%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE145+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:51:43 PM UTC 2026
% Result : Theorem 72.62s 9.62s
% Output : Proof 72.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 18
% Syntax : Number of formulae : 282 ( 268 unt; 0 def)
% Number of atoms : 300 ( 274 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 12 |; 4 &)
% ( 1 <=>; 1 =>; 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 : 455 ( 29 sgn 86 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,conjecture,
! [X0] :
( leq(strong_iteration(X0),star(strong_iteration(X0)))
& leq(star(strong_iteration(X0)),strong_iteration(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(X0),star(strong_iteration(X0)))
& leq(star(strong_iteration(X0)),strong_iteration(X0)) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0] :
( ~ leq(strong_iteration(X0),star(strong_iteration(X0)))
| ~ leq(star(strong_iteration(X0)),strong_iteration(X0)) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( ~ leq(strong_iteration(sk0),star(strong_iteration(sk0)))
| ~ leq(star(strong_iteration(sk0)),strong_iteration(sk0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c19,plain,
( ~ leq(strong_iteration(sk0),star(strong_iteration(sk0)))
| ~ leq(star(strong_iteration(sk0)),strong_iteration(sk0)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t21,plain,
ifeq(leq(star(strong_iteration(sk0)),strong_iteration(sk0)),true,ifeq(leq(strong_iteration(sk0),star(strong_iteration(sk0))),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t125,plain,
ifeq(leq(star(strong_iteration(sk0)),strong_iteration(sk0)),true,ifeq(leq(strong_iteration(sk0),star(strong_iteration(sk0))),true,false,true),true) = true,
inference(orient,[status(thm)],[t21]) ).
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(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t13,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t77,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t13]) ).
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(t12,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t48,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
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(t24,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t51,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t48,t24]) ).
cnf(t146,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t51]) ).
cnf(t155,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t77,t146]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t26,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t75512,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t155,t26]) ).
cnf(t169,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t75512]) ).
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(t17,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t35,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
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(t4,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t23,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t37,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t35,t23]) ).
cnf(t230,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t37]) ).
cnf(c17,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t14,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t27,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t14]) ).
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(t6,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t43,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t174,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t169,t43]) ).
cnf(t180,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t174]) ).
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(t10,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t72,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t182,plain,
true = leq(multiplication(star(X1),X1),star(X1)),
inference(cp,[status(thm)],[t180,t72]) ).
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)],[t27,t297]) ).
cnf(t75536,plain,
star(X1) = addition(multiplication(star(X1),X1),star(X1)),
inference(step,[status(thm)],[t298,t26]) ).
cnf(t75537,plain,
star(X1) = addition(star(X1),multiplication(star(X1),X1)),
inference(step,[status(thm)],[t75536,t43]) ).
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(t16,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t31,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
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(t3,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t22,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t32,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t31,t22]) ).
cnf(t218,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t32]) ).
cnf(t75538,plain,
star(X1) = multiplication(star(X1),addition(one,X1)),
inference(step,[status(thm)],[t75537,t218]) ).
cnf(t656,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t75538]) ).
cnf(t669,plain,
multiplication(addition(one,star(X1)),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t230,t656]) ).
cnf(t149,plain,
addition(one,multiplication(star(X1),X1)) = addition(one,star(X1)),
inference(cp,[status(thm)],[t146,t72]) ).
cnf(t75508,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t149,t72]) ).
cnf(t159,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t75508]) ).
cnf(t75539,plain,
multiplication(star(X1),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t669,t159]) ).
cnf(t75540,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t75539,t656]) ).
cnf(t75541,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t75540,t48]) ).
cnf(t185,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t180,t48]) ).
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,t43]) ).
cnf(t75517,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t354,t48]) ).
cnf(t429,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t75517]) ).
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)],[t27,t453]) ).
cnf(t75524,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t456,t26]) ).
cnf(t585,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t75524]) ).
cnf(t75542,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t75541,t585]) ).
cnf(t684,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t75542]) ).
cnf(t690,plain,
true = leq(X1,star(X1)),
inference(cp,[status(thm)],[t169,t684]) ).
cnf(t699,plain,
leq(X1,star(X1)) = true,
inference(orient,[status(thm)],[t690]) ).
cnf(t75543,plain,
ifeq(leq(star(strong_iteration(sk0)),strong_iteration(sk0)),true,ifeq(true,true,false,true),true) = true,
inference(step,[status(thm)],[t125,t699]) ).
cnf(t75544,plain,
ifeq(leq(star(strong_iteration(sk0)),strong_iteration(sk0)),true,false,true) = true,
inference(step,[status(thm)],[t75543,t26]) ).
cnf(t702,plain,
ifeq(leq(star(strong_iteration(sk0)),strong_iteration(sk0)),true,false,true) = true,
inference(rw,[status(thm)],[t75544]) ).
cnf(t63649,plain,
ifeq(leq(star(strong_iteration(sk0)),strong_iteration(sk0)),true,false,true) = true,
inference(orient,[status(thm)],[t702]) ).
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(t20,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(t99,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t102,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true),
inference(cp,[status(thm)],[t99,t24]) ).
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(t15,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t30,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
cnf(t235,plain,
multiplication(addition(one,multiplication(X1,X2)),X3) = addition(X3,multiplication(X1,multiplication(X2,X3))),
inference(cp,[status(thm)],[t230,t30]) ).
cnf(t46438,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(orient,[status(thm)],[t235]) ).
cnf(t46439,plain,
multiplication(addition(one,multiplication(X1,X2)),X1) = multiplication(X1,addition(one,multiplication(X2,X1))),
inference(cp,[status(thm)],[t46438,t218]) ).
cnf(t50930,plain,
multiplication(addition(one,multiplication(X1,X2)),X1) = multiplication(X1,addition(one,multiplication(X2,X1))),
inference(orient,[status(thm)],[t46439]) ).
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(t9,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t66,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t50935,plain,
multiplication(X1,addition(one,multiplication(star(X1),X1))) = multiplication(star(X1),X1),
inference(cp,[status(thm)],[t50930,t66]) ).
cnf(t76060,plain,
multiplication(X1,star(X1)) = multiplication(star(X1),X1),
inference(step,[status(thm)],[t50935,t72]) ).
cnf(t51109,plain,
multiplication(star(X1),X1) = multiplication(X1,star(X1)),
inference(orient,[status(thm)],[t76060]) ).
cnf(t51123,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(multiplication(X1,star(X1)),X2),
inference(cp,[status(thm)],[t30,t51109]) ).
cnf(t76065,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(X1,multiplication(star(X1),X2)),
inference(step,[status(thm)],[t51123,t30]) ).
cnf(t51176,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(X1,multiplication(star(X1),X2)),
inference(orient,[status(thm)],[t76065]) ).
cnf(t76290,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(X1,multiplication(star(X1),X2)),X2),true),
inference(step,[status(thm)],[t102,t51176]) ).
cnf(t75298,plain,
ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(X1,multiplication(star(X1),X2)),X2),true) = true,
inference(orient,[status(thm)],[t76290]) ).
cnf(t47,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t27,t43]) ).
cnf(t3133,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t47]) ).
cnf(t101,plain,
true = ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true),
inference(cp,[status(thm)],[t99,t35]) ).
cnf(t70138,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t101]) ).
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(t8,plain,
addition(multiplication(X1,strong_iteration(X1)),one) = strong_iteration(X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t75502,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(step,[status(thm)],[t8,t43]) ).
cnf(t57,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(orient,[status(thm)],[t75502]) ).
cnf(t183,plain,
true = leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t180,t57]) ).
cnf(t341,plain,
leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t183]) ).
cnf(t343,plain,
strong_iteration(X1) = ifeq(true,true,addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t27,t341]) ).
cnf(t75572,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t343,t26]) ).
cnf(t75573,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))),
inference(step,[status(thm)],[t75572,t43]) ).
cnf(t75574,plain,
strong_iteration(X1) = multiplication(addition(one,X1),strong_iteration(X1)),
inference(step,[status(thm)],[t75573,t230]) ).
cnf(t1622,plain,
multiplication(addition(one,X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t75574]) ).
cnf(t1652,plain,
strong_iteration(X1) = multiplication(addition(X1,one),strong_iteration(X1)),
inference(cp,[status(thm)],[t1622,t43]) ).
cnf(t1677,plain,
multiplication(addition(X1,one),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t1652]) ).
cnf(t70154,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)],[t70138,t1677]) ).
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(t2,plain,
leq(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi3]) ).
cnf(t76,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t76223,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),true),
inference(step,[status(thm)],[t70154,t76]) ).
cnf(t76224,plain,
true = leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),
inference(step,[status(thm)],[t76223,t26]) ).
cnf(t76225,plain,
true = leq(multiplication(star(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t76224,t23]) ).
cnf(t36,plain,
multiplication(addition(multiplication(X1,X2),X3),Y3) = addition(multiplication(X1,multiplication(X2,Y3)),multiplication(X3,Y3)),
inference(cp,[status(thm)],[t35,t30]) ).
cnf(t806,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(Y3,X3)) = multiplication(addition(multiplication(X1,X2),Y3),X3),
inference(orient,[status(thm)],[t36]) ).
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(t5,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t41,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t823,plain,
multiplication(addition(multiplication(X1,zero),X2),X3) = addition(multiplication(X1,zero),multiplication(X2,X3)),
inference(cp,[status(thm)],[t806,t41]) ).
cnf(t48168,plain,
addition(multiplication(X1,zero),multiplication(X2,X3)) = multiplication(addition(multiplication(X1,zero),X2),X3),
inference(orient,[status(thm)],[t823]) ).
cnf(t48169,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(cp,[status(thm)],[t48168,t35]) ).
cnf(t48478,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t48169]) ).
cnf(t48482,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(multiplication(addition(X1,X2),zero),zero),
inference(cp,[status(thm)],[t48478,t35]) ).
cnf(t76040,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),multiplication(zero,zero)),
inference(step,[status(thm)],[t48482,t30]) ).
cnf(t76041,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(step,[status(thm)],[t76040,t41]) ).
cnf(t48696,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t76041]) ).
cnf(t48724,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,t48696]) ).
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(t25,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t76042,plain,
multiplication(addition(X1,multiplication(X2,zero)),one) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t48724,t25]) ).
cnf(t76043,plain,
addition(X1,multiplication(X2,zero)) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t76042,t22]) ).
cnf(t76044,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,addition(multiplication(X2,zero),multiplication(addition(X1,X2),zero))),
inference(step,[status(thm)],[t76043,t48]) ).
cnf(t76045,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(multiplication(X2,zero),addition(X1,X2)),zero)),
inference(step,[status(thm)],[t76044,t48168]) ).
cnf(t76046,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,addition(X1,X2)),zero)),
inference(step,[status(thm)],[t76045,t48478]) ).
cnf(t153,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t146,t43]) ).
cnf(t197,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t153]) ).
cnf(t76047,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t76046,t197]) ).
cnf(t48875,plain,
addition(X1,multiplication(addition(X2,X1),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t76047]) ).
cnf(t48925,plain,
addition(addition(X1,X2),multiplication(X2,zero)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(cp,[status(thm)],[t48875,t197]) ).
cnf(t76144,plain,
addition(X1,addition(X2,multiplication(X2,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t48925,t48]) ).
cnf(t76145,plain,
addition(X1,multiplication(X2,addition(one,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t76144,t218]) ).
cnf(t76146,plain,
addition(X1,multiplication(X2,one)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t76145,t25]) ).
cnf(t76147,plain,
addition(X1,X2) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t76146,t22]) ).
cnf(t76148,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(addition(X2,X1),zero))),
inference(step,[status(thm)],[t76147,t48]) ).
cnf(t48973,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X1,X2),zero)),
inference(cp,[status(thm)],[t48875,t43]) ).
cnf(t49179,plain,
addition(X1,multiplication(addition(X1,X2),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t48973]) ).
cnf(t76149,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(X1,zero))),
inference(step,[status(thm)],[t76148,t49179]) ).
cnf(t59653,plain,
addition(X1,addition(X2,multiplication(X1,zero))) = addition(X1,X2),
inference(orient,[status(thm)],[t76149]) ).
cnf(t59764,plain,
true = leq(multiplication(X1,zero),addition(X1,X2)),
inference(cp,[status(thm)],[t352,t59653]) ).
cnf(t59840,plain,
leq(multiplication(X1,zero),addition(X1,X2)) = true,
inference(orient,[status(thm)],[t59764]) ).
cnf(t59848,plain,
true = leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)),
inference(cp,[status(thm)],[t59840,t230]) ).
cnf(t60943,plain,
leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)) = true,
inference(orient,[status(thm)],[t59848]) ).
cnf(t60971,plain,
true = leq(multiplication(X1,zero),multiplication(star(X2),X1)),
inference(cp,[status(thm)],[t60943,t159]) ).
cnf(t61006,plain,
leq(multiplication(X1,zero),multiplication(star(X2),X1)) = true,
inference(orient,[status(thm)],[t60971]) ).
cnf(t61028,plain,
multiplication(star(X1),X2) = ifeq(true,true,addition(multiplication(star(X1),X2),multiplication(X2,zero)),multiplication(star(X1),X2)),
inference(cp,[status(thm)],[t3133,t61006]) ).
cnf(t76160,plain,
multiplication(star(X1),X2) = addition(multiplication(star(X1),X2),multiplication(X2,zero)),
inference(step,[status(thm)],[t61028,t26]) ).
cnf(t38,plain,
multiplication(addition(X1,multiplication(X2,X3)),Y3) = addition(multiplication(X1,Y3),multiplication(X2,multiplication(X3,Y3))),
inference(cp,[status(thm)],[t35,t30]) ).
cnf(t1269,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(Y3,X2))) = multiplication(addition(X1,multiplication(X3,Y3)),X2),
inference(orient,[status(thm)],[t38]) ).
cnf(t1301,plain,
multiplication(addition(X1,multiplication(X2,zero)),X3) = addition(multiplication(X1,X3),multiplication(X2,zero)),
inference(cp,[status(thm)],[t1269,t41]) ).
cnf(t49428,plain,
addition(multiplication(X1,X2),multiplication(X3,zero)) = multiplication(addition(X1,multiplication(X3,zero)),X2),
inference(orient,[status(thm)],[t1301]) ).
cnf(t76161,plain,
multiplication(star(X1),X2) = multiplication(addition(star(X1),multiplication(X2,zero)),X2),
inference(step,[status(thm)],[t76160,t49428]) ).
cnf(t62110,plain,
multiplication(addition(star(X1),multiplication(X2,zero)),X2) = multiplication(star(X1),X2),
inference(orient,[status(thm)],[t76161]) ).
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(t11,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t63,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t65,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(cp,[status(thm)],[t48,t63]) ).
cnf(t17330,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(orient,[status(thm)],[t65]) ).
cnf(t17336,plain,
addition(strong_iteration(X1),multiplication(strong_iteration(X1),X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(cp,[status(thm)],[t17330,t31]) ).
cnf(t75913,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(step,[status(thm)],[t17336,t218]) ).
cnf(t44,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t43,t25]) ).
cnf(t132,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t44]) ).
cnf(t75914,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),X2)),
inference(step,[status(thm)],[t75913,t132]) ).
cnf(t29625,plain,
addition(star(X1),multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(one,X2)),
inference(orient,[status(thm)],[t75914]) ).
cnf(t62111,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(multiplication(strong_iteration(X1),addition(one,zero)),strong_iteration(X1)),
inference(cp,[status(thm)],[t62110,t29625]) ).
cnf(t76162,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(addition(one,zero),strong_iteration(X1))),
inference(step,[status(thm)],[t62111,t30]) ).
cnf(t76163,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(one,strong_iteration(X1))),
inference(step,[status(thm)],[t76162,t25]) ).
cnf(t76164,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t76163,t23]) ).
cnf(t62258,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(orient,[status(thm)],[t76164]) ).
cnf(t76226,plain,
true = leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t76225,t62258]) ).
cnf(t70548,plain,
leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t76226]) ).
cnf(t70552,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)],[t3133,t70548]) ).
cnf(t76227,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(strong_iteration(X1),strong_iteration(X1))),
inference(step,[status(thm)],[t70552,t26]) ).
cnf(t76228,plain,
strong_iteration(X1) = multiplication(addition(one,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t76227,t230]) ).
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(t76229,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),addition(one,strong_iteration(X1))),
inference(step,[status(thm)],[t76228,t265]) ).
cnf(t150,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = addition(one,strong_iteration(X1)),
inference(cp,[status(thm)],[t146,t57]) ).
cnf(t75510,plain,
strong_iteration(X1) = addition(one,strong_iteration(X1)),
inference(step,[status(thm)],[t150,t57]) ).
cnf(t164,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t75510]) ).
cnf(t76230,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t76229,t164]) ).
cnf(t70555,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t76230]) ).
cnf(t75360,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)],[t75298,t70555]) ).
cnf(t76291,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)],[t75360,t76]) ).
cnf(t76292,plain,
true = leq(multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),strong_iteration(X1))),strong_iteration(X1)),
inference(step,[status(thm)],[t76291,t26]) ).
cnf(t184,plain,
true = leq(multiplication(X1,star(X1)),star(X1)),
inference(cp,[status(thm)],[t180,t66]) ).
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)],[t27,t346]) ).
cnf(t75575,plain,
star(X1) = addition(multiplication(X1,star(X1)),star(X1)),
inference(step,[status(thm)],[t348,t26]) ).
cnf(t75576,plain,
star(X1) = addition(star(X1),multiplication(X1,star(X1))),
inference(step,[status(thm)],[t75575,t43]) ).
cnf(t75577,plain,
star(X1) = multiplication(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t75576,t230]) ).
cnf(t1728,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t75577]) ).
cnf(t1733,plain,
star(strong_iteration(X1)) = multiplication(strong_iteration(X1),star(strong_iteration(X1))),
inference(cp,[status(thm)],[t1728,t164]) ).
cnf(t1793,plain,
multiplication(strong_iteration(X1),star(strong_iteration(X1))) = star(strong_iteration(X1)),
inference(orient,[status(thm)],[t1733]) ).
cnf(t1798,plain,
multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),X2)) = multiplication(star(strong_iteration(X1)),X2),
inference(cp,[status(thm)],[t30,t1793]) ).
cnf(t55296,plain,
multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),X2)) = multiplication(star(strong_iteration(X1)),X2),
inference(orient,[status(thm)],[t1798]) ).
cnf(t76293,plain,
true = leq(multiplication(star(strong_iteration(X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t76292,t55296]) ).
cnf(t661,plain,
star(strong_iteration(X1)) = multiplication(star(strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t656,t164]) ).
cnf(t944,plain,
multiplication(star(strong_iteration(X1)),strong_iteration(X1)) = star(strong_iteration(X1)),
inference(orient,[status(thm)],[t661]) ).
cnf(t76294,plain,
true = leq(star(strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t76293,t944]) ).
cnf(t75490,plain,
leq(star(strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t76294]) ).
cnf(t76295,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t63649,t75490]) ).
cnf(t76296,plain,
false = true,
inference(step,[status(thm)],[t76295,t26]) ).
cnf(t75500,plain,
false = true,
inference(rw,[status(thm)],[t76296]) ).
cnf(t75501,plain,
false = true,
inference(orient,[status(thm)],[t75500]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t75501]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE145+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 19:04:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 72.62/9.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 72.62/9.62 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------