%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE143+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:51:42 PM UTC 2026
% Result : Theorem 51.68s 7.80s
% Output : Proof 51.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 18
% Syntax : Number of formulae : 213 ( 195 unt; 0 def)
% Number of atoms : 235 ( 201 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 15 |; 4 &)
% ( 1 <=>; 2 =>; 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 : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 382 ( 22 sgn 92 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f15_nnf,plain,
! [A,B,C] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [C,A,B] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t20,plain,
ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t89,plain,
ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
inference(orient,[status(thm)],[t20]) ).
fof(f17,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f17_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t15,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t79,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t15]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t14,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t50,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
fof(f3_nnf,plain,
! [A] : addition(A,A) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : addition(A,A) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t0,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t26,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t53,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t50,t26]) ).
cnf(t148,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t53]) ).
cnf(t157,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t79,t148]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t70609,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t157,t28]) ).
cnf(t171,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t70609]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f0_nnf,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t8,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t45,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t176,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t171,t45]) ).
cnf(t182,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t176]) ).
cnf(t192,plain,
true = ifeq(true,true,leq(X1,multiplication(strong_iteration(X2),X1)),true),
inference(cp,[status(thm)],[t89,t182]) ).
cnf(t70612,plain,
true = leq(X1,multiplication(strong_iteration(X2),X1)),
inference(step,[status(thm)],[t192,t28]) ).
cnf(t215,plain,
leq(X1,multiplication(strong_iteration(X2),X1)) = true,
inference(orient,[status(thm)],[t70612]) ).
fof(f12,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction1) ).
fof(f12_nnf,plain,
! [A,B,C] :
( leq(multiplication(star(A),B),C)
| ~ leq(addition(multiplication(A,C),B),C) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,C,B] :
( leq(multiplication(star(A),B),C)
| ~ leq(addition(multiplication(A,C),B),C) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t22,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t102,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/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f8_nnf,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t19,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t37,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t19]) ).
cnf(t104,plain,
true = ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true),
inference(cp,[status(thm)],[t102,t37]) ).
cnf(t70182,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t104]) ).
cnf(c17,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t16,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t29,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t16]) ).
fof(f14,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f14_nnf,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t10,plain,
addition(multiplication(X1,strong_iteration(X1)),one) = strong_iteration(X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t70599,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(step,[status(thm)],[t10,t45]) ).
cnf(t59,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(orient,[status(thm)],[t70599]) ).
cnf(t185,plain,
true = leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t182,t59]) ).
cnf(t344,plain,
leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t185]) ).
cnf(t346,plain,
strong_iteration(X1) = ifeq(true,true,addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t29,t344]) ).
cnf(t70669,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t346,t28]) ).
cnf(t70670,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))),
inference(step,[status(thm)],[t70669,t45]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f6_nnf,plain,
! [A] : multiplication(one,A) = A,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : multiplication(one,A) = A,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t6,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t25,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t39,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t37,t25]) ).
cnf(t233,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t39]) ).
cnf(t70671,plain,
strong_iteration(X1) = multiplication(addition(one,X1),strong_iteration(X1)),
inference(step,[status(thm)],[t70670,t233]) ).
cnf(t1624,plain,
multiplication(addition(one,X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t70671]) ).
cnf(t1654,plain,
strong_iteration(X1) = multiplication(addition(X1,one),strong_iteration(X1)),
inference(cp,[status(thm)],[t1624,t45]) ).
cnf(t1679,plain,
multiplication(addition(X1,one),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t1654]) ).
cnf(t70198,plain,
true = ifeq(leq(strong_iteration(X1),strong_iteration(X1)),true,leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),true),
inference(cp,[status(thm)],[t70182,t1679]) ).
cnf(hi18,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(hi3,axiom,
addition(X0,X0) = X0,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t3,plain,
leq(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi3]) ).
cnf(t78,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t71320,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),true),
inference(step,[status(thm)],[t70198,t78]) ).
cnf(t71321,plain,
true = leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),
inference(step,[status(thm)],[t71320,t28]) ).
cnf(t71322,plain,
true = leq(multiplication(star(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t71321,t25]) ).
cnf(t49,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t29,t45]) ).
cnf(t3135,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t49]) ).
cnf(t187,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t182,t50]) ).
cnf(t355,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t187]) ).
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f7_nnf,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t18,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t33,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t5,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t24,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t34,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t33,t24]) ).
cnf(t221,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t34]) ).
fof(f4,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f4_nnf,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t17,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t32,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
cnf(t38,plain,
multiplication(addition(multiplication(X1,X2),X3),Y3) = addition(multiplication(X1,multiplication(X2,Y3)),multiplication(X3,Y3)),
inference(cp,[status(thm)],[t37,t32]) ).
cnf(t808,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(Y3,X3)) = multiplication(addition(multiplication(X1,X2),Y3),X3),
inference(orient,[status(thm)],[t38]) ).
fof(f9,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f9_nnf,plain,
! [A] : multiplication(zero,A) = zero,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : multiplication(zero,A) = zero,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t7,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t43,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t7]) ).
cnf(t825,plain,
multiplication(addition(multiplication(X1,zero),X2),X3) = addition(multiplication(X1,zero),multiplication(X2,X3)),
inference(cp,[status(thm)],[t808,t43]) ).
cnf(t48170,plain,
addition(multiplication(X1,zero),multiplication(X2,X3)) = multiplication(addition(multiplication(X1,zero),X2),X3),
inference(orient,[status(thm)],[t825]) ).
cnf(t48171,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(cp,[status(thm)],[t48170,t37]) ).
cnf(t48480,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t48171]) ).
cnf(t48484,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(multiplication(addition(X1,X2),zero),zero),
inference(cp,[status(thm)],[t48480,t37]) ).
cnf(t71137,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),multiplication(zero,zero)),
inference(step,[status(thm)],[t48484,t32]) ).
cnf(t71138,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(step,[status(thm)],[t71137,t43]) ).
cnf(t48698,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t71138]) ).
cnf(t48726,plain,
multiplication(addition(X1,multiplication(X2,zero)),addition(one,zero)) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(cp,[status(thm)],[t221,t48698]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f2_nnf,plain,
! [A] : addition(A,zero) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : addition(A,zero) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t1,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t27,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t71139,plain,
multiplication(addition(X1,multiplication(X2,zero)),one) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t48726,t27]) ).
cnf(t71140,plain,
addition(X1,multiplication(X2,zero)) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t71139,t24]) ).
cnf(t71141,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,addition(multiplication(X2,zero),multiplication(addition(X1,X2),zero))),
inference(step,[status(thm)],[t71140,t50]) ).
cnf(t71142,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(multiplication(X2,zero),addition(X1,X2)),zero)),
inference(step,[status(thm)],[t71141,t48170]) ).
cnf(t71143,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,addition(X1,X2)),zero)),
inference(step,[status(thm)],[t71142,t48480]) ).
cnf(t155,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t148,t45]) ).
cnf(t199,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t155]) ).
cnf(t71144,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t71143,t199]) ).
cnf(t48877,plain,
addition(X1,multiplication(addition(X2,X1),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t71144]) ).
cnf(t48927,plain,
addition(addition(X1,X2),multiplication(X2,zero)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(cp,[status(thm)],[t48877,t199]) ).
cnf(t71241,plain,
addition(X1,addition(X2,multiplication(X2,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t48927,t50]) ).
cnf(t71242,plain,
addition(X1,multiplication(X2,addition(one,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t71241,t221]) ).
cnf(t71243,plain,
addition(X1,multiplication(X2,one)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t71242,t27]) ).
cnf(t71244,plain,
addition(X1,X2) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t71243,t24]) ).
cnf(t71245,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(addition(X2,X1),zero))),
inference(step,[status(thm)],[t71244,t50]) ).
cnf(t48975,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X1,X2),zero)),
inference(cp,[status(thm)],[t48877,t45]) ).
cnf(t49181,plain,
addition(X1,multiplication(addition(X1,X2),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t48975]) ).
cnf(t71246,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(X1,zero))),
inference(step,[status(thm)],[t71245,t49181]) ).
cnf(t59655,plain,
addition(X1,addition(X2,multiplication(X1,zero))) = addition(X1,X2),
inference(orient,[status(thm)],[t71246]) ).
cnf(t59766,plain,
true = leq(multiplication(X1,zero),addition(X1,X2)),
inference(cp,[status(thm)],[t355,t59655]) ).
cnf(t59842,plain,
leq(multiplication(X1,zero),addition(X1,X2)) = true,
inference(orient,[status(thm)],[t59766]) ).
cnf(t59850,plain,
true = leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)),
inference(cp,[status(thm)],[t59842,t233]) ).
cnf(t60945,plain,
leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)) = true,
inference(orient,[status(thm)],[t59850]) ).
fof(f11,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
fof(f11_nnf,plain,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t74,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t151,plain,
addition(one,multiplication(star(X1),X1)) = addition(one,star(X1)),
inference(cp,[status(thm)],[t148,t74]) ).
cnf(t70605,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t151,t74]) ).
cnf(t161,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t70605]) ).
cnf(t60973,plain,
true = leq(multiplication(X1,zero),multiplication(star(X2),X1)),
inference(cp,[status(thm)],[t60945,t161]) ).
cnf(t61008,plain,
leq(multiplication(X1,zero),multiplication(star(X2),X1)) = true,
inference(orient,[status(thm)],[t60973]) ).
cnf(t61030,plain,
multiplication(star(X1),X2) = ifeq(true,true,addition(multiplication(star(X1),X2),multiplication(X2,zero)),multiplication(star(X1),X2)),
inference(cp,[status(thm)],[t3135,t61008]) ).
cnf(t71257,plain,
multiplication(star(X1),X2) = addition(multiplication(star(X1),X2),multiplication(X2,zero)),
inference(step,[status(thm)],[t61030,t28]) ).
cnf(t40,plain,
multiplication(addition(X1,multiplication(X2,X3)),Y3) = addition(multiplication(X1,Y3),multiplication(X2,multiplication(X3,Y3))),
inference(cp,[status(thm)],[t37,t32]) ).
cnf(t1271,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(Y3,X2))) = multiplication(addition(X1,multiplication(X3,Y3)),X2),
inference(orient,[status(thm)],[t40]) ).
cnf(t1303,plain,
multiplication(addition(X1,multiplication(X2,zero)),X3) = addition(multiplication(X1,X3),multiplication(X2,zero)),
inference(cp,[status(thm)],[t1271,t43]) ).
cnf(t49430,plain,
addition(multiplication(X1,X2),multiplication(X3,zero)) = multiplication(addition(X1,multiplication(X3,zero)),X2),
inference(orient,[status(thm)],[t1303]) ).
cnf(t71258,plain,
multiplication(star(X1),X2) = multiplication(addition(star(X1),multiplication(X2,zero)),X2),
inference(step,[status(thm)],[t71257,t49430]) ).
cnf(t62112,plain,
multiplication(addition(star(X1),multiplication(X2,zero)),X2) = multiplication(star(X1),X2),
inference(orient,[status(thm)],[t71258]) ).
fof(f16,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
fof(f16_nnf,plain,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t13,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t65,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t67,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(cp,[status(thm)],[t50,t65]) ).
cnf(t17332,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(orient,[status(thm)],[t67]) ).
cnf(t17338,plain,
addition(strong_iteration(X1),multiplication(strong_iteration(X1),X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(cp,[status(thm)],[t17332,t33]) ).
cnf(t71010,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(step,[status(thm)],[t17338,t221]) ).
cnf(t46,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t45,t27]) ).
cnf(t134,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t46]) ).
cnf(t71011,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),X2)),
inference(step,[status(thm)],[t71010,t134]) ).
cnf(t29627,plain,
addition(star(X1),multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(one,X2)),
inference(orient,[status(thm)],[t71011]) ).
cnf(t62113,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(multiplication(strong_iteration(X1),addition(one,zero)),strong_iteration(X1)),
inference(cp,[status(thm)],[t62112,t29627]) ).
cnf(t71259,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(addition(one,zero),strong_iteration(X1))),
inference(step,[status(thm)],[t62113,t32]) ).
cnf(t71260,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(one,strong_iteration(X1))),
inference(step,[status(thm)],[t71259,t27]) ).
cnf(t71261,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t71260,t25]) ).
cnf(t62260,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(orient,[status(thm)],[t71261]) ).
cnf(t71323,plain,
true = leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t71322,t62260]) ).
cnf(t70592,plain,
leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t71323]) ).
fof(f18,conjecture,
! [X0] :
( leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0)))
& leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0)))
& leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0] :
( ~ leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0)))
| ~ leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( ~ leq(strong_iteration(sk0),multiplication(strong_iteration(sk0),strong_iteration(sk0)))
| ~ leq(multiplication(strong_iteration(sk0),strong_iteration(sk0)),strong_iteration(sk0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c19,plain,
( ~ leq(strong_iteration(sk0),multiplication(strong_iteration(sk0),strong_iteration(sk0)))
| ~ leq(multiplication(strong_iteration(sk0),strong_iteration(sk0)),strong_iteration(sk0)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != ifeq(leq(multiplication(strong_iteration(sk0),strong_iteration(sk0)),strong_iteration(sk0)),true,ifeq(leq(strong_iteration(sk0),multiplication(strong_iteration(sk0),strong_iteration(sk0))),true,false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(leq(multiplication(strong_iteration(sk0),strong_iteration(sk0)),strong_iteration(sk0)),true,ifeq(true,true,false,true),true),
inference(rw,[status(thm)],[g0_0,t215]) ).
cnf(g0_2,plain,
true != ifeq(leq(multiplication(strong_iteration(sk0),strong_iteration(sk0)),strong_iteration(sk0)),true,false,true),
inference(rw,[status(thm)],[g0_1,t28]) ).
cnf(g0_3,plain,
true != ifeq(true,true,false,true),
inference(rw,[status(thm)],[g0_2,t70592]) ).
cnf(g0_4,plain,
true != false,
inference(rw,[status(thm)],[g0_3,t28]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE143+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 19:09:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 51.68/7.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.68/7.80 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------