%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE143+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 : n014.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 56.54s 7.64s
% Output : Proof 56.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 17
% Syntax : Number of formulae : 211 ( 202 unt; 0 def)
% Number of atoms : 224 ( 208 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 9 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 369 ( 19 sgn 83 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t28,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t16]) ).
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(t44,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t48,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t28,t44]) ).
cnf(t3139,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t48]) ).
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(t100,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(t36,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t19]) ).
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)],[t100,t36]) ).
cnf(t70188,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(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(t78,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(t49,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(t25,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t52,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t49,t25]) ).
cnf(t146,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t52]) ).
cnf(t155,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t78,t146]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t70665,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t155,t27]) ).
cnf(t169,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t70665]) ).
cnf(t174,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t169,t44]) ).
cnf(t180,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t174]) ).
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(t70655,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(step,[status(thm)],[t10,t44]) ).
cnf(t58,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(orient,[status(thm)],[t70655]) ).
cnf(t183,plain,
true = leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t180,t58]) ).
cnf(t302,plain,
leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t183]) ).
cnf(t304,plain,
strong_iteration(X1) = ifeq(true,true,addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t28,t302]) ).
cnf(t70723,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t304,t27]) ).
cnf(t70724,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))),
inference(step,[status(thm)],[t70723,t44]) ).
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(t24,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t38,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t36,t24]) ).
cnf(t230,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t38]) ).
cnf(t70725,plain,
strong_iteration(X1) = multiplication(addition(one,X1),strong_iteration(X1)),
inference(step,[status(thm)],[t70724,t230]) ).
cnf(t1621,plain,
multiplication(addition(one,X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t70725]) ).
cnf(t1651,plain,
strong_iteration(X1) = multiplication(addition(X1,one),strong_iteration(X1)),
inference(cp,[status(thm)],[t1621,t44]) ).
cnf(t1676,plain,
multiplication(addition(X1,one),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t1651]) ).
cnf(t70204,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)],[t70188,t1676]) ).
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(t77,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t71374,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),true),
inference(step,[status(thm)],[t70204,t77]) ).
cnf(t71375,plain,
true = leq(multiplication(star(X1),multiplication(one,strong_iteration(X1))),strong_iteration(X1)),
inference(step,[status(thm)],[t71374,t27]) ).
cnf(t71376,plain,
true = leq(multiplication(star(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t71375,t24]) ).
cnf(t185,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t180,t49]) ).
cnf(t352,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t185]) ).
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(t32,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(t23,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t33,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t32,t23]) ).
cnf(t218,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t33]) ).
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(t31,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
cnf(t37,plain,
multiplication(addition(multiplication(X1,X2),X3),Y3) = addition(multiplication(X1,multiplication(X2,Y3)),multiplication(X3,Y3)),
inference(cp,[status(thm)],[t36,t31]) ).
cnf(t816,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(Y3,X3)) = multiplication(addition(multiplication(X1,X2),Y3),X3),
inference(orient,[status(thm)],[t37]) ).
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(t42,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t7]) ).
cnf(t833,plain,
multiplication(addition(multiplication(X1,zero),X2),X3) = addition(multiplication(X1,zero),multiplication(X2,X3)),
inference(cp,[status(thm)],[t816,t42]) ).
cnf(t48101,plain,
addition(multiplication(X1,zero),multiplication(X2,X3)) = multiplication(addition(multiplication(X1,zero),X2),X3),
inference(orient,[status(thm)],[t833]) ).
cnf(t48102,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(cp,[status(thm)],[t48101,t36]) ).
cnf(t48470,plain,
multiplication(addition(multiplication(X1,zero),X2),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t48102]) ).
cnf(t48474,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(multiplication(addition(X1,X2),zero),zero),
inference(cp,[status(thm)],[t48470,t36]) ).
cnf(t71191,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),multiplication(zero,zero)),
inference(step,[status(thm)],[t48474,t31]) ).
cnf(t71192,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(step,[status(thm)],[t71191,t42]) ).
cnf(t48688,plain,
multiplication(addition(X1,multiplication(X2,zero)),zero) = multiplication(addition(X1,X2),zero),
inference(orient,[status(thm)],[t71192]) ).
cnf(t48716,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)],[t218,t48688]) ).
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(t26,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t71193,plain,
multiplication(addition(X1,multiplication(X2,zero)),one) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t48716,t26]) ).
cnf(t71194,plain,
addition(X1,multiplication(X2,zero)) = addition(addition(X1,multiplication(X2,zero)),multiplication(addition(X1,X2),zero)),
inference(step,[status(thm)],[t71193,t23]) ).
cnf(t71195,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,addition(multiplication(X2,zero),multiplication(addition(X1,X2),zero))),
inference(step,[status(thm)],[t71194,t49]) ).
cnf(t71196,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(multiplication(X2,zero),addition(X1,X2)),zero)),
inference(step,[status(thm)],[t71195,t48101]) ).
cnf(t71197,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,addition(X1,X2)),zero)),
inference(step,[status(thm)],[t71196,t48470]) ).
cnf(t153,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t146,t44]) ).
cnf(t197,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t153]) ).
cnf(t71198,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t71197,t197]) ).
cnf(t48867,plain,
addition(X1,multiplication(addition(X2,X1),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t71198]) ).
cnf(t48917,plain,
addition(addition(X1,X2),multiplication(X2,zero)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(cp,[status(thm)],[t48867,t197]) ).
cnf(t71295,plain,
addition(X1,addition(X2,multiplication(X2,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t48917,t49]) ).
cnf(t71296,plain,
addition(X1,multiplication(X2,addition(one,zero))) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t71295,t218]) ).
cnf(t71297,plain,
addition(X1,multiplication(X2,one)) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t71296,t26]) ).
cnf(t71298,plain,
addition(X1,X2) = addition(addition(X1,X2),multiplication(addition(X2,X1),zero)),
inference(step,[status(thm)],[t71297,t23]) ).
cnf(t71299,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(addition(X2,X1),zero))),
inference(step,[status(thm)],[t71298,t49]) ).
cnf(t48965,plain,
addition(X1,multiplication(X2,zero)) = addition(X1,multiplication(addition(X1,X2),zero)),
inference(cp,[status(thm)],[t48867,t44]) ).
cnf(t49171,plain,
addition(X1,multiplication(addition(X1,X2),zero)) = addition(X1,multiplication(X2,zero)),
inference(orient,[status(thm)],[t48965]) ).
cnf(t71300,plain,
addition(X1,X2) = addition(X1,addition(X2,multiplication(X1,zero))),
inference(step,[status(thm)],[t71299,t49171]) ).
cnf(t59644,plain,
addition(X1,addition(X2,multiplication(X1,zero))) = addition(X1,X2),
inference(orient,[status(thm)],[t71300]) ).
cnf(t59755,plain,
true = leq(multiplication(X1,zero),addition(X1,X2)),
inference(cp,[status(thm)],[t352,t59644]) ).
cnf(t59831,plain,
leq(multiplication(X1,zero),addition(X1,X2)) = true,
inference(orient,[status(thm)],[t59755]) ).
cnf(t59839,plain,
true = leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)),
inference(cp,[status(thm)],[t59831,t230]) ).
cnf(t60934,plain,
leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)) = true,
inference(orient,[status(thm)],[t59839]) ).
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(t73,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t149,plain,
addition(one,multiplication(star(X1),X1)) = addition(one,star(X1)),
inference(cp,[status(thm)],[t146,t73]) ).
cnf(t70661,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t149,t73]) ).
cnf(t159,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t70661]) ).
cnf(t60962,plain,
true = leq(multiplication(X1,zero),multiplication(star(X2),X1)),
inference(cp,[status(thm)],[t60934,t159]) ).
cnf(t60997,plain,
leq(multiplication(X1,zero),multiplication(star(X2),X1)) = true,
inference(orient,[status(thm)],[t60962]) ).
cnf(t61019,plain,
multiplication(star(X1),X2) = ifeq(true,true,addition(multiplication(star(X1),X2),multiplication(X2,zero)),multiplication(star(X1),X2)),
inference(cp,[status(thm)],[t3139,t60997]) ).
cnf(t71311,plain,
multiplication(star(X1),X2) = addition(multiplication(star(X1),X2),multiplication(X2,zero)),
inference(step,[status(thm)],[t61019,t27]) ).
cnf(t39,plain,
multiplication(addition(X1,multiplication(X2,X3)),Y3) = addition(multiplication(X1,Y3),multiplication(X2,multiplication(X3,Y3))),
inference(cp,[status(thm)],[t36,t31]) ).
cnf(t1285,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(Y3,X2))) = multiplication(addition(X1,multiplication(X3,Y3)),X2),
inference(orient,[status(thm)],[t39]) ).
cnf(t1317,plain,
multiplication(addition(X1,multiplication(X2,zero)),X3) = addition(multiplication(X1,X3),multiplication(X2,zero)),
inference(cp,[status(thm)],[t1285,t42]) ).
cnf(t49420,plain,
addition(multiplication(X1,X2),multiplication(X3,zero)) = multiplication(addition(X1,multiplication(X3,zero)),X2),
inference(orient,[status(thm)],[t1317]) ).
cnf(t71312,plain,
multiplication(star(X1),X2) = multiplication(addition(star(X1),multiplication(X2,zero)),X2),
inference(step,[status(thm)],[t71311,t49420]) ).
cnf(t62101,plain,
multiplication(addition(star(X1),multiplication(X2,zero)),X2) = multiplication(star(X1),X2),
inference(orient,[status(thm)],[t71312]) ).
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(t64,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t66,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(cp,[status(thm)],[t49,t64]) ).
cnf(t17366,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(orient,[status(thm)],[t66]) ).
cnf(t17372,plain,
addition(strong_iteration(X1),multiplication(strong_iteration(X1),X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(cp,[status(thm)],[t17366,t32]) ).
cnf(t71064,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(step,[status(thm)],[t17372,t218]) ).
cnf(t45,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t44,t26]) ).
cnf(t132,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t45]) ).
cnf(t71065,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),X2)),
inference(step,[status(thm)],[t71064,t132]) ).
cnf(t29074,plain,
addition(star(X1),multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(one,X2)),
inference(orient,[status(thm)],[t71065]) ).
cnf(t62102,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(multiplication(strong_iteration(X1),addition(one,zero)),strong_iteration(X1)),
inference(cp,[status(thm)],[t62101,t29074]) ).
cnf(t71313,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(addition(one,zero),strong_iteration(X1))),
inference(step,[status(thm)],[t62102,t31]) ).
cnf(t71314,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),multiplication(one,strong_iteration(X1))),
inference(step,[status(thm)],[t71313,t26]) ).
cnf(t71315,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t71314,t24]) ).
cnf(t62249,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(orient,[status(thm)],[t71315]) ).
cnf(t71377,plain,
true = leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t71376,t62249]) ).
cnf(t70598,plain,
leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t71377]) ).
cnf(t70602,plain,
strong_iteration(X1) = ifeq(true,true,addition(strong_iteration(X1),multiplication(strong_iteration(X1),strong_iteration(X1))),strong_iteration(X1)),
inference(cp,[status(thm)],[t3139,t70598]) ).
cnf(t71378,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(strong_iteration(X1),strong_iteration(X1))),
inference(step,[status(thm)],[t70602,t27]) ).
cnf(t71379,plain,
strong_iteration(X1) = multiplication(addition(one,strong_iteration(X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t71378,t230]) ).
cnf(t231,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(cp,[status(thm)],[t230,t218]) ).
cnf(t265,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(orient,[status(thm)],[t231]) ).
cnf(t71380,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),addition(one,strong_iteration(X1))),
inference(step,[status(thm)],[t71379,t265]) ).
cnf(t150,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = addition(one,strong_iteration(X1)),
inference(cp,[status(thm)],[t146,t58]) ).
cnf(t70663,plain,
strong_iteration(X1) = addition(one,strong_iteration(X1)),
inference(step,[status(thm)],[t150,t58]) ).
cnf(t164,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t70663]) ).
cnf(t71381,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t71380,t164]) ).
cnf(t70605,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t71381]) ).
fof(f18,conjecture,
! [X0] : multiplication(strong_iteration(X0),strong_iteration(X0)) = strong_iteration(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0] : multiplication(strong_iteration(X0),strong_iteration(X0)) = strong_iteration(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0] : multiplication(strong_iteration(X0),strong_iteration(X0)) != strong_iteration(X0),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
multiplication(strong_iteration(sk0),strong_iteration(sk0)) != strong_iteration(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c19,plain,
multiplication(strong_iteration(sk0),strong_iteration(sk0)) != strong_iteration(sk0),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(strong_iteration(sk0),strong_iteration(sk0)) != strong_iteration(sk0),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
strong_iteration(sk0) != strong_iteration(sk0),
inference(rw,[status(thm)],[goal_0,t70605]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE143+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n014.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Wed Sep 23 19:04:03 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 56.54/7.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 56.54/7.64 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------