%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 01:51:42 PM UTC 2026
% Result : Theorem 160.79s 31.08s
% Output : Proof 160.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 88
% Number of leaves : 17
% Syntax : Number of formulae : 303 ( 289 unt; 0 def)
% Number of atoms : 321 ( 295 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 : 409 ( 103 sgn 83 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,conjecture,
! [X0] :
( leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
& leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
& leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0] :
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
| ~ leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sk0)))
| ~ leq(strong_iteration(strong_iteration(sk0)),strong_iteration(one)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c19,plain,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sk0)))
| ~ leq(strong_iteration(strong_iteration(sk0)),strong_iteration(one)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t23,plain,
ifeq(leq(strong_iteration(strong_iteration(sk0)),strong_iteration(one)),true,ifeq(leq(strong_iteration(one),strong_iteration(strong_iteration(sk0))),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t127,plain,
ifeq(leq(strong_iteration(strong_iteration(sk0)),strong_iteration(one)),true,ifeq(leq(strong_iteration(one),strong_iteration(strong_iteration(sk0))),true,false,true),true) = true,
inference(orient,[status(thm)],[t23]) ).
fof(f17,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/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(t15,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t79,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/sandbox/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(t50,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/sandbox/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(t26,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t53,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t50,t26]) ).
cnf(t148,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t53]) ).
cnf(t157,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t79,t148]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t84603,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t157,t28]) ).
cnf(t171,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t84603]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/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(t45,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t176,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t171,t45]) ).
cnf(t182,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t176]) ).
cnf(t187,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t182,t50]) ).
cnf(t354,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t187]) ).
cnf(t356,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t354,t45]) ).
cnf(t84608,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t356,t50]) ).
cnf(t431,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t84608]) ).
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(t29,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t16]) ).
fof(f8,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/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(t37,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t19]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/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(t25,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t39,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t37,t25]) ).
cnf(t232,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t39]) ).
fof(f11,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('/export/starexec/sandbox/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(t71,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t184,plain,
true = leq(multiplication(star(X1),X1),star(X1)),
inference(cp,[status(thm)],[t182,t71]) ).
cnf(t299,plain,
leq(multiplication(star(X1),X1),star(X1)) = true,
inference(orient,[status(thm)],[t184]) ).
cnf(t300,plain,
star(X1) = ifeq(true,true,addition(multiplication(star(X1),X1),star(X1)),star(X1)),
inference(cp,[status(thm)],[t29,t299]) ).
cnf(t84627,plain,
star(X1) = addition(multiplication(star(X1),X1),star(X1)),
inference(step,[status(thm)],[t300,t28]) ).
cnf(t84628,plain,
star(X1) = addition(star(X1),multiplication(star(X1),X1)),
inference(step,[status(thm)],[t84627,t45]) ).
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/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(t33,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/sandbox/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(t24,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t34,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t33,t24]) ).
cnf(t220,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t34]) ).
cnf(t84629,plain,
star(X1) = multiplication(star(X1),addition(one,X1)),
inference(step,[status(thm)],[t84628,t220]) ).
cnf(t658,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t84629]) ).
cnf(t671,plain,
multiplication(addition(one,star(X1)),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t232,t658]) ).
cnf(t151,plain,
addition(one,multiplication(star(X1),X1)) = addition(one,star(X1)),
inference(cp,[status(thm)],[t148,t71]) ).
cnf(t84599,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t151,t71]) ).
cnf(t161,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t84599]) ).
cnf(t84630,plain,
multiplication(star(X1),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t671,t161]) ).
cnf(t84631,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t84630,t658]) ).
cnf(t84632,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t84631,t50]) ).
cnf(t437,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t431,t161]) ).
cnf(t455,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t437]) ).
cnf(t458,plain,
addition(X1,star(X2)) = ifeq(true,true,addition(one,addition(X1,star(X2))),addition(X1,star(X2))),
inference(cp,[status(thm)],[t29,t455]) ).
cnf(t84615,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t458,t28]) ).
cnf(t587,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t84615]) ).
cnf(t84633,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t84632,t587]) ).
cnf(t686,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t84633]) ).
cnf(t696,plain,
true = leq(X1,addition(X2,star(X1))),
inference(cp,[status(thm)],[t431,t686]) ).
cnf(t713,plain,
leq(X1,addition(X2,star(X1))) = true,
inference(orient,[status(thm)],[t696]) ).
fof(f16,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
file('/export/starexec/sandbox/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(t75,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t150,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = addition(star(X1),strong_iteration(X1)),
inference(cp,[status(thm)],[t148,t75]) ).
cnf(t84604,plain,
strong_iteration(X1) = addition(star(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t150,t75]) ).
cnf(t84605,plain,
strong_iteration(X1) = addition(strong_iteration(X1),star(X1)),
inference(step,[status(thm)],[t84604,t45]) ).
cnf(t195,plain,
addition(strong_iteration(X1),star(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t84605]) ).
cnf(t714,plain,
true = leq(X1,strong_iteration(X1)),
inference(cp,[status(thm)],[t713,t195]) ).
cnf(t722,plain,
leq(X1,strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t714]) ).
cnf(t723,plain,
strong_iteration(X1) = ifeq(true,true,addition(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t29,t722]) ).
cnf(t84634,plain,
strong_iteration(X1) = addition(X1,strong_iteration(X1)),
inference(step,[status(thm)],[t723,t28]) ).
cnf(t727,plain,
addition(X1,strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t84634]) ).
cnf(t734,plain,
true = leq(X1,addition(X2,strong_iteration(X1))),
inference(cp,[status(thm)],[t431,t727]) ).
cnf(t789,plain,
leq(X1,addition(X2,strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t734]) ).
cnf(t791,plain,
true = leq(X1,addition(strong_iteration(X1),X2)),
inference(cp,[status(thm)],[t789,t45]) ).
cnf(t850,plain,
leq(X1,addition(strong_iteration(X1),X2)) = true,
inference(orient,[status(thm)],[t791]) ).
cnf(t856,plain,
true = leq(X1,multiplication(addition(one,X2),strong_iteration(X1))),
inference(cp,[status(thm)],[t850,t232]) ).
cnf(t2724,plain,
leq(X1,multiplication(addition(one,X2),strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t856]) ).
cnf(t2729,plain,
true = leq(X1,multiplication(star(X2),strong_iteration(X1))),
inference(cp,[status(thm)],[t2724,t161]) ).
cnf(t2751,plain,
leq(X1,multiplication(star(X2),strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t2729]) ).
fof(f4,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/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(t32,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/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(t27,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t46,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t45,t27]) ).
cnf(t134,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t46]) ).
cnf(t234,plain,
multiplication(addition(one,X1),zero) = multiplication(X1,zero),
inference(cp,[status(thm)],[t232,t134]) ).
cnf(t247,plain,
multiplication(addition(one,X1),zero) = multiplication(X1,zero),
inference(orient,[status(thm)],[t234]) ).
cnf(t248,plain,
multiplication(multiplication(star(X1),X1),zero) = multiplication(star(X1),zero),
inference(cp,[status(thm)],[t247,t71]) ).
cnf(t84611,plain,
multiplication(star(X1),multiplication(X1,zero)) = multiplication(star(X1),zero),
inference(step,[status(thm)],[t248,t32]) ).
cnf(t526,plain,
multiplication(star(X1),multiplication(X1,zero)) = multiplication(star(X1),zero),
inference(orient,[status(thm)],[t84611]) ).
cnf(t531,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = addition(star(X1),multiplication(star(X1),zero)),
inference(cp,[status(thm)],[t220,t526]) ).
cnf(t84707,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = multiplication(star(X1),addition(one,zero)),
inference(step,[status(thm)],[t531,t220]) ).
cnf(t84708,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = multiplication(star(X1),one),
inference(step,[status(thm)],[t84707,t27]) ).
cnf(t84709,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = star(X1),
inference(step,[status(thm)],[t84708,t24]) ).
cnf(t5727,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = star(X1),
inference(orient,[status(thm)],[t84709]) ).
fof(f14,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/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(t84593,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(step,[status(thm)],[t10,t45]) ).
cnf(t59,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(orient,[status(thm)],[t84593]) ).
cnf(t61,plain,
strong_iteration(multiplication(X1,X2)) = addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))),
inference(cp,[status(thm)],[t59,t32]) ).
cnf(t10992,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(orient,[status(thm)],[t61]) ).
fof(f9,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/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(t43,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t7]) ).
cnf(t10994,plain,
strong_iteration(multiplication(X1,zero)) = addition(one,multiplication(X1,zero)),
inference(cp,[status(thm)],[t10992,t43]) ).
cnf(t11107,plain,
addition(one,multiplication(X1,zero)) = strong_iteration(multiplication(X1,zero)),
inference(orient,[status(thm)],[t10994]) ).
cnf(t84777,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(step,[status(thm)],[t5727,t11107]) ).
cnf(t11154,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(rw,[status(thm)],[t84777]) ).
cnf(t11264,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(orient,[status(thm)],[t11154]) ).
fof(f15,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox/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(t89,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(t433,plain,
true = leq(X1,addition(X2,multiplication(X1,addition(one,X3)))),
inference(cp,[status(thm)],[t431,t220]) ).
cnf(t12817,plain,
leq(X1,addition(X2,multiplication(X1,addition(one,X3)))) = true,
inference(orient,[status(thm)],[t433]) ).
cnf(t152,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = addition(one,strong_iteration(X1)),
inference(cp,[status(thm)],[t148,t59]) ).
cnf(t84601,plain,
strong_iteration(X1) = addition(one,strong_iteration(X1)),
inference(step,[status(thm)],[t152,t59]) ).
cnf(t166,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t84601]) ).
cnf(t12834,plain,
true = leq(X1,addition(X2,multiplication(X1,strong_iteration(X3)))),
inference(cp,[status(thm)],[t12817,t166]) ).
cnf(t12914,plain,
leq(X1,addition(X2,multiplication(X1,strong_iteration(X3)))) = true,
inference(orient,[status(thm)],[t12834]) ).
cnf(t12919,plain,
true = leq(X1,addition(multiplication(X1,strong_iteration(X2)),X3)),
inference(cp,[status(thm)],[t12914,t45]) ).
cnf(t13027,plain,
leq(X1,addition(multiplication(X1,strong_iteration(X2)),X3)) = true,
inference(orient,[status(thm)],[t12919]) ).
cnf(t13108,plain,
true = ifeq(true,true,leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)),true),
inference(cp,[status(thm)],[t89,t13027]) ).
cnf(t84821,plain,
true = leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)),
inference(step,[status(thm)],[t13108,t28]) ).
cnf(t13636,plain,
leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)) = true,
inference(orient,[status(thm)],[t84821]) ).
cnf(t60,plain,
strong_iteration(zero) = addition(one,zero),
inference(cp,[status(thm)],[t59,t43]) ).
cnf(t84594,plain,
strong_iteration(zero) = one,
inference(step,[status(thm)],[t60,t27]) ).
cnf(t128,plain,
strong_iteration(zero) = one,
inference(orient,[status(thm)],[t84594]) ).
cnf(t13637,plain,
true = leq(one,multiplication(strong_iteration(strong_iteration(zero)),X1)),
inference(cp,[status(thm)],[t13636,t128]) ).
cnf(t84822,plain,
true = leq(one,multiplication(strong_iteration(one),X1)),
inference(step,[status(thm)],[t13637,t128]) ).
cnf(t13645,plain,
leq(one,multiplication(strong_iteration(one),X1)) = true,
inference(orient,[status(thm)],[t84822]) ).
cnf(t13648,plain,
multiplication(strong_iteration(one),X1) = ifeq(true,true,addition(one,multiplication(strong_iteration(one),X1)),multiplication(strong_iteration(one),X1)),
inference(cp,[status(thm)],[t29,t13645]) ).
cnf(t84823,plain,
multiplication(strong_iteration(one),X1) = addition(one,multiplication(strong_iteration(one),X1)),
inference(step,[status(thm)],[t13648,t28]) ).
cnf(t13662,plain,
addition(one,multiplication(strong_iteration(one),X1)) = multiplication(strong_iteration(one),X1),
inference(orient,[status(thm)],[t84823]) ).
cnf(t13663,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(multiplication(strong_iteration(one),zero)),
inference(cp,[status(thm)],[t13662,t11107]) ).
cnf(t13708,plain,
strong_iteration(multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(orient,[status(thm)],[t13663]) ).
cnf(t13723,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),multiplication(strong_iteration(one),zero)),
inference(cp,[status(thm)],[t11264,t13708]) ).
cnf(t84824,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),zero),
inference(step,[status(thm)],[t13723,t526]) ).
cnf(t13790,plain,
multiplication(star(strong_iteration(one)),zero) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t84824]) ).
cnf(t13800,plain,
multiplication(star(strong_iteration(one)),multiplication(zero,X1)) = multiplication(star(strong_iteration(one)),X1),
inference(cp,[status(thm)],[t32,t13790]) ).
cnf(t84829,plain,
multiplication(star(strong_iteration(one)),zero) = multiplication(star(strong_iteration(one)),X1),
inference(step,[status(thm)],[t13800,t43]) ).
cnf(t84830,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),X1),
inference(step,[status(thm)],[t84829,t13790]) ).
cnf(t13937,plain,
multiplication(star(strong_iteration(one)),X1) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t84830]) ).
cnf(t13950,plain,
true = leq(X1,star(strong_iteration(one))),
inference(cp,[status(thm)],[t2751,t13937]) ).
cnf(t13972,plain,
leq(X1,star(strong_iteration(one))) = true,
inference(orient,[status(thm)],[t13950]) ).
cnf(t13938,plain,
multiplication(addition(one,star(strong_iteration(one))),X1) = addition(X1,star(strong_iteration(one))),
inference(cp,[status(thm)],[t232,t13937]) ).
cnf(t84831,plain,
multiplication(star(strong_iteration(one)),X1) = addition(X1,star(strong_iteration(one))),
inference(step,[status(thm)],[t13938,t161]) ).
cnf(t84832,plain,
star(strong_iteration(one)) = addition(X1,star(strong_iteration(one))),
inference(step,[status(thm)],[t84831,t13937]) ).
cnf(t13978,plain,
addition(X1,star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t84832]) ).
cnf(t13979,plain,
star(strong_iteration(one)) = strong_iteration(strong_iteration(one)),
inference(cp,[status(thm)],[t13978,t195]) ).
cnf(t14000,plain,
star(strong_iteration(one)) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t13979]) ).
cnf(t84835,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(step,[status(thm)],[t13972,t14000]) ).
cnf(t14022,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(rw,[status(thm)],[t84835]) ).
cnf(t14109,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(orient,[status(thm)],[t14022]) ).
cnf(t49,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t29,t45]) ).
cnf(t3134,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t49]) ).
cnf(t14112,plain,
strong_iteration(strong_iteration(one)) = ifeq(true,true,addition(strong_iteration(strong_iteration(one)),X1),strong_iteration(strong_iteration(one))),
inference(cp,[status(thm)],[t3134,t14109]) ).
cnf(t84842,plain,
strong_iteration(strong_iteration(one)) = addition(strong_iteration(strong_iteration(one)),X1),
inference(step,[status(thm)],[t14112,t28]) ).
cnf(t14157,plain,
addition(strong_iteration(strong_iteration(one)),X1) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t84842]) ).
cnf(t716,plain,
true = leq(X1,addition(star(X1),X2)),
inference(cp,[status(thm)],[t713,t45]) ).
cnf(t741,plain,
leq(X1,addition(star(X1),X2)) = true,
inference(orient,[status(thm)],[t716]) ).
cnf(t745,plain,
true = leq(X1,multiplication(addition(one,X2),star(X1))),
inference(cp,[status(thm)],[t741,t232]) ).
cnf(t2630,plain,
leq(X1,multiplication(addition(one,X2),star(X1))) = true,
inference(orient,[status(thm)],[t745]) ).
cnf(t2635,plain,
true = leq(X1,multiplication(star(X2),star(X1))),
inference(cp,[status(thm)],[t2630,t161]) ).
cnf(t2657,plain,
leq(X1,multiplication(star(X2),star(X1))) = true,
inference(orient,[status(thm)],[t2635]) ).
cnf(t2658,plain,
multiplication(star(X1),star(X2)) = ifeq(true,true,addition(X2,multiplication(star(X1),star(X2))),multiplication(star(X1),star(X2))),
inference(cp,[status(thm)],[t29,t2657]) ).
cnf(t84743,plain,
multiplication(star(X1),star(X2)) = addition(X2,multiplication(star(X1),star(X2))),
inference(step,[status(thm)],[t2658,t28]) ).
cnf(t8845,plain,
addition(X1,multiplication(star(X2),star(X1))) = multiplication(star(X2),star(X1)),
inference(orient,[status(thm)],[t84743]) ).
cnf(t14158,plain,
strong_iteration(strong_iteration(one)) = multiplication(star(X1),star(strong_iteration(strong_iteration(one)))),
inference(cp,[status(thm)],[t14157,t8845]) ).
cnf(t13791,plain,
strong_iteration(multiplication(star(strong_iteration(one)),zero)) = addition(one,star(strong_iteration(one))),
inference(cp,[status(thm)],[t11107,t13790]) ).
cnf(t84825,plain,
strong_iteration(star(strong_iteration(one))) = addition(one,star(strong_iteration(one))),
inference(step,[status(thm)],[t13791,t13790]) ).
cnf(t84826,plain,
strong_iteration(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t84825,t161]) ).
cnf(t13841,plain,
strong_iteration(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t84826]) ).
cnf(t13845,plain,
strong_iteration(star(strong_iteration(one))) = addition(star(strong_iteration(one)),star(star(strong_iteration(one)))),
inference(cp,[status(thm)],[t195,t13841]) ).
cnf(t84827,plain,
star(strong_iteration(one)) = addition(star(strong_iteration(one)),star(star(strong_iteration(one)))),
inference(step,[status(thm)],[t13845,t13841]) ).
cnf(t84828,plain,
star(strong_iteration(one)) = star(star(strong_iteration(one))),
inference(step,[status(thm)],[t84827,t686]) ).
cnf(t13893,plain,
star(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t84828]) ).
cnf(t84838,plain,
star(strong_iteration(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t13893,t14000]) ).
cnf(t84839,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t84838,t14000]) ).
cnf(t14024,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(rw,[status(thm)],[t84839]) ).
cnf(t14026,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14024]) ).
cnf(t84847,plain,
strong_iteration(strong_iteration(one)) = multiplication(star(X1),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t14158,t14026]) ).
cnf(t14223,plain,
multiplication(star(X1),strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t84847]) ).
cnf(t13710,plain,
strong_iteration(multiplication(strong_iteration(one),zero)) = addition(multiplication(strong_iteration(one),zero),star(multiplication(strong_iteration(one),zero))),
inference(cp,[status(thm)],[t195,t13708]) ).
cnf(t84845,plain,
multiplication(strong_iteration(one),zero) = addition(multiplication(strong_iteration(one),zero),star(multiplication(strong_iteration(one),zero))),
inference(step,[status(thm)],[t13710,t13708]) ).
cnf(t84846,plain,
multiplication(strong_iteration(one),zero) = star(multiplication(strong_iteration(one),zero)),
inference(step,[status(thm)],[t84845,t686]) ).
cnf(t14180,plain,
star(multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(orient,[status(thm)],[t84846]) ).
cnf(t14224,plain,
strong_iteration(strong_iteration(one)) = multiplication(multiplication(strong_iteration(one),zero),strong_iteration(strong_iteration(one))),
inference(cp,[status(thm)],[t14223,t14180]) ).
cnf(t84848,plain,
strong_iteration(strong_iteration(one)) = multiplication(strong_iteration(one),multiplication(zero,strong_iteration(strong_iteration(one)))),
inference(step,[status(thm)],[t14224,t32]) ).
cnf(t84849,plain,
strong_iteration(strong_iteration(one)) = multiplication(strong_iteration(one),zero),
inference(step,[status(thm)],[t84848,t43]) ).
cnf(t14240,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t84849]) ).
cnf(t14245,plain,
multiplication(strong_iteration(one),addition(one,zero)) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(cp,[status(thm)],[t220,t14240]) ).
cnf(t84850,plain,
multiplication(strong_iteration(one),one) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t14245,t27]) ).
cnf(t84851,plain,
strong_iteration(one) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t84850,t24]) ).
cnf(t84833,plain,
addition(X1,strong_iteration(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t13978,t14000]) ).
cnf(t84834,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t84833,t14000]) ).
cnf(t14021,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(rw,[status(thm)],[t84834]) ).
cnf(t14115,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14021]) ).
cnf(t84852,plain,
strong_iteration(one) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t84851,t14115]) ).
cnf(t14284,plain,
strong_iteration(strong_iteration(one)) = strong_iteration(one),
inference(orient,[status(thm)],[t84852]) ).
cnf(t84865,plain,
leq(X1,strong_iteration(one)) = true,
inference(step,[status(thm)],[t14109,t14284]) ).
cnf(t14323,plain,
leq(X1,strong_iteration(one)) = true,
inference(rw,[status(thm)],[t84865]) ).
cnf(t14324,plain,
leq(X1,strong_iteration(one)) = true,
inference(orient,[status(thm)],[t14323]) ).
cnf(t84866,plain,
ifeq(true,true,ifeq(leq(strong_iteration(one),strong_iteration(strong_iteration(sk0))),true,false,true),true) = true,
inference(step,[status(thm)],[t127,t14324]) ).
cnf(t84867,plain,
ifeq(leq(strong_iteration(one),strong_iteration(strong_iteration(sk0))),true,false,true) = true,
inference(step,[status(thm)],[t84866,t28]) ).
cnf(t14330,plain,
ifeq(leq(strong_iteration(one),strong_iteration(strong_iteration(sk0))),true,false,true) = true,
inference(rw,[status(thm)],[t84867]) ).
cnf(t84859,plain,
addition(strong_iteration(one),X1) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t14157,t14284]) ).
cnf(t84860,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(step,[status(thm)],[t84859,t14284]) ).
cnf(t14320,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(rw,[status(thm)],[t84860]) ).
cnf(t14331,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(orient,[status(thm)],[t14320]) ).
cnf(t719,plain,
true = ifeq(true,true,leq(X1,multiplication(strong_iteration(X2),star(X1))),true),
inference(cp,[status(thm)],[t89,t713]) ).
cnf(t84641,plain,
true = leq(X1,multiplication(strong_iteration(X2),star(X1))),
inference(step,[status(thm)],[t719,t28]) ).
cnf(t988,plain,
leq(X1,multiplication(strong_iteration(X2),star(X1))) = true,
inference(orient,[status(thm)],[t84641]) ).
cnf(t989,plain,
multiplication(strong_iteration(X1),star(X2)) = ifeq(true,true,addition(X2,multiplication(strong_iteration(X1),star(X2))),multiplication(strong_iteration(X1),star(X2))),
inference(cp,[status(thm)],[t29,t988]) ).
cnf(t84717,plain,
multiplication(strong_iteration(X1),star(X2)) = addition(X2,multiplication(strong_iteration(X1),star(X2))),
inference(step,[status(thm)],[t989,t28]) ).
cnf(t6829,plain,
addition(X1,multiplication(strong_iteration(X2),star(X1))) = multiplication(strong_iteration(X2),star(X1)),
inference(orient,[status(thm)],[t84717]) ).
cnf(t14340,plain,
strong_iteration(one) = multiplication(strong_iteration(X1),star(strong_iteration(one))),
inference(cp,[status(thm)],[t14331,t6829]) ).
cnf(t84853,plain,
star(strong_iteration(one)) = strong_iteration(one),
inference(step,[status(thm)],[t14000,t14284]) ).
cnf(t14285,plain,
star(strong_iteration(one)) = strong_iteration(one),
inference(orient,[status(thm)],[t84853]) ).
cnf(t84868,plain,
strong_iteration(one) = multiplication(strong_iteration(X1),strong_iteration(one)),
inference(step,[status(thm)],[t14340,t14285]) ).
cnf(t14426,plain,
multiplication(strong_iteration(X1),strong_iteration(one)) = strong_iteration(one),
inference(orient,[status(thm)],[t84868]) ).
cnf(t14439,plain,
true = ifeq(leq(strong_iteration(one),addition(strong_iteration(one),X1)),true,leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X2)),X1)),true),
inference(cp,[status(thm)],[t89,t14426]) ).
cnf(t84878,plain,
true = ifeq(true,true,leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X2)),X1)),true),
inference(step,[status(thm)],[t14439,t171]) ).
cnf(t84879,plain,
true = leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X2)),X1)),
inference(step,[status(thm)],[t84878,t28]) ).
cnf(t15232,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),X2)) = true,
inference(orient,[status(thm)],[t84879]) ).
cnf(t15238,plain,
multiplication(strong_iteration(strong_iteration(X1)),X2) = ifeq(true,true,addition(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),X2)),multiplication(strong_iteration(strong_iteration(X1)),X2)),
inference(cp,[status(thm)],[t29,t15232]) ).
cnf(t84880,plain,
multiplication(strong_iteration(strong_iteration(X1)),X2) = addition(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),X2)),
inference(step,[status(thm)],[t15238,t28]) ).
cnf(t84881,plain,
multiplication(strong_iteration(strong_iteration(X1)),X2) = strong_iteration(one),
inference(step,[status(thm)],[t84880,t14331]) ).
cnf(t15242,plain,
multiplication(strong_iteration(strong_iteration(X1)),X2) = strong_iteration(one),
inference(orient,[status(thm)],[t84881]) ).
cnf(t15246,plain,
strong_iteration(one) = strong_iteration(strong_iteration(X1)),
inference(cp,[status(thm)],[t15242,t24]) ).
cnf(t15338,plain,
strong_iteration(strong_iteration(X1)) = strong_iteration(one),
inference(orient,[status(thm)],[t15246]) ).
cnf(t85491,plain,
ifeq(leq(strong_iteration(one),strong_iteration(one)),true,false,true) = true,
inference(step,[status(thm)],[t14330,t15338]) ).
cnf(t85492,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t85491,t14324]) ).
cnf(t85493,plain,
false = true,
inference(step,[status(thm)],[t85492,t28]) ).
cnf(t84592,plain,
false = true,
inference(orient,[status(thm)],[t85493]) ).
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,t84592]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/10.66 % Computer : n010.cluster.edu
% 0.17/10.66 % Model : x86_64 x86_64
% 0.17/10.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.66 % Memory : 8046.5625MB
% 0.17/10.66 % OS : Linux 6.8.0-71-generic
% 0.17/10.66 % CPULimit : 300
% 0.17/10.66 % WCLimit : 300
% 0.17/10.66 % DateTime : Wed Sep 23 19:04:15 UTC 2026
% 0.17/10.66 % CPUTime :
% 0.17/10.66 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 160.79/31.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 160.79/31.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------