%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE041+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 01:51:28 PM UTC 2026
% Result : Theorem 62.33s 8.39s
% Output : Proof 62.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 12
% Syntax : Number of formulae : 186 ( 173 unt; 0 def)
% Number of atoms : 203 ( 173 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 15 ~; 9 |; 4 &)
% ( 1 <=>; 3 =>; 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 : 269 ( 48 sgn 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/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(t14,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t89,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t14]) ).
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(t13,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t36,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/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(t25,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t39,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t36,t25]) ).
cnf(t144,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t39]) ).
cnf(t151,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t89,t144]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t20236,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t151,t29]) ).
cnf(t159,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t20236]) ).
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',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(t21,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t57,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t21]) ).
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(t7,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t27,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t59,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t57,t27]) ).
cnf(t215,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t59]) ).
cnf(t223,plain,
true = leq(X1,multiplication(X1,addition(one,X2))),
inference(cp,[status(thm)],[t159,t215]) ).
cnf(t359,plain,
leq(X1,multiplication(X1,addition(one,X2))) = true,
inference(orient,[status(thm)],[t223]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
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/sandbox/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(t19,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(hyper_resolution,[status(thm)],[hi11,hi13]) ).
cnf(t20224,plain,
addition(one,addition(multiplication(X1,star(X1)),star(X1))) = star(X1),
inference(step,[status(thm)],[t19,t36]) ).
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(t11,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t33,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t20225,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(step,[status(thm)],[t20224,t33]) ).
cnf(t43,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(orient,[status(thm)],[t20225]) ).
cnf(t146,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = addition(one,star(X1)),
inference(cp,[status(thm)],[t144,t43]) ).
cnf(t20234,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t146,t43]) ).
cnf(t154,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t20234]) ).
cnf(t361,plain,
true = leq(X1,multiplication(X1,star(X2))),
inference(cp,[status(thm)],[t359,t154]) ).
cnf(t366,plain,
leq(X1,multiplication(X1,star(X2))) = true,
inference(orient,[status(thm)],[t361]) ).
cnf(t15,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t30,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t35,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t30,t33]) ).
cnf(t308,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t35]) ).
fof(f14,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox/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(t24,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(t101,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(orient,[status(thm)],[t24]) ).
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',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(t22,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t51,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t22]) ).
cnf(t102,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,t51]) ).
cnf(t19830,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t102]) ).
cnf(t160,plain,
true = leq(multiplication(X1,X2),multiplication(addition(X1,X3),X2)),
inference(cp,[status(thm)],[t159,t51]) ).
cnf(t3208,plain,
leq(multiplication(X1,X2),multiplication(addition(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t160]) ).
cnf(t163,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t159,t33]) ).
cnf(t166,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t163]) ).
cnf(t171,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t166,t36]) ).
cnf(t255,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t171]) ).
cnf(t258,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t255,t33]) ).
cnf(t20241,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t258,t36]) ).
cnf(t372,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t20241]) ).
fof(f16,conjecture,
! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1] :
( ~ leq(star(X0),star(X1))
& leq(X0,X1) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( ~ leq(star(sk0),star(sk1))
& leq(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f16_nnf]) ).
cnf(c17,plain,
leq(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi17,negated_conjecture,
leq(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t2,plain,
addition(sk0,sk1) = sk1,
inference(hyper_resolution,[status(thm)],[hi11,hi17]) ).
cnf(t20228,plain,
addition(sk1,sk0) = sk1,
inference(step,[status(thm)],[t2,t33]) ).
cnf(t63,plain,
addition(sk1,sk0) = sk1,
inference(orient,[status(thm)],[t20228]) ).
cnf(t65,plain,
addition(sk1,addition(sk0,X1)) = addition(sk1,X1),
inference(cp,[status(thm)],[t36,t63]) ).
cnf(t176,plain,
addition(sk1,addition(sk0,X1)) = addition(sk1,X1),
inference(orient,[status(thm)],[t65]) ).
cnf(t177,plain,
addition(sk1,X1) = addition(sk1,addition(X1,sk0)),
inference(cp,[status(thm)],[t176,t33]) ).
cnf(t194,plain,
addition(sk1,addition(X1,sk0)) = addition(sk1,X1),
inference(orient,[status(thm)],[t177]) ).
cnf(t256,plain,
true = leq(sk0,addition(sk1,X1)),
inference(cp,[status(thm)],[t255,t194]) ).
cnf(t273,plain,
leq(sk0,addition(sk1,X1)) = true,
inference(orient,[status(thm)],[t256]) ).
cnf(t275,plain,
true = leq(sk0,multiplication(sk1,addition(one,X1))),
inference(cp,[status(thm)],[t273,t215]) ).
cnf(t409,plain,
leq(sk0,multiplication(sk1,addition(one,X1))) = true,
inference(orient,[status(thm)],[t275]) ).
cnf(t410,plain,
true = leq(sk0,multiplication(sk1,star(X1))),
inference(cp,[status(thm)],[t409,t154]) ).
cnf(t415,plain,
leq(sk0,multiplication(sk1,star(X1))) = true,
inference(orient,[status(thm)],[t410]) ).
cnf(t416,plain,
multiplication(sk1,star(X1)) = ifeq(true,true,addition(sk0,multiplication(sk1,star(X1))),multiplication(sk1,star(X1))),
inference(cp,[status(thm)],[t30,t415]) ).
cnf(t20246,plain,
multiplication(sk1,star(X1)) = addition(sk0,multiplication(sk1,star(X1))),
inference(step,[status(thm)],[t416,t29]) ).
cnf(t510,plain,
addition(sk0,multiplication(sk1,star(X1))) = multiplication(sk1,star(X1)),
inference(orient,[status(thm)],[t20246]) ).
cnf(t515,plain,
true = leq(sk0,addition(X1,multiplication(sk1,star(X2)))),
inference(cp,[status(thm)],[t372,t510]) ).
cnf(t633,plain,
leq(sk0,addition(X1,multiplication(sk1,star(X2)))) = true,
inference(orient,[status(thm)],[t515]) ).
cnf(t635,plain,
true = leq(sk0,multiplication(addition(X1,sk1),star(X2))),
inference(cp,[status(thm)],[t633,t51]) ).
cnf(t811,plain,
leq(sk0,multiplication(addition(X1,sk1),star(X2))) = true,
inference(orient,[status(thm)],[t635]) ).
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(t9,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t28,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t53,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t51,t28]) ).
cnf(t201,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t53]) ).
cnf(t20237,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(step,[status(thm)],[t43,t201]) ).
cnf(t214,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[t20237]) ).
cnf(t847,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(orient,[status(thm)],[t214]) ).
cnf(t856,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)],[t30,t847]) ).
cnf(t380,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t372,t154]) ).
cnf(t386,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t380]) ).
cnf(t388,plain,
true = leq(one,addition(star(X1),X2)),
inference(cp,[status(thm)],[t386,t33]) ).
cnf(t392,plain,
leq(one,addition(star(X1),X2)) = true,
inference(orient,[status(thm)],[t388]) ).
cnf(t393,plain,
true = leq(one,multiplication(addition(one,X1),star(X2))),
inference(cp,[status(thm)],[t392,t201]) ).
cnf(t533,plain,
leq(one,multiplication(addition(one,X1),star(X2))) = true,
inference(orient,[status(thm)],[t393]) ).
cnf(t20250,plain,
multiplication(addition(one,X1),star(X1)) = ifeq(true,true,star(X1),multiplication(addition(one,X1),star(X1))),
inference(step,[status(thm)],[t856,t533]) ).
cnf(t20251,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(step,[status(thm)],[t20250,t29]) ).
cnf(t871,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t20251]) ).
cnf(t886,plain,
true = leq(sk0,star(sk1)),
inference(cp,[status(thm)],[t811,t871]) ).
cnf(t891,plain,
leq(sk0,star(sk1)) = true,
inference(orient,[status(thm)],[t886]) ).
cnf(t892,plain,
star(sk1) = ifeq(true,true,addition(sk0,star(sk1)),star(sk1)),
inference(cp,[status(thm)],[t30,t891]) ).
cnf(t20256,plain,
star(sk1) = addition(sk0,star(sk1)),
inference(step,[status(thm)],[t892,t29]) ).
cnf(t924,plain,
addition(sk0,star(sk1)) = star(sk1),
inference(orient,[status(thm)],[t20256]) ).
cnf(t3245,plain,
true = leq(multiplication(sk0,X1),multiplication(star(sk1),X1)),
inference(cp,[status(thm)],[t3208,t924]) ).
cnf(t3282,plain,
leq(multiplication(sk0,X1),multiplication(star(sk1),X1)) = true,
inference(orient,[status(thm)],[t3245]) ).
cnf(t877,plain,
star(X1) = multiplication(addition(X1,one),star(X1)),
inference(cp,[status(thm)],[t871,t33]) ).
cnf(t1032,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(orient,[status(thm)],[t877]) ).
cnf(t19838,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t19830,t1032]) ).
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(t4,plain,
leq(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi3]) ).
cnf(t77,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t20402,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(step,[status(thm)],[t19838,t77]) ).
cnf(t20403,plain,
true = leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),
inference(step,[status(thm)],[t20402,t29]) ).
cnf(t20404,plain,
true = leq(multiplication(star(X1),star(X1)),star(X1)),
inference(step,[status(thm)],[t20403,t28]) ).
cnf(t19996,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t20404]) ).
cnf(t19999,plain,
star(X1) = ifeq(true,true,addition(star(X1),multiplication(star(X1),star(X1))),star(X1)),
inference(cp,[status(thm)],[t308,t19996]) ).
cnf(t20405,plain,
star(X1) = addition(star(X1),multiplication(star(X1),star(X1))),
inference(step,[status(thm)],[t19999,t29]) ).
cnf(t20406,plain,
star(X1) = multiplication(addition(one,star(X1)),star(X1)),
inference(step,[status(thm)],[t20405,t201]) ).
cnf(t216,plain,
multiplication(X1,addition(one,X1)) = multiplication(addition(one,X1),X1),
inference(cp,[status(thm)],[t215,t201]) ).
cnf(t229,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(orient,[status(thm)],[t216]) ).
cnf(t20407,plain,
star(X1) = multiplication(star(X1),addition(one,star(X1))),
inference(step,[status(thm)],[t20406,t229]) ).
cnf(t20408,plain,
star(X1) = multiplication(star(X1),star(X1)),
inference(step,[status(thm)],[t20407,t154]) ).
cnf(t20003,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t20408]) ).
cnf(t20031,plain,
true = leq(multiplication(sk0,star(sk1)),star(sk1)),
inference(cp,[status(thm)],[t3282,t20003]) ).
cnf(t20082,plain,
leq(multiplication(sk0,star(sk1)),star(sk1)) = true,
inference(orient,[status(thm)],[t20031]) ).
cnf(t20085,plain,
star(sk1) = ifeq(true,true,addition(star(sk1),multiplication(sk0,star(sk1))),star(sk1)),
inference(cp,[status(thm)],[t308,t20082]) ).
cnf(t20413,plain,
star(sk1) = addition(star(sk1),multiplication(sk0,star(sk1))),
inference(step,[status(thm)],[t20085,t29]) ).
cnf(t20414,plain,
star(sk1) = multiplication(addition(one,sk0),star(sk1)),
inference(step,[status(thm)],[t20413,t201]) ).
cnf(t20415,plain,
star(sk1) = multiplication(addition(sk0,one),star(sk1)),
inference(step,[status(thm)],[t20414,t33]) ).
cnf(t20088,plain,
multiplication(addition(sk0,one),star(sk1)) = star(sk1),
inference(orient,[status(thm)],[t20415]) ).
cnf(t20121,plain,
true = ifeq(leq(star(sk1),star(sk1)),true,leq(multiplication(star(sk0),multiplication(one,star(sk1))),star(sk1)),true),
inference(cp,[status(thm)],[t19830,t20088]) ).
cnf(t20416,plain,
true = ifeq(true,true,leq(multiplication(star(sk0),multiplication(one,star(sk1))),star(sk1)),true),
inference(step,[status(thm)],[t20121,t77]) ).
cnf(t20417,plain,
true = leq(multiplication(star(sk0),multiplication(one,star(sk1))),star(sk1)),
inference(step,[status(thm)],[t20416,t29]) ).
cnf(t20418,plain,
true = leq(multiplication(star(sk0),star(sk1)),star(sk1)),
inference(step,[status(thm)],[t20417,t28]) ).
cnf(t20158,plain,
leq(multiplication(star(sk0),star(sk1)),star(sk1)) = true,
inference(orient,[status(thm)],[t20418]) ).
cnf(t20161,plain,
star(sk1) = ifeq(true,true,addition(star(sk1),multiplication(star(sk0),star(sk1))),star(sk1)),
inference(cp,[status(thm)],[t308,t20158]) ).
cnf(t20419,plain,
star(sk1) = addition(star(sk1),multiplication(star(sk0),star(sk1))),
inference(step,[status(thm)],[t20161,t29]) ).
cnf(t20420,plain,
star(sk1) = multiplication(addition(one,star(sk0)),star(sk1)),
inference(step,[status(thm)],[t20419,t201]) ).
cnf(t20421,plain,
star(sk1) = multiplication(star(sk0),star(sk1)),
inference(step,[status(thm)],[t20420,t154]) ).
cnf(t20165,plain,
multiplication(star(sk0),star(sk1)) = star(sk1),
inference(orient,[status(thm)],[t20421]) ).
cnf(t20199,plain,
true = leq(star(sk0),star(sk1)),
inference(cp,[status(thm)],[t366,t20165]) ).
cnf(t20219,plain,
leq(star(sk0),star(sk1)) = true,
inference(orient,[status(thm)],[t20199]) ).
cnf(c18,plain,
~ leq(star(sk0),star(sk1)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
leq(star(sk0),star(sk1)) != true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t20219]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE041+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 18:47:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 62.33/8.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.33/8.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------