%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE044+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 : n015.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 208.37s 31.95s
% Output : Proof 208.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 14
% Syntax : Number of formulae : 266 ( 257 unt; 0 def)
% Number of atoms : 279 ( 255 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 9 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 434 ( 40 sgn 74 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(t31,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t9]) ).
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(t13,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t28,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t13]) ).
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(t92,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(orient,[status(thm)],[t22]) ).
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(t49,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t20]) ).
cnf(t93,plain,
true = ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true),
inference(cp,[status(thm)],[t92,t49]) ).
cnf(t20391,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t93]) ).
cnf(t33,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t28,t31]) ).
cnf(t322,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t33]) ).
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]) ).
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(t34,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t716804,plain,
addition(one,addition(multiplication(X1,star(X1)),star(X1))) = star(X1),
inference(step,[status(thm)],[t17,t34]) ).
cnf(t716805,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(step,[status(thm)],[t716804,t31]) ).
cnf(t41,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(orient,[status(thm)],[t716805]) ).
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(t26,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t51,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t49,t26]) ).
cnf(t179,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t51]) ).
cnf(t716816,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(step,[status(thm)],[t41,t179]) ).
cnf(t191,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[t716816]) ).
cnf(t473,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(orient,[status(thm)],[t191]) ).
cnf(t480,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)],[t28,t473]) ).
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(t82,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t12]) ).
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(t23,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t37,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t34,t23]) ).
cnf(t135,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t37]) ).
cnf(t142,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t82,t135]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t716815,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t142,t27]) ).
cnf(t150,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t716815]) ).
cnf(t154,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t150,t31]) ).
cnf(t157,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t154]) ).
cnf(t162,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t157,t34]) ).
cnf(t229,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t162]) ).
cnf(t231,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t229,t31]) ).
cnf(t716818,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t231,t34]) ).
cnf(t277,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t716818]) ).
cnf(t137,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = addition(one,star(X1)),
inference(cp,[status(thm)],[t135,t41]) ).
cnf(t716813,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t137,t41]) ).
cnf(t145,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t716813]) ).
cnf(t283,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t277,t145]) ).
cnf(t289,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t283]) ).
cnf(t291,plain,
true = leq(one,addition(star(X1),X2)),
inference(cp,[status(thm)],[t289,t31]) ).
cnf(t294,plain,
leq(one,addition(star(X1),X2)) = true,
inference(orient,[status(thm)],[t291]) ).
cnf(t295,plain,
true = leq(one,multiplication(addition(one,X1),star(X2))),
inference(cp,[status(thm)],[t294,t179]) ).
cnf(t382,plain,
leq(one,multiplication(addition(one,X1),star(X2))) = true,
inference(orient,[status(thm)],[t295]) ).
cnf(t716825,plain,
multiplication(addition(one,X1),star(X1)) = ifeq(true,true,star(X1),multiplication(addition(one,X1),star(X1))),
inference(step,[status(thm)],[t480,t382]) ).
cnf(t716826,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(step,[status(thm)],[t716825,t27]) ).
cnf(t494,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t716826]) ).
cnf(t500,plain,
star(X1) = multiplication(addition(X1,one),star(X1)),
inference(cp,[status(thm)],[t494,t31]) ).
cnf(t581,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(orient,[status(thm)],[t500]) ).
cnf(t20399,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t20391,t581]) ).
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(t72,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t716909,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(step,[status(thm)],[t20399,t72]) ).
cnf(t716910,plain,
true = leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),
inference(step,[status(thm)],[t716909,t27]) ).
cnf(t716911,plain,
true = leq(multiplication(star(X1),star(X1)),star(X1)),
inference(step,[status(thm)],[t716910,t26]) ).
cnf(t20514,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t716911]) ).
cnf(t20517,plain,
star(X1) = ifeq(true,true,addition(star(X1),multiplication(star(X1),star(X1))),star(X1)),
inference(cp,[status(thm)],[t322,t20514]) ).
cnf(t716912,plain,
star(X1) = addition(star(X1),multiplication(star(X1),star(X1))),
inference(step,[status(thm)],[t20517,t27]) ).
cnf(t716913,plain,
star(X1) = multiplication(addition(one,star(X1)),star(X1)),
inference(step,[status(thm)],[t716912,t179]) ).
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(t55,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(t25,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t57,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t55,t25]) ).
cnf(t192,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t57]) ).
cnf(t193,plain,
multiplication(X1,addition(one,X1)) = multiplication(addition(one,X1),X1),
inference(cp,[status(thm)],[t192,t179]) ).
cnf(t205,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(orient,[status(thm)],[t193]) ).
cnf(t716914,plain,
star(X1) = multiplication(star(X1),addition(one,star(X1))),
inference(step,[status(thm)],[t716913,t205]) ).
cnf(t716915,plain,
star(X1) = multiplication(star(X1),star(X1)),
inference(step,[status(thm)],[t716914,t145]) ).
cnf(t20521,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t716915]) ).
cnf(t20525,plain,
multiplication(addition(star(X1),X2),star(X1)) = addition(star(X1),multiplication(X2,star(X1))),
inference(cp,[status(thm)],[t49,t20521]) ).
cnf(t716921,plain,
multiplication(addition(star(X1),X2),star(X1)) = multiplication(addition(one,X2),star(X1)),
inference(step,[status(thm)],[t20525,t179]) ).
cnf(t20742,plain,
multiplication(addition(star(X1),X2),star(X1)) = multiplication(addition(one,X2),star(X1)),
inference(orient,[status(thm)],[t716921]) ).
cnf(t140,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t135,t31]) ).
cnf(t167,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t140]) ).
cnf(t20752,plain,
multiplication(addition(one,addition(X1,star(X2))),star(X2)) = multiplication(addition(star(X2),X1),star(X2)),
inference(cp,[status(thm)],[t20742,t167]) ).
cnf(t292,plain,
addition(X1,star(X2)) = ifeq(true,true,addition(one,addition(X1,star(X2))),addition(X1,star(X2))),
inference(cp,[status(thm)],[t28,t289]) ).
cnf(t716819,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t292,t27]) ).
cnf(t343,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t716819]) ).
cnf(t716924,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(star(X2),X1),star(X2)),
inference(step,[status(thm)],[t20752,t343]) ).
cnf(t716925,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(one,X1),star(X2)),
inference(step,[status(thm)],[t716924,t20742]) ).
cnf(t20964,plain,
multiplication(addition(X1,star(X2)),star(X2)) = multiplication(addition(one,X1),star(X2)),
inference(orient,[status(thm)],[t716925]) ).
cnf(t501,plain,
multiplication(addition(one,X1),addition(one,star(X1))) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t192,t494]) ).
cnf(t716827,plain,
multiplication(addition(one,X1),star(X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t501,t145]) ).
cnf(t716828,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t716827,t494]) ).
cnf(t716829,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t716828,t34]) ).
cnf(t716830,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t716829,t343]) ).
cnf(t511,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t716830]) ).
cnf(t512,plain,
star(addition(X1,X2)) = addition(X1,addition(X2,star(addition(X1,X2)))),
inference(cp,[status(thm)],[t511,t34]) ).
cnf(t5848,plain,
addition(X1,addition(X2,star(addition(X1,X2)))) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t512]) ).
cnf(t5870,plain,
star(addition(X1,addition(X1,X2))) = addition(X1,addition(addition(X1,X2),star(addition(X1,X2)))),
inference(cp,[status(thm)],[t5848,t135]) ).
cnf(t716874,plain,
star(addition(X1,X2)) = addition(X1,addition(addition(X1,X2),star(addition(X1,X2)))),
inference(step,[status(thm)],[t5870,t135]) ).
cnf(t716875,plain,
star(addition(X1,X2)) = addition(X1,addition(X1,addition(X2,star(addition(X1,X2))))),
inference(step,[status(thm)],[t716874,t34]) ).
cnf(t716876,plain,
star(addition(X1,X2)) = addition(X1,star(addition(X1,X2))),
inference(step,[status(thm)],[t716875,t5848]) ).
cnf(t6145,plain,
addition(X1,star(addition(X1,X2))) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t716876]) ).
cnf(t20970,plain,
multiplication(addition(one,X1),star(addition(X1,X2))) = multiplication(star(addition(X1,X2)),star(addition(X1,X2))),
inference(cp,[status(thm)],[t20964,t6145]) ).
cnf(t716928,plain,
multiplication(addition(one,X1),star(addition(X1,X2))) = star(addition(X1,X2)),
inference(step,[status(thm)],[t20970,t20521]) ).
cnf(t21338,plain,
multiplication(addition(one,X1),star(addition(X1,X2))) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t716928]) ).
cnf(t21366,plain,
star(addition(X1,X2)) = multiplication(addition(X1,one),star(addition(X1,X2))),
inference(cp,[status(thm)],[t21338,t31]) ).
cnf(t21797,plain,
multiplication(addition(X1,one),star(addition(X1,X2))) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t21366]) ).
cnf(t21863,plain,
true = ifeq(leq(star(addition(X1,X2)),star(addition(X1,X2))),true,leq(multiplication(star(X1),multiplication(one,star(addition(X1,X2)))),star(addition(X1,X2))),true),
inference(cp,[status(thm)],[t20391,t21797]) ).
cnf(t718435,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,star(addition(X1,X2)))),star(addition(X1,X2))),true),
inference(step,[status(thm)],[t21863,t72]) ).
cnf(t718436,plain,
true = leq(multiplication(star(X1),multiplication(one,star(addition(X1,X2)))),star(addition(X1,X2))),
inference(step,[status(thm)],[t718435,t27]) ).
cnf(t718437,plain,
true = leq(multiplication(star(X1),star(addition(X1,X2))),star(addition(X1,X2))),
inference(step,[status(thm)],[t718436,t26]) ).
cnf(t715450,plain,
leq(multiplication(star(X1),star(addition(X1,X2))),star(addition(X1,X2))) = true,
inference(orient,[status(thm)],[t718437]) ).
cnf(t20523,plain,
multiplication(star(X1),addition(star(X1),X2)) = addition(star(X1),multiplication(star(X1),X2)),
inference(cp,[status(thm)],[t55,t20521]) ).
cnf(t716920,plain,
multiplication(star(X1),addition(star(X1),X2)) = multiplication(star(X1),addition(one,X2)),
inference(step,[status(thm)],[t20523,t192]) ).
cnf(t20626,plain,
multiplication(star(X1),addition(star(X1),X2)) = multiplication(star(X1),addition(one,X2)),
inference(orient,[status(thm)],[t716920]) ).
cnf(t20638,plain,
multiplication(star(X1),addition(one,addition(X2,star(X1)))) = multiplication(star(X1),addition(star(X1),X2)),
inference(cp,[status(thm)],[t20626,t167]) ).
cnf(t716922,plain,
multiplication(star(X1),addition(X2,star(X1))) = multiplication(star(X1),addition(star(X1),X2)),
inference(step,[status(thm)],[t20638,t343]) ).
cnf(t716923,plain,
multiplication(star(X1),addition(X2,star(X1))) = multiplication(star(X1),addition(one,X2)),
inference(step,[status(thm)],[t716922,t20626]) ).
cnf(t20853,plain,
multiplication(star(X1),addition(X2,star(X1))) = multiplication(star(X1),addition(one,X2)),
inference(orient,[status(thm)],[t716923]) ).
cnf(t5963,plain,
true = leq(X1,star(addition(X2,X1))),
inference(cp,[status(thm)],[t277,t5848]) ).
cnf(t6043,plain,
leq(X1,star(addition(X2,X1))) = true,
inference(orient,[status(thm)],[t5963]) ).
cnf(t6060,plain,
star(addition(X1,X2)) = ifeq(true,true,addition(X2,star(addition(X1,X2))),star(addition(X1,X2))),
inference(cp,[status(thm)],[t28,t6043]) ).
cnf(t716877,plain,
star(addition(X1,X2)) = addition(X2,star(addition(X1,X2))),
inference(step,[status(thm)],[t6060,t27]) ).
cnf(t6244,plain,
addition(X1,star(addition(X2,X1))) = star(addition(X2,X1)),
inference(orient,[status(thm)],[t716877]) ).
cnf(t20860,plain,
multiplication(star(addition(X1,X2)),addition(one,X2)) = multiplication(star(addition(X1,X2)),star(addition(X1,X2))),
inference(cp,[status(thm)],[t20853,t6244]) ).
cnf(t716927,plain,
multiplication(star(addition(X1,X2)),addition(one,X2)) = star(addition(X1,X2)),
inference(step,[status(thm)],[t20860,t20521]) ).
cnf(t21207,plain,
multiplication(star(addition(X1,X2)),addition(one,X2)) = star(addition(X1,X2)),
inference(orient,[status(thm)],[t716927]) ).
cnf(t199,plain,
true = leq(X1,multiplication(X1,addition(one,X2))),
inference(cp,[status(thm)],[t150,t192]) ).
cnf(t266,plain,
leq(X1,multiplication(X1,addition(one,X2))) = true,
inference(orient,[status(thm)],[t199]) ).
cnf(t268,plain,
true = leq(X1,multiplication(X1,star(X2))),
inference(cp,[status(thm)],[t266,t145]) ).
cnf(t272,plain,
leq(X1,multiplication(X1,star(X2))) = true,
inference(orient,[status(thm)],[t268]) ).
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(t61,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t274,plain,
true = leq(multiplication(X1,X2),multiplication(X1,multiplication(X2,star(X3)))),
inference(cp,[status(thm)],[t272,t61]) ).
cnf(t11268,plain,
leq(multiplication(X1,X2),multiplication(X1,multiplication(X2,star(X3)))) = true,
inference(orient,[status(thm)],[t274]) ).
cnf(t11303,plain,
true = leq(multiplication(X1,addition(X2,one)),multiplication(X1,star(X2))),
inference(cp,[status(thm)],[t11268,t581]) ).
cnf(t26541,plain,
leq(multiplication(X1,addition(X2,one)),multiplication(X1,star(X2))) = true,
inference(orient,[status(thm)],[t11303]) ).
cnf(t95,plain,
true = ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true),
inference(cp,[status(thm)],[t92,t23]) ).
cnf(t26053,plain,
ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true) = true,
inference(orient,[status(thm)],[t95]) ).
cnf(t26091,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(addition(one,X1)),multiplication(addition(one,X1),star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t26053,t494]) ).
cnf(t716955,plain,
true = ifeq(true,true,leq(multiplication(star(addition(one,X1)),multiplication(addition(one,X1),star(X1))),star(X1)),true),
inference(step,[status(thm)],[t26091,t72]) ).
cnf(t716956,plain,
true = leq(multiplication(star(addition(one,X1)),multiplication(addition(one,X1),star(X1))),star(X1)),
inference(step,[status(thm)],[t716955,t27]) ).
cnf(t716957,plain,
true = leq(multiplication(star(addition(one,X1)),star(X1)),star(X1)),
inference(step,[status(thm)],[t716956,t494]) ).
cnf(t30373,plain,
leq(multiplication(star(addition(one,X1)),star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t716957]) ).
cnf(t30386,plain,
star(X1) = ifeq(true,true,addition(star(X1),multiplication(star(addition(one,X1)),star(X1))),star(X1)),
inference(cp,[status(thm)],[t322,t30373]) ).
cnf(t716958,plain,
star(X1) = addition(star(X1),multiplication(star(addition(one,X1)),star(X1))),
inference(step,[status(thm)],[t30386,t27]) ).
cnf(t716959,plain,
star(X1) = multiplication(addition(one,star(addition(one,X1))),star(X1)),
inference(step,[status(thm)],[t716958,t179]) ).
cnf(t716960,plain,
star(X1) = multiplication(star(addition(one,X1)),star(X1)),
inference(step,[status(thm)],[t716959,t145]) ).
cnf(t30389,plain,
multiplication(star(addition(one,X1)),star(X1)) = star(X1),
inference(orient,[status(thm)],[t716960]) ).
cnf(t30407,plain,
true = leq(multiplication(star(addition(one,X1)),addition(X1,one)),star(X1)),
inference(cp,[status(thm)],[t26541,t30389]) ).
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(t716806,plain,
addition(one,addition(multiplication(star(X1),X1),star(X1))) = star(X1),
inference(step,[status(thm)],[t18,t34]) ).
cnf(t716807,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(step,[status(thm)],[t716806,t31]) ).
cnf(t45,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(orient,[status(thm)],[t716807]) ).
cnf(t716817,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(step,[status(thm)],[t45,t192]) ).
cnf(t204,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(rw,[status(thm)],[t716817]) ).
cnf(t1174,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(orient,[status(thm)],[t204]) ).
cnf(t1190,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)],[t28,t1174]) ).
cnf(t296,plain,
true = leq(one,multiplication(star(X1),addition(one,X2))),
inference(cp,[status(thm)],[t294,t192]) ).
cnf(t399,plain,
leq(one,multiplication(star(X1),addition(one,X2))) = true,
inference(orient,[status(thm)],[t296]) ).
cnf(t716840,plain,
multiplication(star(X1),addition(one,X1)) = ifeq(true,true,star(X1),multiplication(star(X1),addition(one,X1))),
inference(step,[status(thm)],[t1190,t399]) ).
cnf(t716841,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(step,[status(thm)],[t716840,t27]) ).
cnf(t1217,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t716841]) ).
cnf(t1227,plain,
star(addition(one,X1)) = multiplication(star(addition(one,X1)),addition(one,X1)),
inference(cp,[status(thm)],[t1217,t135]) ).
cnf(t9009,plain,
multiplication(star(addition(one,X1)),addition(one,X1)) = star(addition(one,X1)),
inference(orient,[status(thm)],[t1227]) ).
cnf(t9023,plain,
star(addition(one,X1)) = multiplication(star(addition(one,X1)),addition(X1,one)),
inference(cp,[status(thm)],[t9009,t31]) ).
cnf(t9607,plain,
multiplication(star(addition(one,X1)),addition(X1,one)) = star(addition(one,X1)),
inference(orient,[status(thm)],[t9023]) ).
cnf(t716961,plain,
true = leq(star(addition(one,X1)),star(X1)),
inference(step,[status(thm)],[t30407,t9607]) ).
cnf(t30466,plain,
leq(star(addition(one,X1)),star(X1)) = true,
inference(orient,[status(thm)],[t716961]) ).
cnf(t30471,plain,
true = leq(star(addition(X1,one)),star(X1)),
inference(cp,[status(thm)],[t30466,t31]) ).
cnf(t30480,plain,
leq(star(addition(X1,one)),star(X1)) = true,
inference(orient,[status(thm)],[t30471]) ).
cnf(t30483,plain,
star(X1) = ifeq(true,true,addition(star(addition(X1,one)),star(X1)),star(X1)),
inference(cp,[status(thm)],[t28,t30480]) ).
cnf(t716965,plain,
star(X1) = addition(star(addition(X1,one)),star(X1)),
inference(step,[status(thm)],[t30483,t27]) ).
cnf(t716966,plain,
star(X1) = addition(star(X1),star(addition(X1,one))),
inference(step,[status(thm)],[t716965,t31]) ).
cnf(t30700,plain,
addition(star(X1),star(addition(X1,one))) = star(X1),
inference(orient,[status(thm)],[t716966]) ).
cnf(t30730,plain,
star(addition(star(X1),star(addition(X1,one)))) = multiplication(star(star(X1)),addition(one,star(addition(X1,one)))),
inference(cp,[status(thm)],[t21207,t30700]) ).
cnf(t716971,plain,
star(star(X1)) = multiplication(star(star(X1)),addition(one,star(addition(X1,one)))),
inference(step,[status(thm)],[t30730,t30700]) ).
cnf(t26078,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)],[t26053,t20521]) ).
cnf(t716932,plain,
true = ifeq(true,true,leq(multiplication(star(star(X1)),multiplication(star(X1),star(X1))),star(X1)),true),
inference(step,[status(thm)],[t26078,t72]) ).
cnf(t716933,plain,
true = leq(multiplication(star(star(X1)),multiplication(star(X1),star(X1))),star(X1)),
inference(step,[status(thm)],[t716932,t27]) ).
cnf(t1218,plain,
star(star(X1)) = multiplication(star(star(X1)),star(X1)),
inference(cp,[status(thm)],[t1217,t145]) ).
cnf(t1251,plain,
multiplication(star(star(X1)),star(X1)) = star(star(X1)),
inference(orient,[status(thm)],[t1218]) ).
cnf(t1252,plain,
multiplication(star(star(X1)),multiplication(star(X1),X2)) = multiplication(star(star(X1)),X2),
inference(cp,[status(thm)],[t61,t1251]) ).
cnf(t10842,plain,
multiplication(star(star(X1)),multiplication(star(X1),X2)) = multiplication(star(star(X1)),X2),
inference(orient,[status(thm)],[t1252]) ).
cnf(t716934,plain,
true = leq(multiplication(star(star(X1)),star(X1)),star(X1)),
inference(step,[status(thm)],[t716933,t10842]) ).
cnf(t716935,plain,
true = leq(star(star(X1)),star(X1)),
inference(step,[status(thm)],[t716934,t1251]) ).
cnf(t26155,plain,
leq(star(star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t716935]) ).
cnf(t26158,plain,
star(X1) = ifeq(true,true,addition(star(X1),star(star(X1))),star(X1)),
inference(cp,[status(thm)],[t322,t26155]) ).
cnf(t716936,plain,
star(X1) = addition(star(X1),star(star(X1))),
inference(step,[status(thm)],[t26158,t27]) ).
cnf(t716937,plain,
star(X1) = star(star(X1)),
inference(step,[status(thm)],[t716936,t511]) ).
cnf(t26162,plain,
star(star(X1)) = star(X1),
inference(orient,[status(thm)],[t716937]) ).
cnf(t716972,plain,
star(X1) = multiplication(star(star(X1)),addition(one,star(addition(X1,one)))),
inference(step,[status(thm)],[t716971,t26162]) ).
cnf(t716973,plain,
star(X1) = multiplication(star(X1),addition(one,star(addition(X1,one)))),
inference(step,[status(thm)],[t716972,t26162]) ).
cnf(t716974,plain,
star(X1) = multiplication(star(X1),star(addition(X1,one))),
inference(step,[status(thm)],[t716973,t145]) ).
cnf(t30915,plain,
multiplication(star(X1),star(addition(X1,one))) = star(X1),
inference(orient,[status(thm)],[t716974]) ).
cnf(t715451,plain,
true = leq(star(X1),star(addition(X1,one))),
inference(cp,[status(thm)],[t715450,t30915]) ).
cnf(t715825,plain,
leq(star(X1),star(addition(X1,one))) = true,
inference(orient,[status(thm)],[t715451]) ).
cnf(t715832,plain,
star(addition(X1,one)) = ifeq(true,true,addition(star(X1),star(addition(X1,one))),star(addition(X1,one))),
inference(cp,[status(thm)],[t28,t715825]) ).
cnf(t718438,plain,
star(addition(X1,one)) = addition(star(X1),star(addition(X1,one))),
inference(step,[status(thm)],[t715832,t27]) ).
cnf(t718439,plain,
star(addition(X1,one)) = star(X1),
inference(step,[status(thm)],[t718438,t30700]) ).
cnf(t715839,plain,
star(addition(X1,one)) = star(X1),
inference(orient,[status(thm)],[t718439]) ).
fof(f16,conjecture,
! [X0] : star(addition(one,X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0] : star(addition(one,X0)) = star(X0),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0] : star(addition(one,X0)) != star(X0),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
star(addition(one,sk0)) != star(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f16_nnf]) ).
cnf(c17,plain,
star(addition(one,sk0)) != star(sk0),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
star(addition(one,sk0)) != star(sk0),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
star(addition(sk0,one)) != star(sk0),
inference(rw,[status(thm)],[goal_0,t31]) ).
cnf(g0_1,plain,
star(sk0) != star(sk0),
inference(rw,[status(thm)],[g0_0,t715839]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE044+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n015.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 18:49:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 208.37/31.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 208.37/31.95 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------