[t199782]) ).
cnf(t182,plain,
true = leq(multiplication(star(X1),X1),star(X1)),
inference(cp,[status(thm)],[t180,t73]) ).
cnf(t297,plain,
leq(multiplication(star(X1),X1),star(X1)) = true,
inference(orient,[status(thm)],[t182]) ).
cnf(t298,plain,
star(X1) = ifeq(true,true,addition(multiplication(star(X1),X1),star(X1)),star(X1)),
inference(cp,[status(thm)],[t28,t297]) ).
cnf(t199059,plain,
star(X1) = addition(multiplication(star(X1),X1),star(X1)),
inference(step,[status(thm)],[t298,t27]) ).
cnf(t199060,plain,
star(X1) = addition(star(X1),multiplication(star(X1),X1)),
inference(step,[status(thm)],[t199059,t44]) ).
cnf(t199061,plain,
star(X1) = multiplication(star(X1),addition(one,X1)),
inference(step,[status(thm)],[t199060,t218]) ).
cnf(t656,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t199061]) ).
cnf(t669,plain,
multiplication(addition(one,star(X1)),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t230,t656]) ).
cnf(t199062,plain,
multiplication(star(X1),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t669,t159]) ).
cnf(t199063,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t199062,t656]) ).
cnf(t199064,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t199063,t49]) ).
cnf(t199065,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t199064,t585]) ).
cnf(t684,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t199065]) ).
cnf(t685,plain,
star(addition(X1,X2)) = addition(X1,addition(X2,star(addition(X1,X2)))),
inference(cp,[status(thm)],[t684,t49]) ).
cnf(t30560,plain,
addition(X1,addition(X2,star(addition(X1,X2)))) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t685]) ).
cnf(t30606,plain,
star(addition(X1,addition(X1,X2))) = addition(X1,addition(addition(X1,X2),star(addition(X1,X2)))),
inference(cp,[status(thm)],[t30560,t146]) ).
cnf(t199455,plain,
star(addition(X1,X2)) = addition(X1,addition(addition(X1,X2),star(addition(X1,X2)))),
inference(step,[status(thm)],[t30606,t146]) ).
cnf(t199456,plain,
star(addition(X1,X2)) = addition(X1,addition(X1,addition(X2,star(addition(X1,X2))))),
inference(step,[status(thm)],[t199455,t49]) ).
cnf(t199457,plain,
star(addition(X1,X2)) = addition(X1,star(addition(X1,X2))),
inference(step,[status(thm)],[t199456,t30560]) ).
cnf(t31149,plain,
addition(X1,star(addition(X1,X2))) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t199457]) ).
fof(f16,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).
fof(f16_nnf,plain,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t13,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t64,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t66,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(cp,[status(thm)],[t49,t64]) ).
cnf(t17366,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(orient,[status(thm)],[t66]) ).
cnf(t31194,plain,
star(addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2))) = addition(star(X1),star(addition(strong_iteration(X1),X2))),
inference(cp,[status(thm)],[t31149,t17366]) ).
cnf(t199639,plain,
star(addition(strong_iteration(X1),X2)) = addition(star(X1),star(addition(strong_iteration(X1),X2))),
inference(step,[status(thm)],[t31194,t17366]) ).
cnf(t57948,plain,
addition(star(X1),star(addition(strong_iteration(X1),X2))) = star(addition(strong_iteration(X1),X2)),
inference(orient,[status(thm)],[t199639]) ).
cnf(t71772,plain,
multiplication(addition(one,star(X1)),star(addition(strong_iteration(X1),X2))) = multiplication(star(addition(strong_iteration(X1),X2)),star(addition(strong_iteration(X1),X2))),
inference(cp,[status(thm)],[t71748,t57948]) ).
cnf(t199863,plain,
multiplication(star(X1),star(addition(strong_iteration(X1),X2))) = multiplication(star(addition(strong_iteration(X1),X2)),star(addition(strong_iteration(X1),X2))),
inference(step,[status(thm)],[t71772,t159]) ).
cnf(t199864,plain,
multiplication(star(X1),star(addition(strong_iteration(X1),X2))) = star(addition(strong_iteration(X1),X2)),
inference(step,[status(thm)],[t199863,t70550]) ).
cnf(t75906,plain,
multiplication(star(X1),star(addition(strong_iteration(X1),X2))) = star(addition(strong_iteration(X1),X2)),
inference(orient,[status(thm)],[t199864]) ).
fof(f15,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f15_nnf,plain,
! [A,B,C] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [C,A,B] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t20,plain,
ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t88,plain,
ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t99,plain,
true = ifeq(leq(X1,addition(multiplication(X2,X1),one)),true,leq(X1,strong_iteration(X2)),true),
inference(cp,[status(thm)],[t88,t23]) ).
cnf(t199715,plain,
true = ifeq(leq(X1,addition(one,multiplication(X2,X1))),true,leq(X1,strong_iteration(X2)),true),
inference(step,[status(thm)],[t99,t44]) ).
cnf(t65125,plain,
ifeq(leq(X1,addition(one,multiplication(X2,X1))),true,leq(X1,strong_iteration(X2)),true) = true,
inference(orient,[status(thm)],[t199715]) ).
fof(f14,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f14_nnf,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t10,plain,
addition(multiplication(X1,strong_iteration(X1)),one) = strong_iteration(X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t199025,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(step,[status(thm)],[t10,t44]) ).
cnf(t58,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(orient,[status(thm)],[t199025]) ).
cnf(t63,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(cp,[status(thm)],[t49,t58]) ).
cnf(t14463,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(orient,[status(thm)],[t63]) ).
cnf(t14476,plain,
addition(strong_iteration(X1),multiplication(X2,strong_iteration(X1))) = addition(one,multiplication(addition(X1,X2),strong_iteration(X1))),
inference(cp,[status(thm)],[t14463,t36]) ).
cnf(t200376,plain,
multiplication(addition(one,X2),strong_iteration(X1)) = addition(one,multiplication(addition(X1,X2),strong_iteration(X1))),
inference(step,[status(thm)],[t14476,t230]) ).
cnf(t184194,plain,
addition(one,multiplication(addition(X1,X2),strong_iteration(X1))) = multiplication(addition(one,X2),strong_iteration(X1)),
inference(orient,[status(thm)],[t200376]) ).
cnf(t184931,plain,
true = ifeq(leq(strong_iteration(X1),multiplication(addition(one,X2),strong_iteration(X1))),true,leq(strong_iteration(X1),strong_iteration(addition(X1,X2))),true),
inference(cp,[status(thm)],[t65125,t184194]) ).
cnf(t239,plain,
true = leq(X1,multiplication(addition(one,X2),X1)),
inference(cp,[status(thm)],[t169,t230]) ).
cnf(t419,plain,
leq(X1,multiplication(addition(one,X2),X1)) = true,
inference(orient,[status(thm)],[t239]) ).
cnf(t200377,plain,
true = ifeq(true,true,leq(strong_iteration(X1),strong_iteration(addition(X1,X2))),true),
inference(step,[status(thm)],[t184931,t419]) ).
cnf(t200378,plain,
true = leq(strong_iteration(X1),strong_iteration(addition(X1,X2))),
inference(step,[status(thm)],[t200377,t27]) ).
cnf(t185048,plain,
leq(strong_iteration(X1),strong_iteration(addition(X1,X2))) = true,
inference(orient,[status(thm)],[t200378]) ).
cnf(t185126,plain,
true = leq(strong_iteration(X1),strong_iteration(multiplication(addition(one,X2),X1))),
inference(cp,[status(thm)],[t185048,t230]) ).
cnf(t188469,plain,
leq(strong_iteration(X1),strong_iteration(multiplication(addition(one,X2),X1))) = true,
inference(orient,[status(thm)],[t185126]) ).
cnf(t188598,plain,
true = leq(strong_iteration(X1),strong_iteration(multiplication(star(X2),X1))),
inference(cp,[status(thm)],[t188469,t159]) ).
cnf(t188748,plain,
leq(strong_iteration(X1),strong_iteration(multiplication(star(X2),X1))) = true,
inference(orient,[status(thm)],[t188598]) ).
cnf(t188848,plain,
strong_iteration(multiplication(star(X1),X2)) = ifeq(true,true,addition(strong_iteration(X2),strong_iteration(multiplication(star(X1),X2))),strong_iteration(multiplication(star(X1),X2))),
inference(cp,[status(thm)],[t28,t188748]) ).
cnf(t200446,plain,
strong_iteration(multiplication(star(X1),X2)) = addition(strong_iteration(X2),strong_iteration(multiplication(star(X1),X2))),
inference(step,[status(thm)],[t188848,t27]) ).
cnf(t194130,plain,
addition(strong_iteration(X1),strong_iteration(multiplication(star(X2),X1))) = strong_iteration(multiplication(star(X2),X1)),
inference(orient,[status(thm)],[t200446]) ).
cnf(t194480,plain,
star(addition(strong_iteration(X1),strong_iteration(multiplication(star(X2),X1)))) = multiplication(star(X1),star(strong_iteration(multiplication(star(X2),X1)))),
inference(cp,[status(thm)],[t75906,t194130]) ).
cnf(t200500,plain,
star(strong_iteration(multiplication(star(X2),X1))) = multiplication(star(X1),star(strong_iteration(multiplication(star(X2),X1)))),
inference(step,[status(thm)],[t194480,t194130]) ).
cnf(t103,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true),
inference(cp,[status(thm)],[t100,t25]) ).
fof(f4,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f4_nnf,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t17,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t31,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
cnf(t235,plain,
multiplication(addition(one,multiplication(X1,X2)),X3) = addition(X3,multiplication(X1,multiplication(X2,X3))),
inference(cp,[status(thm)],[t230,t31]) ).
cnf(t46430,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(orient,[status(thm)],[t235]) ).
cnf(t46431,plain,
multiplication(addition(one,multiplication(X1,X2)),X1) = multiplication(X1,addition(one,multiplication(X2,X1))),
inference(cp,[status(thm)],[t46430,t218]) ).
cnf(t50922,plain,
multiplication(addition(one,multiplication(X1,X2)),X1) = multiplication(X1,addition(one,multiplication(X2,X1))),
inference(orient,[status(thm)],[t46431]) ).
cnf(t50927,plain,
multiplication(X1,addition(one,multiplication(star(X1),X1))) = multiplication(star(X1),X1),
inference(cp,[status(thm)],[t50922,t67]) ).
cnf(t199581,plain,
multiplication(X1,star(X1)) = multiplication(star(X1),X1),
inference(step,[status(thm)],[t50927,t73]) ).
cnf(t51101,plain,
multiplication(star(X1),X1) = multiplication(X1,star(X1)),
inference(orient,[status(thm)],[t199581]) ).
cnf(t51115,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(multiplication(X1,star(X1)),X2),
inference(cp,[status(thm)],[t31,t51101]) ).
cnf(t199586,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(X1,multiplication(star(X1),X2)),
inference(step,[status(thm)],[t51115,t31]) ).
cnf(t51168,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(X1,multiplication(star(X1),X2)),
inference(orient,[status(thm)],[t199586]) ).
cnf(t199811,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(X1,multiplication(star(X1),X2)),X2),true),
inference(step,[status(thm)],[t103,t51168]) ).
cnf(t75348,plain,
ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(X1,multiplication(star(X1),X2)),X2),true) = true,
inference(orient,[status(thm)],[t199811]) ).
cnf(t183,plain,
true = leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t180,t58]) ).
cnf(t302,plain,
leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t183]) ).
cnf(t304,plain,
strong_iteration(X1) = ifeq(true,true,addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t28,t302]) ).
cnf(t199093,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t304,t27]) ).
cnf(t199094,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))),
inference(step,[status(thm)],[t199093,t44]) ).
cnf(t199095,plain,
strong_iteration(X1) = multiplication(addition(one,X1),strong_iteration(X1)),
inference(step,[status(thm)],[t199094,t230]) ).
cnf(t1621,plain,
multiplication(addition(one,X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t199095]) ).
cnf(t1651,plain,
strong_iteration(X1) = multiplication(addition(X1,one),strong_iteration(X1)),
inference(cp,[status(thm)],[t1621,t44]) ).
cnf(t1676,plain,
multiplication(addition(X1,one),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t1651]) ).
cnf(t70204,plain,
true = ifeq(leq(strong_iteration(X1),strong_iteration(X1)),true,leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),true),
inference(cp,[status(thm)],[t70188,t1676]) ).
cnf(t199744,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),true),
inference(step,[status(thm)],[t70204,t77]) ).
cnf(t199745,plain,
true = leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),
inference(step,[status(thm)],[t199744,t27]) ).
cnf(t199746,plain,
true = leq(multiplication(star(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199745,t24]) ).
cnf(t37,plain,
multiplication(addition(multiplication(X1,X2),X3),Y3) = addition(multiplication(X1,multiplication(X2,Y3)),multiplication(X3,Y3)),
inference(cp,[status(thm)],[t36,t31]) ).
cnf(t816,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(Y3,X3)) = multiplication(addition(multiplication(X1,X2),Y3),X3),
inference(orient,[status(thm)],[t37]) ).
fof(f9,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f9_nnf,plain,
! [A] : multiplication(zero,A) = zero,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : multiplication(zero,A) = zero,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t7,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t42,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t7]) ).
cnf(t833,plain,
multiplication(addition(multiplication(X1,zero),X2),X3) = addition(multiplication(X1,zero),multiplication(X2,X3)),
inference(cp,[status(thm)],[t816,t42]) ).
cnf(t48101,plain,
addition(multiplication(X1,zero),multiplication(X2,X3)) = multiplication(addition(multiplication(X1,zero),X2),X3),
inference(orient,[status(thm)],[t833]) ).
cnf(t48102,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(cp,[status(thm)],[t48101,t36]) ).
cnf(t48470,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t48102]) ).
cnf(t48474,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(multiplication(addition(X1,X2),zero),zero),
inference(cp,[status(thm)],[t48470,t36]) ).
cnf(t199561,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),multiplication(zero,zero)),
inference(step,[status(thm)],[t48474,t31]) ).
cnf(t199562,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(step,[status(thm)],[t199561,t42]) ).
cnf(t48688,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t199562]) ).
cnf(t48716,plain,
multiplication(addition(X1,multiplication(X2,zero)),addition(one,zero)) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(cp,[status(thm)],[t218,t48688]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f2_nnf,plain,
! [A] : addition(A,zero) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : addition(A,zero) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t1,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t26,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t199563,plain,
multiplication(addition(X1,multiplication(X2,zero)),one) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t48716,t26]) ).
cnf(t199564,plain,
addition(X1,multiplication(X2,zero)) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t199563,t23]) ).
cnf(t199565,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,addition(multiplication(X2,zero),multiplication(addition(X1,X2),zero))),
inference(step,[status(thm)],[t199564,t49]) ).
cnf(t199566,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(multiplication(X2,zero),addition(X1,X2)),zero)),
inference(step,[status(thm)],[t199565,t48101]) ).
cnf(t199567,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,addition(X1,X2)),zero)),
inference(step,[status(thm)],[t199566,t48470]) ).
cnf(t199568,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t199567,t197]) ).
cnf(t48867,plain,
addition(X1,multiplication(addition(X2,X1),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t199568]) ).
cnf(t48917,plain,
addition(addition(X1,X2),multiplication(X2,zero)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(cp,[status(thm)],[t48867,t197]) ).
cnf(t199665,plain,
addition(X1,addition(X2,multiplication(X2,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t48917,t49]) ).
cnf(t199666,plain,
addition(X1,multiplication(X2,addition(one,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t199665,t218]) ).
cnf(t199667,plain,
addition(X1,multiplication(X2,one)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t199666,t26]) ).
cnf(t199668,plain,
addition(X1,X2) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t199667,t23]) ).
cnf(t199669,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(addition(X2,X1),zero))),
inference(step,[status(thm)],[t199668,t49]) ).
cnf(t48965,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X1,X2),zero)),
inference(cp,[status(thm)],[t48867,t44]) ).
cnf(t49171,plain,
addition(X1,multiplication(addition(X1,X2),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t48965]) ).
cnf(t199670,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(X1,zero))),
inference(step,[status(thm)],[t199669,t49171]) ).
cnf(t59644,plain,
addition(X1,addition(X2,multiplication(X1,zero))) = addition(X1,X2),
inference(orient,[status(thm)],[t199670]) ).
cnf(t59755,plain,
true = leq(multiplication(X1,zero),addition(X1,X2)),
inference(cp,[status(thm)],[t352,t59644]) ).
cnf(t59831,plain,
leq(multiplication(X1,zero),addition(X1,X2)) = true,
inference(orient,[status(thm)],[t59755]) ).
cnf(t59839,plain,
true = leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)),
inference(cp,[status(thm)],[t59831,t230]) ).
cnf(t60934,plain,
leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)) = true,
inference(orient,[status(thm)],[t59839]) ).
cnf(t60962,plain,
true = leq(multiplication(X1,zero),multiplication(star(X2),X1)),
inference(cp,[status(thm)],[t60934,t159]) ).
cnf(t60997,plain,
leq(multiplication(X1,zero),multiplication(star(X2),X1)) = true,
inference(orient,[status(thm)],[t60962]) ).
cnf(t61019,plain,
multiplication(star(X1),X2) = ifeq(true,true,addition(multiplication(star(X1),X2),multiplication(X2,zero)),multiplication(star(X1),X2)),
inference(cp,[status(thm)],[t3139,t60997]) ).
cnf(t199681,plain,
multiplication(star(X1),X2) = addition(multiplication(star(X1),X2),multiplication(X2,zero)),
inference(step,[status(thm)],[t61019,t27]) ).
cnf(t39,plain,
multiplication(addition(X1,multiplication(X2,X3)),Y3) = addition(multiplication(X1,Y3),multiplication(X2,multiplication(X3,Y3))),
inference(cp,[status(thm)],[t36,t31]) ).
cnf(t1285,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(Y3,X2))) = multiplication(addition(X1,multiplication(X3,Y3)),X2),
inference(orient,[status(thm)],[t39]) ).
cnf(t1317,plain,
multiplication(addition(X1,multiplication(X2,zero)),X3) = addition(multiplication(X1,X3),multiplication(X2,zero)),
inference(cp,[status(thm)],[t1285,t42]) ).
cnf(t49420,plain,
addition(multiplication(X1,X2),multiplication(X3,zero)) = multiplication(addition(X1,multiplication(X3,zero)),X2),
inference(orient,[status(thm)],[t1317]) ).
cnf(t199682,plain,
multiplication(star(X1),X2) = multiplication(addition(star(X1),multiplication(X2,zero)),X2),
inference(step,[status(thm)],[t199681,t49420]) ).
cnf(t62101,plain,
multiplication(addition(star(X1),multiplication(X2,zero)),X2) = multiplication(star(X1),X2),
inference(orient,[status(thm)],[t199682]) ).
cnf(t17372,plain,
addition(strong_iteration(X1),multiplication(strong_iteration(X1),X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(cp,[status(thm)],[t17366,t32]) ).
cnf(t199434,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(step,[status(thm)],[t17372,t218]) ).
cnf(t45,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t44,t26]) ).
cnf(t132,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t45]) ).
cnf(t199435,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),X2)),
inference(step,[status(thm)],[t199434,t132]) ).
cnf(t29074,plain,
addition(star(X1),multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(one,X2)),
inference(orient,[status(thm)],[t199435]) ).
cnf(t62102,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(multiplication(strong_iteration(X1),addition(one,zero)),strong_iteration(X1)),
inference(cp,[status(thm)],[t62101,t29074]) ).
cnf(t199683,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(addition(one,zero),strong_iteration(X1))),
inference(step,[status(thm)],[t62102,t31]) ).
cnf(t199684,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(one,strong_iteration(X1))),
inference(step,[status(thm)],[t199683,t26]) ).
cnf(t199685,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t199684,t24]) ).
cnf(t62249,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(orient,[status(thm)],[t199685]) ).
cnf(t199747,plain,
true = leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199746,t62249]) ).
cnf(t70598,plain,
leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t199747]) ).
cnf(t70602,plain,
strong_iteration(X1) = ifeq(true,true,addition(strong_iteration(X1),multiplication(strong_iteration(X1),strong_iteration(X1))),strong_iteration(X1)),
inference(cp,[status(thm)],[t3139,t70598]) ).
cnf(t199748,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(strong_iteration(X1),strong_iteration(X1))),
inference(step,[status(thm)],[t70602,t27]) ).
cnf(t199749,plain,
strong_iteration(X1) = multiplication(addition(one,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199748,t230]) ).
cnf(t199750,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),addition(one,strong_iteration(X1))),
inference(step,[status(thm)],[t199749,t265]) ).
cnf(t150,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = addition(one,strong_iteration(X1)),
inference(cp,[status(thm)],[t146,t58]) ).
cnf(t199033,plain,
strong_iteration(X1) = addition(one,strong_iteration(X1)),
inference(step,[status(thm)],[t150,t58]) ).
cnf(t164,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t199033]) ).
cnf(t199751,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t199750,t164]) ).
cnf(t70605,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t199751]) ).
cnf(t75410,plain,
true = ifeq(leq(strong_iteration(X1),strong_iteration(X1)),true,leq(multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),strong_iteration(X1))),strong_iteration(X1)),true),
inference(cp,[status(thm)],[t75348,t70605]) ).
cnf(t199812,plain,
true = ifeq(true,true,leq(multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),strong_iteration(X1))),strong_iteration(X1)),true),
inference(step,[status(thm)],[t75410,t77]) ).
cnf(t199813,plain,
true = leq(multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),strong_iteration(X1))),strong_iteration(X1)),
inference(step,[status(thm)],[t199812,t27]) ).
cnf(t1732,plain,
star(strong_iteration(X1)) = multiplication(strong_iteration(X1),star(strong_iteration(X1))),
inference(cp,[status(thm)],[t1727,t164]) ).
cnf(t1792,plain,
multiplication(strong_iteration(X1),star(strong_iteration(X1))) = star(strong_iteration(X1)),
inference(orient,[status(thm)],[t1732]) ).
cnf(t1797,plain,
multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),X2)) = multiplication(star(strong_iteration(X1)),X2),
inference(cp,[status(thm)],[t31,t1792]) ).
cnf(t55287,plain,
multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),X2)) = multiplication(star(strong_iteration(X1)),X2),
inference(orient,[status(thm)],[t1797]) ).
cnf(t199814,plain,
true = leq(multiplication(star(strong_iteration(X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199813,t55287]) ).
cnf(t661,plain,
star(strong_iteration(X1)) = multiplication(star(strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t656,t164]) ).
cnf(t943,plain,
multiplication(star(strong_iteration(X1)),strong_iteration(X1)) = star(strong_iteration(X1)),
inference(orient,[status(thm)],[t661]) ).
cnf(t199815,plain,
true = leq(star(strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199814,t943]) ).
cnf(t75540,plain,
leq(star(strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t199815]) ).
cnf(t75545,plain,
strong_iteration(X1) = ifeq(true,true,addition(strong_iteration(X1),star(strong_iteration(X1))),strong_iteration(X1)),
inference(cp,[status(thm)],[t3139,t75540]) ).
cnf(t199816,plain,
strong_iteration(X1) = addition(strong_iteration(X1),star(strong_iteration(X1))),
inference(step,[status(thm)],[t75545,t27]) ).
cnf(t199817,plain,
strong_iteration(X1) = star(strong_iteration(X1)),
inference(step,[status(thm)],[t199816,t684]) ).
cnf(t75550,plain,
star(strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t199817]) ).
cnf(t200501,plain,
strong_iteration(multiplication(star(X2),X1)) = multiplication(star(X1),star(strong_iteration(multiplication(star(X2),X1)))),
inference(step,[status(thm)],[t200500,t75550]) ).
cnf(t200502,plain,
strong_iteration(multiplication(star(X2),X1)) = multiplication(star(X1),strong_iteration(multiplication(star(X2),X1))),
inference(step,[status(thm)],[t200501,t75550]) ).
cnf(t198882,plain,
multiplication(star(X1),strong_iteration(multiplication(star(X2),X1))) = strong_iteration(multiplication(star(X2),X1)),
inference(orient,[status(thm)],[t200502]) ).
fof(f18,conjecture,
! [X0,X1] : strong_iteration(multiplication(star(X0),X1)) = multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0,X1] : strong_iteration(multiplication(star(X0),X1)) = multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0,X1] : strong_iteration(multiplication(star(X0),X1)) != multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
strong_iteration(multiplication(star(sk0),sk1)) != multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f18_nnf]) ).
cnf(c19,plain,
strong_iteration(multiplication(star(sk0),sk1)) != multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1))),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1))) != strong_iteration(multiplication(star(sk0),sk1)),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
strong_iteration(multiplication(star(sk0),sk1)) != strong_iteration(multiplication(star(sk0),sk1)),
inference(rw,[status(thm)],[goal_0,t198882]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE147+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/15.31 % CPULimit : 300
% 0.10/15.31 % WCLimit : 300
% 0.10/15.31 % DateTime : Wed Sep 23 19:08:05 UTC 2026
% 0.10/15.31 % CPUTime :
% 0.10/15.31 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 119.49/31.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 119.49/31.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------