%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE139+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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:51:41 PM UTC 2026
% Result : Theorem 55.72s 7.66s
% Output : Proof 55.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 17
% Syntax : Number of formulae : 186 ( 173 unt; 0 def)
% Number of atoms : 203 ( 179 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 12 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 323 ( 24 sgn 89 !; 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(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]) ).
fof(f17,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/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]) ).
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/sandbox2/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(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(t23,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t111,plain,
true = ifeq(leq(addition(multiplication(X1,X2),one),X2),true,leq(star(X1),X2),true),
inference(cp,[status(thm)],[t100,t23]) ).
cnf(t96026,plain,
true = ifeq(leq(addition(one,multiplication(X1,X2)),X2),true,leq(star(X1),X2),true),
inference(step,[status(thm)],[t111,t44]) ).
cnf(t92338,plain,
ifeq(leq(addition(one,multiplication(X1,X2)),X2),true,leq(star(X1),X2),true) = true,
inference(orient,[status(thm)],[t96026]) ).
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',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]) ).
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(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]) ).
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(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(t235,plain,
multiplication(addition(one,multiplication(X1,X2)),X3) = addition(X3,multiplication(X1,multiplication(X2,X3))),
inference(cp,[status(thm)],[t230,t31]) ).
cnf(t46430,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(orient,[status(thm)],[t235]) ).
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',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]) ).
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]) ).
cnf(t46431,plain,
multiplication(addition(one,multiplication(X1,X2)),X1) = multiplication(X1,addition(one,multiplication(X2,X1))),
inference(cp,[status(thm)],[t46430,t218]) ).
cnf(t50922,plain,
multiplication(addition(one,multiplication(X1,X2)),X1) = multiplication(X1,addition(one,multiplication(X2,X1))),
inference(orient,[status(thm)],[t46431]) ).
fof(f14,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox2/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(t95091,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)],[t95091]) ).
cnf(t50926,plain,
multiplication(X1,addition(one,multiplication(strong_iteration(X1),X1))) = multiplication(strong_iteration(X1),X1),
inference(cp,[status(thm)],[t50922,t58]) ).
cnf(t51546,plain,
multiplication(X1,addition(one,multiplication(strong_iteration(X1),X1))) = multiplication(strong_iteration(X1),X1),
inference(orient,[status(thm)],[t50926]) ).
cnf(t92353,plain,
true = ifeq(leq(addition(one,multiplication(strong_iteration(X1),X1)),addition(one,multiplication(strong_iteration(X1),X1))),true,leq(star(X1),addition(one,multiplication(strong_iteration(X1),X1))),true),
inference(cp,[status(thm)],[t92338,t51546]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi18,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/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(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(t96069,plain,
true = ifeq(true,true,leq(star(X1),addition(one,multiplication(strong_iteration(X1),X1))),true),
inference(step,[status(thm)],[t92353,t77]) ).
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(t96070,plain,
true = leq(star(X1),addition(one,multiplication(strong_iteration(X1),X1))),
inference(step,[status(thm)],[t96069,t27]) ).
cnf(t93956,plain,
leq(star(X1),addition(one,multiplication(strong_iteration(X1),X1))) = true,
inference(orient,[status(thm)],[t96070]) ).
cnf(t93961,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = ifeq(true,true,addition(addition(one,multiplication(strong_iteration(X1),X1)),star(X1)),addition(one,multiplication(strong_iteration(X1),X1))),
inference(cp,[status(thm)],[t3139,t93956]) ).
cnf(t96099,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = addition(addition(one,multiplication(strong_iteration(X1),X1)),star(X1)),
inference(step,[status(thm)],[t93961,t27]) ).
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(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]) ).
cnf(t96100,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = addition(one,addition(multiplication(strong_iteration(X1),X1),star(X1))),
inference(step,[status(thm)],[t96099,t49]) ).
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]) ).
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(t95101,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)],[t95101]) ).
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]) ).
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]) ).
cnf(t354,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t352,t44]) ).
cnf(t95106,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t354,t49]) ).
cnf(t429,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t95106]) ).
fof(f11,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('/export/starexec/sandbox2/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(t95097,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)],[t95097]) ).
cnf(t435,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t429,t159]) ).
cnf(t453,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t435]) ).
cnf(t456,plain,
addition(X1,star(X2)) = ifeq(true,true,addition(one,addition(X1,star(X2))),addition(X1,star(X2))),
inference(cp,[status(thm)],[t28,t453]) ).
cnf(t95113,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t456,t27]) ).
cnf(t585,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t95113]) ).
cnf(t96101,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = addition(multiplication(strong_iteration(X1),X1),star(X1)),
inference(step,[status(thm)],[t96100,t585]) ).
cnf(t96102,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = addition(star(X1),multiplication(strong_iteration(X1),X1)),
inference(step,[status(thm)],[t96101,t44]) ).
fof(f16,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
file('/export/starexec/sandbox2/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(t95500,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),addition(zero,X2))),
inference(step,[status(thm)],[t17372,t218]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/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(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(t95501,plain,
multiplication(strong_iteration(X1),addition(one,X2)) = addition(star(X1),multiplication(strong_iteration(X1),X2)),
inference(step,[status(thm)],[t95500,t132]) ).
cnf(t29074,plain,
addition(star(X1),multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(one,X2)),
inference(orient,[status(thm)],[t95501]) ).
cnf(t96103,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = multiplication(strong_iteration(X1),addition(one,X1)),
inference(step,[status(thm)],[t96102,t29074]) ).
fof(f15,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox2/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(t88,plain,
ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t99,plain,
true = ifeq(leq(X1,addition(multiplication(X2,X1),one)),true,leq(X1,strong_iteration(X2)),true),
inference(cp,[status(thm)],[t88,t23]) ).
cnf(t95781,plain,
true = ifeq(leq(X1,addition(one,multiplication(X2,X1))),true,leq(X1,strong_iteration(X2)),true),
inference(step,[status(thm)],[t99,t44]) ).
cnf(t65125,plain,
ifeq(leq(X1,addition(one,multiplication(X2,X1))),true,leq(X1,strong_iteration(X2)),true) = true,
inference(orient,[status(thm)],[t95781]) ).
cnf(t65131,plain,
true = ifeq(leq(addition(one,multiplication(strong_iteration(X1),X1)),addition(one,multiplication(strong_iteration(X1),X1))),true,leq(addition(one,multiplication(strong_iteration(X1),X1)),strong_iteration(X1)),true),
inference(cp,[status(thm)],[t65125,t51546]) ).
cnf(t95782,plain,
true = ifeq(true,true,leq(addition(one,multiplication(strong_iteration(X1),X1)),strong_iteration(X1)),true),
inference(step,[status(thm)],[t65131,t77]) ).
cnf(t95783,plain,
true = leq(addition(one,multiplication(strong_iteration(X1),X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t95782,t27]) ).
cnf(t65325,plain,
leq(addition(one,multiplication(strong_iteration(X1),X1)),strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t95783]) ).
cnf(t65326,plain,
strong_iteration(X1) = ifeq(true,true,addition(addition(one,multiplication(strong_iteration(X1),X1)),strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t28,t65325]) ).
cnf(t95784,plain,
strong_iteration(X1) = addition(addition(one,multiplication(strong_iteration(X1),X1)),strong_iteration(X1)),
inference(step,[status(thm)],[t65326,t27]) ).
cnf(t95785,plain,
strong_iteration(X1) = addition(one,addition(multiplication(strong_iteration(X1),X1),strong_iteration(X1))),
inference(step,[status(thm)],[t95784,t49]) ).
cnf(t150,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = addition(one,strong_iteration(X1)),
inference(cp,[status(thm)],[t146,t58]) ).
cnf(t95099,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)],[t95099]) ).
cnf(t434,plain,
true = leq(one,addition(X1,strong_iteration(X2))),
inference(cp,[status(thm)],[t429,t164]) ).
cnf(t447,plain,
leq(one,addition(X1,strong_iteration(X2))) = true,
inference(orient,[status(thm)],[t434]) ).
cnf(t450,plain,
addition(X1,strong_iteration(X2)) = ifeq(true,true,addition(one,addition(X1,strong_iteration(X2))),addition(X1,strong_iteration(X2))),
inference(cp,[status(thm)],[t28,t447]) ).
cnf(t95112,plain,
addition(X1,strong_iteration(X2)) = addition(one,addition(X1,strong_iteration(X2))),
inference(step,[status(thm)],[t450,t27]) ).
cnf(t574,plain,
addition(one,addition(X1,strong_iteration(X2))) = addition(X1,strong_iteration(X2)),
inference(orient,[status(thm)],[t95112]) ).
cnf(t95786,plain,
strong_iteration(X1) = addition(multiplication(strong_iteration(X1),X1),strong_iteration(X1)),
inference(step,[status(thm)],[t95785,t574]) ).
cnf(t95787,plain,
strong_iteration(X1) = addition(strong_iteration(X1),multiplication(strong_iteration(X1),X1)),
inference(step,[status(thm)],[t95786,t44]) ).
cnf(t95788,plain,
strong_iteration(X1) = multiplication(strong_iteration(X1),addition(one,X1)),
inference(step,[status(thm)],[t95787,t218]) ).
cnf(t65332,plain,
multiplication(strong_iteration(X1),addition(one,X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t95788]) ).
cnf(t96104,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = strong_iteration(X1),
inference(step,[status(thm)],[t96103,t65332]) ).
cnf(t94895,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t96104]) ).
fof(f18,conjecture,
! [X0] : strong_iteration(X0) = addition(multiplication(strong_iteration(X0),X0),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0] : strong_iteration(X0) = addition(multiplication(strong_iteration(X0),X0),one),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0] : strong_iteration(X0) != addition(multiplication(strong_iteration(X0),X0),one),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
strong_iteration(sk0) != addition(multiplication(strong_iteration(sk0),sk0),one),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c19,plain,
strong_iteration(sk0) != addition(multiplication(strong_iteration(sk0),sk0),one),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
addition(multiplication(strong_iteration(sk0),sk0),one) != strong_iteration(sk0),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
addition(one,multiplication(strong_iteration(sk0),sk0)) != strong_iteration(sk0),
inference(rw,[status(thm)],[goal_0,t44]) ).
cnf(g0_1,plain,
strong_iteration(sk0) != strong_iteration(sk0),
inference(rw,[status(thm)],[g0_0,t94895]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE139+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 19:05:48 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 55.72/7.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.72/7.66 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------