%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE039+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 01:51:27 PM UTC 2026
% Result : Theorem 16.75s 2.56s
% Output : Proof 16.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 14
% Syntax : Number of formulae : 181 ( 172 unt; 0 def)
% Number of atoms : 194 ( 170 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 9 |; 2 &)
% ( 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 : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 299 ( 32 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(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t11,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t26,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t11]) ).
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(t7,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t29,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t31,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t26,t29]) ).
cnf(t320,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t31]) ).
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(t20,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(t90,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(orient,[status(thm)],[t20]) ).
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(t21,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t93,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true),
inference(cp,[status(thm)],[t90,t21]) ).
cnf(t26051,plain,
ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true) = true,
inference(orient,[status(thm)],[t93]) ).
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(t18,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t47,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t18]) ).
cnf(t91,plain,
true = ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true),
inference(cp,[status(thm)],[t90,t47]) ).
cnf(t20389,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t91]) ).
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(t15,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(hyper_resolution,[status(thm)],[hi11,hi13]) ).
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(t9,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t32,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t26182,plain,
addition(one,addition(multiplication(X1,star(X1)),star(X1))) = star(X1),
inference(step,[status(thm)],[t15,t32]) ).
cnf(t26183,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(step,[status(thm)],[t26182,t29]) ).
cnf(t39,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(orient,[status(thm)],[t26183]) ).
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(t5,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t24,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t49,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t47,t24]) ).
cnf(t177,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t49]) ).
cnf(t26194,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(step,[status(thm)],[t39,t177]) ).
cnf(t189,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[t26194]) ).
cnf(t471,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(orient,[status(thm)],[t189]) ).
cnf(t478,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)],[t26,t471]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t10,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t80,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t35,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t32,t21]) ).
cnf(t133,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t35]) ).
cnf(t140,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t80,t133]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t25,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t26193,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t140,t25]) ).
cnf(t148,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t26193]) ).
cnf(t152,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t148,t29]) ).
cnf(t155,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t152]) ).
cnf(t160,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t155,t32]) ).
cnf(t227,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t160]) ).
cnf(t229,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t227,t29]) ).
cnf(t26196,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t229,t32]) ).
cnf(t275,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t26196]) ).
cnf(t135,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = addition(one,star(X1)),
inference(cp,[status(thm)],[t133,t39]) ).
cnf(t26191,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t135,t39]) ).
cnf(t143,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t26191]) ).
cnf(t281,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t275,t143]) ).
cnf(t287,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t281]) ).
cnf(t289,plain,
true = leq(one,addition(star(X1),X2)),
inference(cp,[status(thm)],[t287,t29]) ).
cnf(t292,plain,
leq(one,addition(star(X1),X2)) = true,
inference(orient,[status(thm)],[t289]) ).
cnf(t293,plain,
true = leq(one,multiplication(addition(one,X1),star(X2))),
inference(cp,[status(thm)],[t292,t177]) ).
cnf(t380,plain,
leq(one,multiplication(addition(one,X1),star(X2))) = true,
inference(orient,[status(thm)],[t293]) ).
cnf(t26203,plain,
multiplication(addition(one,X1),star(X1)) = ifeq(true,true,star(X1),multiplication(addition(one,X1),star(X1))),
inference(step,[status(thm)],[t478,t380]) ).
cnf(t26204,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(step,[status(thm)],[t26203,t25]) ).
cnf(t492,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t26204]) ).
cnf(t498,plain,
star(X1) = multiplication(addition(X1,one),star(X1)),
inference(cp,[status(thm)],[t492,t29]) ).
cnf(t579,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(orient,[status(thm)],[t498]) ).
cnf(t20397,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t20389,t579]) ).
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(t2,plain,
leq(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi3]) ).
cnf(t70,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t26287,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(step,[status(thm)],[t20397,t70]) ).
cnf(t26288,plain,
true = leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),
inference(step,[status(thm)],[t26287,t25]) ).
cnf(t26289,plain,
true = leq(multiplication(star(X1),star(X1)),star(X1)),
inference(step,[status(thm)],[t26288,t24]) ).
cnf(t20512,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t26289]) ).
cnf(t20515,plain,
star(X1) = ifeq(true,true,addition(star(X1),multiplication(star(X1),star(X1))),star(X1)),
inference(cp,[status(thm)],[t320,t20512]) ).
cnf(t26290,plain,
star(X1) = addition(star(X1),multiplication(star(X1),star(X1))),
inference(step,[status(thm)],[t20515,t25]) ).
cnf(t26291,plain,
star(X1) = multiplication(addition(one,star(X1)),star(X1)),
inference(step,[status(thm)],[t26290,t177]) ).
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(t17,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t53,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t3,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t23,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t55,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t53,t23]) ).
cnf(t190,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t55]) ).
cnf(t191,plain,
multiplication(X1,addition(one,X1)) = multiplication(addition(one,X1),X1),
inference(cp,[status(thm)],[t190,t177]) ).
cnf(t203,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(orient,[status(thm)],[t191]) ).
cnf(t26292,plain,
star(X1) = multiplication(star(X1),addition(one,star(X1))),
inference(step,[status(thm)],[t26291,t203]) ).
cnf(t26293,plain,
star(X1) = multiplication(star(X1),star(X1)),
inference(step,[status(thm)],[t26292,t143]) ).
cnf(t20519,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t26293]) ).
cnf(t26076,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)],[t26051,t20519]) ).
cnf(t26310,plain,
true = ifeq(true,true,leq(multiplication(star(star(X1)),multiplication(star(X1),star(X1))),star(X1)),true),
inference(step,[status(thm)],[t26076,t70]) ).
cnf(t26311,plain,
true = leq(multiplication(star(star(X1)),multiplication(star(X1),star(X1))),star(X1)),
inference(step,[status(thm)],[t26310,t25]) ).
fof(f4,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f4_nnf,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t14,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t59,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
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(t16,plain,
addition(addition(one,multiplication(star(X1),X1)),star(X1)) = star(X1),
inference(hyper_resolution,[status(thm)],[hi11,hi14]) ).
cnf(t26184,plain,
addition(one,addition(multiplication(star(X1),X1),star(X1))) = star(X1),
inference(step,[status(thm)],[t16,t32]) ).
cnf(t26185,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(step,[status(thm)],[t26184,t29]) ).
cnf(t43,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(orient,[status(thm)],[t26185]) ).
cnf(t26195,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(step,[status(thm)],[t43,t190]) ).
cnf(t202,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(rw,[status(thm)],[t26195]) ).
cnf(t1172,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(orient,[status(thm)],[t202]) ).
cnf(t1188,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)],[t26,t1172]) ).
cnf(t294,plain,
true = leq(one,multiplication(star(X1),addition(one,X2))),
inference(cp,[status(thm)],[t292,t190]) ).
cnf(t397,plain,
leq(one,multiplication(star(X1),addition(one,X2))) = true,
inference(orient,[status(thm)],[t294]) ).
cnf(t26218,plain,
multiplication(star(X1),addition(one,X1)) = ifeq(true,true,star(X1),multiplication(star(X1),addition(one,X1))),
inference(step,[status(thm)],[t1188,t397]) ).
cnf(t26219,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(step,[status(thm)],[t26218,t25]) ).
cnf(t1215,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t26219]) ).
cnf(t1216,plain,
star(star(X1)) = multiplication(star(star(X1)),star(X1)),
inference(cp,[status(thm)],[t1215,t143]) ).
cnf(t1249,plain,
multiplication(star(star(X1)),star(X1)) = star(star(X1)),
inference(orient,[status(thm)],[t1216]) ).
cnf(t1250,plain,
multiplication(star(star(X1)),multiplication(star(X1),X2)) = multiplication(star(star(X1)),X2),
inference(cp,[status(thm)],[t59,t1249]) ).
cnf(t10840,plain,
multiplication(star(star(X1)),multiplication(star(X1),X2)) = multiplication(star(star(X1)),X2),
inference(orient,[status(thm)],[t1250]) ).
cnf(t26312,plain,
true = leq(multiplication(star(star(X1)),star(X1)),star(X1)),
inference(step,[status(thm)],[t26311,t10840]) ).
cnf(t26313,plain,
true = leq(star(star(X1)),star(X1)),
inference(step,[status(thm)],[t26312,t1249]) ).
cnf(t26153,plain,
leq(star(star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t26313]) ).
cnf(t26156,plain,
star(X1) = ifeq(true,true,addition(star(X1),star(star(X1))),star(X1)),
inference(cp,[status(thm)],[t320,t26153]) ).
cnf(t26314,plain,
star(X1) = addition(star(X1),star(star(X1))),
inference(step,[status(thm)],[t26156,t25]) ).
cnf(t499,plain,
multiplication(addition(one,X1),addition(one,star(X1))) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t190,t492]) ).
cnf(t26205,plain,
multiplication(addition(one,X1),star(X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t499,t143]) ).
cnf(t26206,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t26205,t492]) ).
cnf(t26207,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t26206,t32]) ).
cnf(t290,plain,
addition(X1,star(X2)) = ifeq(true,true,addition(one,addition(X1,star(X2))),addition(X1,star(X2))),
inference(cp,[status(thm)],[t26,t287]) ).
cnf(t26197,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t290,t25]) ).
cnf(t341,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t26197]) ).
cnf(t26208,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t26207,t341]) ).
cnf(t509,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t26208]) ).
cnf(t26315,plain,
star(X1) = star(star(X1)),
inference(step,[status(thm)],[t26314,t509]) ).
cnf(t26160,plain,
star(star(X1)) = star(X1),
inference(orient,[status(thm)],[t26315]) ).
fof(f16,conjecture,
! [X0] : star(star(X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0] : star(star(X0)) = star(X0),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0] : star(star(X0)) != star(X0),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
star(star(sk0)) != star(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f16_nnf]) ).
cnf(c17,plain,
star(star(sk0)) != star(sk0),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
star(star(sk0)) != star(sk0),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
star(sk0) != star(sk0),
inference(rw,[status(thm)],[goal_0,t26160]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE039+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 18:44:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.75/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.75/2.56 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------