%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE147+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 : n019.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 125.20s 18.43s
% Output : Proof 125.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 19
% Syntax : Number of formulae : 347 ( 329 unt; 0 def)
% Number of atoms : 369 ( 335 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 15 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 589 ( 40 sgn 97 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t199029,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)],[t199029]) ).
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]) ).
cnf(t241,plain,
true = leq(X1,multiplication(addition(one,X2),X1)),
inference(cp,[status(thm)],[t171,t232]) ).
cnf(t421,plain,
leq(X1,multiplication(addition(one,X2),X1)) = true,
inference(orient,[status(thm)],[t241]) ).
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(t74,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t151,plain,
addition(one,multiplication(star(X1),X1)) = addition(one,star(X1)),
inference(cp,[status(thm)],[t148,t74]) ).
cnf(t199025,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t151,t74]) ).
cnf(t161,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t199025]) ).
cnf(t422,plain,
true = leq(X1,multiplication(star(X2),X1)),
inference(cp,[status(thm)],[t421,t161]) ).
cnf(t428,plain,
leq(X1,multiplication(star(X2),X1)) = true,
inference(orient,[status(thm)],[t422]) ).
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(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(t49,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t29,t45]) ).
cnf(t3135,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t49]) ).
fof(f12,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('/export/starexec/sandbox/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(t101,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t103,plain,
true = ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true),
inference(cp,[status(thm)],[t101,t37]) ).
cnf(t70182,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t103]) ).
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]) ).
fof(f10,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('/export/starexec/sandbox/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(t68,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t186,plain,
true = leq(multiplication(X1,star(X1)),star(X1)),
inference(cp,[status(thm)],[t182,t68]) ).
cnf(t348,plain,
leq(multiplication(X1,star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t186]) ).
cnf(t350,plain,
star(X1) = ifeq(true,true,addition(multiplication(X1,star(X1)),star(X1)),star(X1)),
inference(cp,[status(thm)],[t29,t348]) ).
cnf(t199092,plain,
star(X1) = addition(multiplication(X1,star(X1)),star(X1)),
inference(step,[status(thm)],[t350,t28]) ).
cnf(t199093,plain,
star(X1) = addition(star(X1),multiplication(X1,star(X1))),
inference(step,[status(thm)],[t199092,t45]) ).
cnf(t199094,plain,
star(X1) = multiplication(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t199093,t232]) ).
cnf(t1730,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t199094]) ).
cnf(t1760,plain,
star(X1) = multiplication(addition(X1,one),star(X1)),
inference(cp,[status(thm)],[t1730,t45]) ).
cnf(t1777,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(orient,[status(thm)],[t1760]) ).
cnf(t70197,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t70182,t1777]) ).
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(t78,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t199732,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(step,[status(thm)],[t70197,t78]) ).
cnf(t199733,plain,
true = leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),
inference(step,[status(thm)],[t199732,t28]) ).
cnf(t199734,plain,
true = leq(multiplication(star(X1),star(X1)),star(X1)),
inference(step,[status(thm)],[t199733,t25]) ).
cnf(t70530,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t199734]) ).
cnf(t70542,plain,
star(X1) = ifeq(true,true,addition(star(X1),multiplication(star(X1),star(X1))),star(X1)),
inference(cp,[status(thm)],[t3135,t70530]) ).
cnf(t199735,plain,
star(X1) = addition(star(X1),multiplication(star(X1),star(X1))),
inference(step,[status(thm)],[t70542,t28]) ).
cnf(t199736,plain,
star(X1) = multiplication(addition(one,star(X1)),star(X1)),
inference(step,[status(thm)],[t199735,t232]) ).
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(t233,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(cp,[status(thm)],[t232,t220]) ).
cnf(t267,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(orient,[status(thm)],[t233]) ).
cnf(t199737,plain,
star(X1) = multiplication(star(X1),addition(one,star(X1))),
inference(step,[status(thm)],[t199736,t267]) ).
cnf(t199738,plain,
star(X1) = multiplication(star(X1),star(X1)),
inference(step,[status(thm)],[t199737,t161]) ).
cnf(t70544,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t199738]) ).
cnf(t70553,plain,
multiplication(addition(star(X1),X2),star(X1)) = addition(star(X1),multiplication(X2,star(X1))),
inference(cp,[status(thm)],[t37,t70544]) ).
cnf(t199761,plain,
multiplication(addition(star(X1),X2),star(X1)) = multiplication(addition(one,X2),star(X1)),
inference(step,[status(thm)],[t70553,t232]) ).
cnf(t70992,plain,
multiplication(addition(star(X1),X2),star(X1)) = multiplication(addition(one,X2),star(X1)),
inference(orient,[status(thm)],[t199761]) ).
cnf(t155,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t148,t45]) ).
cnf(t199,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t155]) ).
cnf(t71012,plain,
multiplication(addition(one,addition(X1,star(X2))),star(X2)) = multiplication(addition(star(X2),X1),star(X2)),
inference(cp,[status(thm)],[t70992,t199]) ).
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(t199036,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t356,t50]) ).
cnf(t432,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t199036]) ).
cnf(t438,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t432,t161]) ).
cnf(t456,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t438]) ).
cnf(t459,plain,
addition(X1,star(X2)) = ifeq(true,true,addition(one,addition(X1,star(X2))),addition(X1,star(X2))),
inference(cp,[status(thm)],[t29,t456]) ).
cnf(t199043,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t459,t28]) ).
cnf(t588,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t199043]) ).
cnf(t199777,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(star(X2),X1),star(X2)),
inference(step,[status(thm)],[t71012,t588]) ).
cnf(t199778,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(one,X1),star(X2)),
inference(step,[status(thm)],[t199777,t70992]) ).
cnf(t71742,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(one,X1),star(X2)),
inference(orient,[status(thm)],[t199778]) ).
cnf(t184,plain,
true = leq(multiplication(star(X1),X1),star(X1)),
inference(cp,[status(thm)],[t182,t74]) ).
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(t199055,plain,
star(X1) = addition(multiplication(star(X1),X1),star(X1)),
inference(step,[status(thm)],[t300,t28]) ).
cnf(t199056,plain,
star(X1) = addition(star(X1),multiplication(star(X1),X1)),
inference(step,[status(thm)],[t199055,t45]) ).
cnf(t199057,plain,
star(X1) = multiplication(star(X1),addition(one,X1)),
inference(step,[status(thm)],[t199056,t220]) ).
cnf(t659,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t199057]) ).
cnf(t672,plain,
multiplication(addition(one,star(X1)),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t232,t659]) ).
cnf(t199058,plain,
multiplication(star(X1),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t672,t161]) ).
cnf(t199059,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t199058,t659]) ).
cnf(t199060,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t199059,t50]) ).
cnf(t199061,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t199060,t588]) ).
cnf(t687,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t199061]) ).
cnf(t688,plain,
star(addition(X1,X2)) = addition(X1,addition(X2,star(addition(X1,X2)))),
inference(cp,[status(thm)],[t687,t50]) ).
cnf(t30570,plain,
addition(X1,addition(X2,star(addition(X1,X2)))) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t688]) ).
cnf(t30616,plain,
star(addition(X1,addition(X1,X2))) = addition(X1,addition(addition(X1,X2),star(addition(X1,X2)))),
inference(cp,[status(thm)],[t30570,t148]) ).
cnf(t199451,plain,
star(addition(X1,X2)) = addition(X1,addition(addition(X1,X2),star(addition(X1,X2)))),
inference(step,[status(thm)],[t30616,t148]) ).
cnf(t199452,plain,
star(addition(X1,X2)) = addition(X1,addition(X1,addition(X2,star(addition(X1,X2))))),
inference(step,[status(thm)],[t199451,t50]) ).
cnf(t199453,plain,
star(addition(X1,X2)) = addition(X1,star(addition(X1,X2))),
inference(step,[status(thm)],[t199452,t30570]) ).
cnf(t31159,plain,
addition(X1,star(addition(X1,X2))) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t199453]) ).
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(t65,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t67,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(cp,[status(thm)],[t50,t65]) ).
cnf(t17332,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(orient,[status(thm)],[t67]) ).
cnf(t31204,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)],[t31159,t17332]) ).
cnf(t199635,plain,
star(addition(strong_iteration(X1),X2)) = addition(star(X1),star(addition(strong_iteration(X1),X2))),
inference(step,[status(thm)],[t31204,t17332]) ).
cnf(t57959,plain,
addition(star(X1),star(addition(strong_iteration(X1),X2))) = star(addition(strong_iteration(X1),X2)),
inference(orient,[status(thm)],[t199635]) ).
cnf(t71766,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)],[t71742,t57959]) ).
cnf(t199859,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)],[t71766,t161]) ).
cnf(t199860,plain,
multiplication(star(X1),star(addition(strong_iteration(X1),X2))) = star(addition(strong_iteration(X1),X2)),
inference(step,[status(thm)],[t199859,t70544]) ).
cnf(t75900,plain,
multiplication(star(X1),star(addition(strong_iteration(X1),X2))) = star(addition(strong_iteration(X1),X2)),
inference(orient,[status(thm)],[t199860]) ).
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(t100,plain,
true = ifeq(leq(X1,addition(multiplication(X2,X1),one)),true,leq(X1,strong_iteration(X2)),true),
inference(cp,[status(thm)],[t89,t24]) ).
cnf(t199711,plain,
true = ifeq(leq(X1,addition(one,multiplication(X2,X1))),true,leq(X1,strong_iteration(X2)),true),
inference(step,[status(thm)],[t100,t45]) ).
cnf(t65078,plain,
ifeq(leq(X1,addition(one,multiplication(X2,X1))),true,leq(X1,strong_iteration(X2)),true) = true,
inference(orient,[status(thm)],[t199711]) ).
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(t199019,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)],[t199019]) ).
cnf(t64,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(cp,[status(thm)],[t50,t59]) ).
cnf(t14441,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(orient,[status(thm)],[t64]) ).
cnf(t14454,plain,
addition(strong_iteration(X1),multiplication(X2,strong_iteration(X1))) = addition(one,multiplication(addition(X1,X2),strong_iteration(X1))),
inference(cp,[status(thm)],[t14441,t37]) ).
cnf(t200372,plain,
multiplication(addition(one,X2),strong_iteration(X1)) = addition(one,multiplication(addition(X1,X2),strong_iteration(X1))),
inference(step,[status(thm)],[t14454,t232]) ).
cnf(t184188,plain,
addition(one,multiplication(addition(X1,X2),strong_iteration(X1))) = multiplication(addition(one,X2),strong_iteration(X1)),
inference(orient,[status(thm)],[t200372]) ).
cnf(t184926,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)],[t65078,t184188]) ).
cnf(t200373,plain,
true = ifeq(true,true,leq(strong_iteration(X1),strong_iteration(addition(X1,X2))),true),
inference(step,[status(thm)],[t184926,t421]) ).
cnf(t200374,plain,
true = leq(strong_iteration(X1),strong_iteration(addition(X1,X2))),
inference(step,[status(thm)],[t200373,t28]) ).
cnf(t185042,plain,
leq(strong_iteration(X1),strong_iteration(addition(X1,X2))) = true,
inference(orient,[status(thm)],[t200374]) ).
cnf(t185120,plain,
true = leq(strong_iteration(X1),strong_iteration(multiplication(addition(one,X2),X1))),
inference(cp,[status(thm)],[t185042,t232]) ).
cnf(t188463,plain,
leq(strong_iteration(X1),strong_iteration(multiplication(addition(one,X2),X1))) = true,
inference(orient,[status(thm)],[t185120]) ).
cnf(t188592,plain,
true = leq(strong_iteration(X1),strong_iteration(multiplication(star(X2),X1))),
inference(cp,[status(thm)],[t188463,t161]) ).
cnf(t188742,plain,
leq(strong_iteration(X1),strong_iteration(multiplication(star(X2),X1))) = true,
inference(orient,[status(thm)],[t188592]) ).
cnf(t188842,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)],[t29,t188742]) ).
cnf(t200442,plain,
strong_iteration(multiplication(star(X1),X2)) = addition(strong_iteration(X2),strong_iteration(multiplication(star(X1),X2))),
inference(step,[status(thm)],[t188842,t28]) ).
cnf(t194124,plain,
addition(strong_iteration(X1),strong_iteration(multiplication(star(X2),X1))) = strong_iteration(multiplication(star(X2),X1)),
inference(orient,[status(thm)],[t200442]) ).
cnf(t194474,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)],[t75900,t194124]) ).
cnf(t200496,plain,
star(strong_iteration(multiplication(star(X2),X1))) = multiplication(star(X1),star(strong_iteration(multiplication(star(X2),X1)))),
inference(step,[status(thm)],[t194474,t194124]) ).
cnf(t104,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true),
inference(cp,[status(thm)],[t101,t26]) ).
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]) ).
cnf(t237,plain,
multiplication(addition(one,multiplication(X1,X2)),X3) = addition(X3,multiplication(X1,multiplication(X2,X3))),
inference(cp,[status(thm)],[t232,t32]) ).
cnf(t46440,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(orient,[status(thm)],[t237]) ).
cnf(t46441,plain,
multiplication(addition(one,multiplication(X1,X2)),X1) = multiplication(X1,addition(one,multiplication(X2,X1))),
inference(cp,[status(thm)],[t46440,t220]) ).
cnf(t50932,plain,
multiplication(addition(one,multiplication(X1,X2)),X1) = multiplication(X1,addition(one,multiplication(X2,X1))),
inference(orient,[status(thm)],[t46441]) ).
cnf(t50937,plain,
multiplication(X1,addition(one,multiplication(star(X1),X1))) = multiplication(star(X1),X1),
inference(cp,[status(thm)],[t50932,t68]) ).
cnf(t199577,plain,
multiplication(X1,star(X1)) = multiplication(star(X1),X1),
inference(step,[status(thm)],[t50937,t74]) ).
cnf(t51111,plain,
multiplication(star(X1),X1) = multiplication(X1,star(X1)),
inference(orient,[status(thm)],[t199577]) ).
cnf(t51125,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(multiplication(X1,star(X1)),X2),
inference(cp,[status(thm)],[t32,t51111]) ).
cnf(t199582,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(X1,multiplication(star(X1),X2)),
inference(step,[status(thm)],[t51125,t32]) ).
cnf(t51178,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(X1,multiplication(star(X1),X2)),
inference(orient,[status(thm)],[t199582]) ).
cnf(t199807,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(X1,multiplication(star(X1),X2)),X2),true),
inference(step,[status(thm)],[t104,t51178]) ).
cnf(t75342,plain,
ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(X1,multiplication(star(X1),X2)),X2),true) = true,
inference(orient,[status(thm)],[t199807]) ).
cnf(t185,plain,
true = leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t182,t59]) ).
cnf(t343,plain,
leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t185]) ).
cnf(t345,plain,
strong_iteration(X1) = ifeq(true,true,addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t29,t343]) ).
cnf(t199089,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t345,t28]) ).
cnf(t199090,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))),
inference(step,[status(thm)],[t199089,t45]) ).
cnf(t199091,plain,
strong_iteration(X1) = multiplication(addition(one,X1),strong_iteration(X1)),
inference(step,[status(thm)],[t199090,t232]) ).
cnf(t1624,plain,
multiplication(addition(one,X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t199091]) ).
cnf(t1654,plain,
strong_iteration(X1) = multiplication(addition(X1,one),strong_iteration(X1)),
inference(cp,[status(thm)],[t1624,t45]) ).
cnf(t1679,plain,
multiplication(addition(X1,one),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t1654]) ).
cnf(t70198,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)],[t70182,t1679]) ).
cnf(t199740,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),true),
inference(step,[status(thm)],[t70198,t78]) ).
cnf(t199741,plain,
true = leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),
inference(step,[status(thm)],[t199740,t28]) ).
cnf(t199742,plain,
true = leq(multiplication(star(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199741,t25]) ).
cnf(t38,plain,
multiplication(addition(multiplication(X1,X2),X3),Y3) = addition(multiplication(X1,multiplication(X2,Y3)),multiplication(X3,Y3)),
inference(cp,[status(thm)],[t37,t32]) ).
cnf(t808,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(Y3,X3)) = multiplication(addition(multiplication(X1,X2),Y3),X3),
inference(orient,[status(thm)],[t38]) ).
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(t825,plain,
multiplication(addition(multiplication(X1,zero),X2),X3) = addition(multiplication(X1,zero),multiplication(X2,X3)),
inference(cp,[status(thm)],[t808,t43]) ).
cnf(t48170,plain,
addition(multiplication(X1,zero),multiplication(X2,X3)) = multiplication(addition(multiplication(X1,zero),X2),X3),
inference(orient,[status(thm)],[t825]) ).
cnf(t48171,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(cp,[status(thm)],[t48170,t37]) ).
cnf(t48480,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t48171]) ).
cnf(t48484,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(multiplication(addition(X1,X2),zero),zero),
inference(cp,[status(thm)],[t48480,t37]) ).
cnf(t199557,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),multiplication(zero,zero)),
inference(step,[status(thm)],[t48484,t32]) ).
cnf(t199558,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(step,[status(thm)],[t199557,t43]) ).
cnf(t48698,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t199558]) ).
cnf(t48726,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)],[t220,t48698]) ).
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(t199559,plain,
multiplication(addition(X1,multiplication(X2,zero)),one) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t48726,t27]) ).
cnf(t199560,plain,
addition(X1,multiplication(X2,zero)) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t199559,t24]) ).
cnf(t199561,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,addition(multiplication(X2,zero),multiplication(addition(X1,X2),zero))),
inference(step,[status(thm)],[t199560,t50]) ).
cnf(t199562,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(multiplication(X2,zero),addition(X1,X2)),zero)),
inference(step,[status(thm)],[t199561,t48170]) ).
cnf(t199563,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,addition(X1,X2)),zero)),
inference(step,[status(thm)],[t199562,t48480]) ).
cnf(t199564,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t199563,t199]) ).
cnf(t48877,plain,
addition(X1,multiplication(addition(X2,X1),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t199564]) ).
cnf(t48927,plain,
addition(addition(X1,X2),multiplication(X2,zero)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(cp,[status(thm)],[t48877,t199]) ).
cnf(t199661,plain,
addition(X1,addition(X2,multiplication(X2,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t48927,t50]) ).
cnf(t199662,plain,
addition(X1,multiplication(X2,addition(one,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t199661,t220]) ).
cnf(t199663,plain,
addition(X1,multiplication(X2,one)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t199662,t27]) ).
cnf(t199664,plain,
addition(X1,X2) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t199663,t24]) ).
cnf(t199665,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(addition(X2,X1),zero))),
inference(step,[status(thm)],[t199664,t50]) ).
cnf(t48975,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X1,X2),zero)),
inference(cp,[status(thm)],[t48877,t45]) ).
cnf(t49181,plain,
addition(X1,multiplication(addition(X1,X2),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t48975]) ).
cnf(t199666,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(X1,zero))),
inference(step,[status(thm)],[t199665,t49181]) ).
cnf(t59655,plain,
addition(X1,addition(X2,multiplication(X1,zero))) = addition(X1,X2),
inference(orient,[status(thm)],[t199666]) ).
cnf(t59766,plain,
true = leq(multiplication(X1,zero),addition(X1,X2)),
inference(cp,[status(thm)],[t354,t59655]) ).
cnf(t59842,plain,
leq(multiplication(X1,zero),addition(X1,X2)) = true,
inference(orient,[status(thm)],[t59766]) ).
cnf(t59850,plain,
true = leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)),
inference(cp,[status(thm)],[t59842,t232]) ).
cnf(t60945,plain,
leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)) = true,
inference(orient,[status(thm)],[t59850]) ).
cnf(t60973,plain,
true = leq(multiplication(X1,zero),multiplication(star(X2),X1)),
inference(cp,[status(thm)],[t60945,t161]) ).
cnf(t61008,plain,
leq(multiplication(X1,zero),multiplication(star(X2),X1)) = true,
inference(orient,[status(thm)],[t60973]) ).
cnf(t61030,plain,
multiplication(star(X1),X2) = ifeq(true,true,addition(multiplication(star(X1),X2),multiplication(X2,zero)),multiplication(star(X1),X2)),
inference(cp,[status(thm)],[t3135,t61008]) ).
cnf(t199677,plain,
multiplication(star(X1),X2) = addition(multiplication(star(X1),X2),multiplication(X2,zero)),
inference(step,[status(thm)],[t61030,t28]) ).
cnf(t40,plain,
multiplication(addition(X1,multiplication(X2,X3)),Y3) = addition(multiplication(X1,Y3),multiplication(X2,multiplication(X3,Y3))),
inference(cp,[status(thm)],[t37,t32]) ).
cnf(t1271,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(Y3,X2))) = multiplication(addition(X1,multiplication(X3,Y3)),X2),
inference(orient,[status(thm)],[t40]) ).
cnf(t1303,plain,
multiplication(addition(X1,multiplication(X2,zero)),X3) = addition(multiplication(X1,X3),multiplication(X2,zero)),
inference(cp,[status(thm)],[t1271,t43]) ).
cnf(t49430,plain,
addition(multiplication(X1,X2),multiplication(X3,zero)) = multiplication(addition(X1,multiplication(X3,zero)),X2),
inference(orient,[status(thm)],[t1303]) ).
cnf(t199678,plain,
multiplication(star(X1),X2) = multiplication(addition(star(X1),multiplication(X2,zero)),X2),
inference(step,[status(thm)],[t199677,t49430]) ).
cnf(t62112,plain,
multiplication(addition(star(X1),multiplication(X2,zero)),X2) = multiplication(star(X1),X2),
inference(orient,[status(thm)],[t199678]) ).
cnf(t17338,plain,
addition(strong_iteration(X1),multiplication(strong_iteration(X1),X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(cp,[status(thm)],[t17332,t33]) ).
cnf(t199430,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(step,[status(thm)],[t17338,t220]) ).
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(t199431,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),X2)),
inference(step,[status(thm)],[t199430,t134]) ).
cnf(t29627,plain,
addition(star(X1),multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(one,X2)),
inference(orient,[status(thm)],[t199431]) ).
cnf(t62113,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(multiplication(strong_iteration(X1),addition(one,zero)),strong_iteration(X1)),
inference(cp,[status(thm)],[t62112,t29627]) ).
cnf(t199679,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(addition(one,zero),strong_iteration(X1))),
inference(step,[status(thm)],[t62113,t32]) ).
cnf(t199680,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(one,strong_iteration(X1))),
inference(step,[status(thm)],[t199679,t27]) ).
cnf(t199681,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t199680,t25]) ).
cnf(t62260,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(orient,[status(thm)],[t199681]) ).
cnf(t199743,plain,
true = leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199742,t62260]) ).
cnf(t70592,plain,
leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t199743]) ).
cnf(t70596,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)],[t3135,t70592]) ).
cnf(t199744,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(strong_iteration(X1),strong_iteration(X1))),
inference(step,[status(thm)],[t70596,t28]) ).
cnf(t199745,plain,
strong_iteration(X1) = multiplication(addition(one,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199744,t232]) ).
cnf(t199746,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),addition(one,strong_iteration(X1))),
inference(step,[status(thm)],[t199745,t267]) ).
cnf(t152,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = addition(one,strong_iteration(X1)),
inference(cp,[status(thm)],[t148,t59]) ).
cnf(t199027,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)],[t199027]) ).
cnf(t199747,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t199746,t166]) ).
cnf(t70599,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t199747]) ).
cnf(t75404,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)],[t75342,t70599]) ).
cnf(t199808,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)],[t75404,t78]) ).
cnf(t199809,plain,
true = leq(multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),strong_iteration(X1))),strong_iteration(X1)),
inference(step,[status(thm)],[t199808,t28]) ).
cnf(t1735,plain,
star(strong_iteration(X1)) = multiplication(strong_iteration(X1),star(strong_iteration(X1))),
inference(cp,[status(thm)],[t1730,t166]) ).
cnf(t1795,plain,
multiplication(strong_iteration(X1),star(strong_iteration(X1))) = star(strong_iteration(X1)),
inference(orient,[status(thm)],[t1735]) ).
cnf(t1800,plain,
multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),X2)) = multiplication(star(strong_iteration(X1)),X2),
inference(cp,[status(thm)],[t32,t1795]) ).
cnf(t55298,plain,
multiplication(strong_iteration(X1),multiplication(star(strong_iteration(X1)),X2)) = multiplication(star(strong_iteration(X1)),X2),
inference(orient,[status(thm)],[t1800]) ).
cnf(t199810,plain,
true = leq(multiplication(star(strong_iteration(X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199809,t55298]) ).
cnf(t664,plain,
star(strong_iteration(X1)) = multiplication(star(strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t659,t166]) ).
cnf(t946,plain,
multiplication(star(strong_iteration(X1)),strong_iteration(X1)) = star(strong_iteration(X1)),
inference(orient,[status(thm)],[t664]) ).
cnf(t199811,plain,
true = leq(star(strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t199810,t946]) ).
cnf(t75534,plain,
leq(star(strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t199811]) ).
cnf(t75539,plain,
strong_iteration(X1) = ifeq(true,true,addition(strong_iteration(X1),star(strong_iteration(X1))),strong_iteration(X1)),
inference(cp,[status(thm)],[t3135,t75534]) ).
cnf(t199812,plain,
strong_iteration(X1) = addition(strong_iteration(X1),star(strong_iteration(X1))),
inference(step,[status(thm)],[t75539,t28]) ).
cnf(t199813,plain,
strong_iteration(X1) = star(strong_iteration(X1)),
inference(step,[status(thm)],[t199812,t687]) ).
cnf(t75544,plain,
star(strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t199813]) ).
cnf(t200497,plain,
strong_iteration(multiplication(star(X2),X1)) = multiplication(star(X1),star(strong_iteration(multiplication(star(X2),X1)))),
inference(step,[status(thm)],[t200496,t75544]) ).
cnf(t200498,plain,
strong_iteration(multiplication(star(X2),X1)) = multiplication(star(X1),strong_iteration(multiplication(star(X2),X1))),
inference(step,[status(thm)],[t200497,t75544]) ).
cnf(t198876,plain,
multiplication(star(X1),strong_iteration(multiplication(star(X2),X1))) = strong_iteration(multiplication(star(X2),X1)),
inference(orient,[status(thm)],[t200498]) ).
fof(f18,conjecture,
! [X0,X1] :
( leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1)))
& leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0,X1] :
( leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1)))
& leq(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] :
( ~ leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1)))
| ~ leq(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,
( ~ leq(multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1))),strong_iteration(multiplication(star(sk0),sk1)))
| ~ leq(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,
( ~ leq(multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1))),strong_iteration(multiplication(star(sk0),sk1)))
| ~ leq(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,
true != false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != ifeq(leq(strong_iteration(multiplication(star(sk0),sk1)),multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1)))),true,ifeq(leq(multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1))),strong_iteration(multiplication(star(sk0),sk1))),true,false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(true,true,ifeq(leq(multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1))),strong_iteration(multiplication(star(sk0),sk1))),true,false,true),true),
inference(rw,[status(thm)],[g0_0,t428]) ).
cnf(g0_2,plain,
true != ifeq(leq(multiplication(star(sk1),strong_iteration(multiplication(star(sk0),sk1))),strong_iteration(multiplication(star(sk0),sk1))),true,false,true),
inference(rw,[status(thm)],[g0_1,t28]) ).
cnf(g0_3,plain,
true != ifeq(leq(strong_iteration(multiplication(star(sk0),sk1)),strong_iteration(multiplication(star(sk0),sk1))),true,false,true),
inference(rw,[status(thm)],[g0_2,t198876]) ).
cnf(g0_4,plain,
true != ifeq(true,true,false,true),
inference(rw,[status(thm)],[g0_3,t78]) ).
cnf(g0_5,plain,
true != false,
inference(rw,[status(thm)],[g0_4,t28]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE147+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 19:06:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 125.20/18.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 125.20/18.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------