%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE039+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:51:27 PM UTC 2026
% Result : Theorem 99.22s 13.40s
% Output : Proof 99.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 14
% Syntax : Number of formulae : 191 ( 177 unt; 0 def)
% Number of atoms : 209 ( 175 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 27 ~; 12 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 300 ( 34 sgn 74 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t83,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t12]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t11,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t35,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f3_nnf,plain,
! [A] : addition(A,A) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : addition(A,A) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t0,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t24,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t38,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t35,t24]) ).
cnf(t137,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t38]) ).
cnf(t144,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t83,t137]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t26067,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t144,t28]) ).
cnf(t152,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t26067]) ).
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
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(t19,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t56,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t19]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t5,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t26,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t58,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t56,t26]) ).
cnf(t194,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t58]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t29,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(hi11,axiom,
ifeq(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
fof(f12,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f12_nnf,plain,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi13,axiom,
leq(addition(one,multiplication(X0,star(X0))),star(X0)) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t17,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(hyper_resolution,[status(thm)],[hi11,hi13]) ).
cnf(t26056,plain,
addition(one,addition(multiplication(X1,star(X1)),star(X1))) = star(X1),
inference(step,[status(thm)],[t17,t35]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f0_nnf,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t9,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t32,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t26057,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(step,[status(thm)],[t26056,t32]) ).
cnf(t42,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(orient,[status(thm)],[t26057]) ).
fof(f8,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
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(t20,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t50,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t20]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f6_nnf,plain,
! [A] : multiplication(one,A) = A,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : multiplication(one,A) = A,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t7,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t27,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t52,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t50,t27]) ).
cnf(t181,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t52]) ).
cnf(t26068,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(step,[status(thm)],[t42,t181]) ).
cnf(t193,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[t26068]) ).
cnf(t475,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(orient,[status(thm)],[t193]) ).
cnf(t482,plain,
multiplication(addition(one,X1),star(X1)) = ifeq(leq(one,multiplication(addition(one,X1),star(X1))),true,star(X1),multiplication(addition(one,X1),star(X1))),
inference(cp,[status(thm)],[t29,t475]) ).
cnf(t156,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t152,t32]) ).
cnf(t159,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t156]) ).
cnf(t164,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t159,t35]) ).
cnf(t231,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t164]) ).
cnf(t233,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t231,t32]) ).
cnf(t26070,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t233,t35]) ).
cnf(t279,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t26070]) ).
cnf(t139,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = addition(one,star(X1)),
inference(cp,[status(thm)],[t137,t42]) ).
cnf(t26065,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t139,t42]) ).
cnf(t147,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t26065]) ).
cnf(t285,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t279,t147]) ).
cnf(t291,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t285]) ).
cnf(t293,plain,
true = leq(one,addition(star(X1),X2)),
inference(cp,[status(thm)],[t291,t32]) ).
cnf(t296,plain,
leq(one,addition(star(X1),X2)) = true,
inference(orient,[status(thm)],[t293]) ).
cnf(t297,plain,
true = leq(one,multiplication(addition(one,X1),star(X2))),
inference(cp,[status(thm)],[t296,t181]) ).
cnf(t384,plain,
leq(one,multiplication(addition(one,X1),star(X2))) = true,
inference(orient,[status(thm)],[t297]) ).
cnf(t26075,plain,
multiplication(addition(one,X1),star(X1)) = ifeq(true,true,star(X1),multiplication(addition(one,X1),star(X1))),
inference(step,[status(thm)],[t482,t384]) ).
cnf(t26076,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(step,[status(thm)],[t26075,t28]) ).
cnf(t496,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t26076]) ).
cnf(t503,plain,
multiplication(addition(one,X1),addition(one,star(X1))) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t194,t496]) ).
cnf(t26077,plain,
multiplication(addition(one,X1),star(X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t503,t147]) ).
cnf(t26078,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t26077,t496]) ).
cnf(t26079,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t26078,t35]) ).
cnf(t294,plain,
addition(X1,star(X2)) = ifeq(true,true,addition(one,addition(X1,star(X2))),addition(X1,star(X2))),
inference(cp,[status(thm)],[t29,t291]) ).
cnf(t26071,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t294,t28]) ).
cnf(t345,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t26071]) ).
cnf(t26080,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t26079,t345]) ).
cnf(t513,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t26080]) ).
cnf(t520,plain,
true = leq(X1,star(X1)),
inference(cp,[status(thm)],[t152,t513]) ).
cnf(t529,plain,
leq(X1,star(X1)) = true,
inference(orient,[status(thm)],[t520]) ).
fof(f14,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
fof(f14_nnf,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(esa)],[f14_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)],[c15]) ).
cnf(t93,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t96,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true),
inference(cp,[status(thm)],[t93,t24]) ).
cnf(t25946,plain,
ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true) = true,
inference(orient,[status(thm)],[t96]) ).
cnf(t34,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t29,t32]) ).
cnf(t314,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t34]) ).
cnf(t94,plain,
true = ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true),
inference(cp,[status(thm)],[t93,t50]) ).
cnf(t20335,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t94]) ).
cnf(t502,plain,
star(X1) = multiplication(addition(X1,one),star(X1)),
inference(cp,[status(thm)],[t496,t32]) ).
cnf(t584,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(orient,[status(thm)],[t502]) ).
cnf(t20343,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t20335,t584]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
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)],[hi12,hi3]) ).
cnf(t73,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t26161,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(step,[status(thm)],[t20343,t73]) ).
cnf(t26162,plain,
true = leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),
inference(step,[status(thm)],[t26161,t28]) ).
cnf(t26163,plain,
true = leq(multiplication(star(X1),star(X1)),star(X1)),
inference(step,[status(thm)],[t26162,t27]) ).
cnf(t20458,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t26163]) ).
cnf(t20461,plain,
star(X1) = ifeq(true,true,addition(star(X1),multiplication(star(X1),star(X1))),star(X1)),
inference(cp,[status(thm)],[t314,t20458]) ).
cnf(t26164,plain,
star(X1) = addition(star(X1),multiplication(star(X1),star(X1))),
inference(step,[status(thm)],[t20461,t28]) ).
cnf(t26165,plain,
star(X1) = multiplication(addition(one,star(X1)),star(X1)),
inference(step,[status(thm)],[t26164,t181]) ).
cnf(t195,plain,
multiplication(X1,addition(one,X1)) = multiplication(addition(one,X1),X1),
inference(cp,[status(thm)],[t194,t181]) ).
cnf(t207,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(orient,[status(thm)],[t195]) ).
cnf(t26166,plain,
star(X1) = multiplication(star(X1),addition(one,star(X1))),
inference(step,[status(thm)],[t26165,t207]) ).
cnf(t26167,plain,
star(X1) = multiplication(star(X1),star(X1)),
inference(step,[status(thm)],[t26166,t147]) ).
cnf(t20465,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t26167]) ).
cnf(t25971,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(star(X1)),multiplication(star(X1),star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t25946,t20465]) ).
cnf(t26183,plain,
true = ifeq(true,true,leq(multiplication(star(star(X1)),multiplication(star(X1),star(X1))),star(X1)),true),
inference(step,[status(thm)],[t25971,t73]) ).
cnf(t26184,plain,
true = leq(multiplication(star(star(X1)),multiplication(star(X1),star(X1))),star(X1)),
inference(step,[status(thm)],[t26183,t28]) ).
fof(f4,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f4_nnf,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t16,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t62,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f13_nnf,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi14,axiom,
leq(addition(one,multiplication(star(X0),X0)),star(X0)) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t18,plain,
addition(addition(one,multiplication(star(X1),X1)),star(X1)) = star(X1),
inference(hyper_resolution,[status(thm)],[hi11,hi14]) ).
cnf(t26058,plain,
addition(one,addition(multiplication(star(X1),X1),star(X1))) = star(X1),
inference(step,[status(thm)],[t18,t35]) ).
cnf(t26059,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(step,[status(thm)],[t26058,t32]) ).
cnf(t46,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(orient,[status(thm)],[t26059]) ).
cnf(t26069,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(step,[status(thm)],[t46,t194]) ).
cnf(t206,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(rw,[status(thm)],[t26069]) ).
cnf(t1177,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(orient,[status(thm)],[t206]) ).
cnf(t1193,plain,
multiplication(star(X1),addition(one,X1)) = ifeq(leq(one,multiplication(star(X1),addition(one,X1))),true,star(X1),multiplication(star(X1),addition(one,X1))),
inference(cp,[status(thm)],[t29,t1177]) ).
cnf(t298,plain,
true = leq(one,multiplication(star(X1),addition(one,X2))),
inference(cp,[status(thm)],[t296,t194]) ).
cnf(t401,plain,
leq(one,multiplication(star(X1),addition(one,X2))) = true,
inference(orient,[status(thm)],[t298]) ).
cnf(t26092,plain,
multiplication(star(X1),addition(one,X1)) = ifeq(true,true,star(X1),multiplication(star(X1),addition(one,X1))),
inference(step,[status(thm)],[t1193,t401]) ).
cnf(t26093,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(step,[status(thm)],[t26092,t28]) ).
cnf(t1220,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t26093]) ).
cnf(t1221,plain,
star(star(X1)) = multiplication(star(star(X1)),star(X1)),
inference(cp,[status(thm)],[t1220,t147]) ).
cnf(t1254,plain,
multiplication(star(star(X1)),star(X1)) = star(star(X1)),
inference(orient,[status(thm)],[t1221]) ).
cnf(t1255,plain,
multiplication(star(star(X1)),multiplication(star(X1),X2)) = multiplication(star(star(X1)),X2),
inference(cp,[status(thm)],[t62,t1254]) ).
cnf(t10845,plain,
multiplication(star(star(X1)),multiplication(star(X1),X2)) = multiplication(star(star(X1)),X2),
inference(orient,[status(thm)],[t1255]) ).
cnf(t26185,plain,
true = leq(multiplication(star(star(X1)),star(X1)),star(X1)),
inference(step,[status(thm)],[t26184,t10845]) ).
cnf(t26186,plain,
true = leq(star(star(X1)),star(X1)),
inference(step,[status(thm)],[t26185,t1254]) ).
cnf(t26048,plain,
leq(star(star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t26186]) ).
cnf(t149,plain,
true = ifeq(star(X1),star(X1),leq(one,star(X1)),true),
inference(cp,[status(thm)],[t83,t147]) ).
cnf(t26066,plain,
true = leq(one,star(X1)),
inference(step,[status(thm)],[t149,t28]) ).
cnf(t151,plain,
leq(one,star(X1)) = true,
inference(orient,[status(thm)],[t26066]) ).
fof(f16,conjecture,
! [X0] :
( leq(star(X0),star(star(X0)))
& leq(star(star(X0)),star(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0] :
( leq(star(X0),star(star(X0)))
& leq(star(star(X0)),star(X0)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0] :
( ~ leq(star(X0),star(star(X0)))
| ~ leq(star(star(X0)),star(X0)) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( ~ leq(star(sk0),star(star(sk0)))
| ~ leq(star(star(sk0)),star(sk0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f16_nnf]) ).
cnf(c17,plain,
( ~ leq(star(sk0),star(star(sk0)))
| ~ leq(star(star(sk0)),star(sk0)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
true != ifeq(leq(star(star(sk0)),star(sk0)),true,ifeq(leq(star(sk0),star(star(sk0))),true,false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(leq(star(star(sk0)),star(sk0)),leq(one,star(one)),ifeq(leq(star(sk0),star(star(sk0))),true,false,true),true),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
true != ifeq(leq(star(star(sk0)),star(sk0)),leq(one,star(one)),ifeq(true,true,false,true),true),
inference(rw,[status(thm)],[g0_1,t529]) ).
cnf(g0_3,plain,
true != ifeq(leq(star(star(sk0)),star(sk0)),leq(one,star(one)),false,true),
inference(rw,[status(thm)],[g0_2,t28]) ).
cnf(g0_4,plain,
true != ifeq(leq(star(star(sk0)),star(sk0)),leq(one,star(one)),false,ifeq(leq(star(star(sk0)),star(sk0)),true,false,true)),
inference(rw,[status(thm)],[g0_3]) ).
cnf(g0_5,plain,
true != ifeq(leq(star(star(sk0)),star(sk0)),leq(one,star(one)),false,ifeq(true,true,false,true)),
inference(rw,[status(thm)],[g0_4,t26048]) ).
cnf(g0_6,plain,
true != ifeq(leq(star(star(sk0)),star(sk0)),leq(one,star(one)),false,false),
inference(rw,[status(thm)],[g0_5,t28]) ).
cnf(g0_7,plain,
true != ifeq(leq(star(star(sk0)),star(sk0)),true,false,false),
inference(rw,[status(thm)],[g0_6,t151]) ).
cnf(g0_8,plain,
true != ifeq(true,true,false,false),
inference(rw,[status(thm)],[g0_7,t26048]) ).
cnf(g0_9,plain,
true != false,
inference(rw,[status(thm)],[g0_8,t28]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE039+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 18:46:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 99.22/13.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 99.22/13.40 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------