%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE137+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 : n018.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 9.29s 1.90s
% Output : Proof 9.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 17
% Syntax : Number of formulae : 269 ( 260 unt; 0 def)
% Number of atoms : 282 ( 261 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 9 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 372 ( 80 sgn 83 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/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]) ).
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(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(t14335,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)],[t14335]) ).
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]) ).
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(t14340,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)],[t14340]) ).
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(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(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(t182,plain,
true = leq(multiplication(star(X1),X1),star(X1)),
inference(cp,[status(thm)],[t180,t73]) ).
cnf(t297,plain,
leq(multiplication(star(X1),X1),star(X1)) = true,
inference(orient,[status(thm)],[t182]) ).
cnf(t298,plain,
star(X1) = ifeq(true,true,addition(multiplication(star(X1),X1),star(X1)),star(X1)),
inference(cp,[status(thm)],[t28,t297]) ).
cnf(t14359,plain,
star(X1) = addition(multiplication(star(X1),X1),star(X1)),
inference(step,[status(thm)],[t298,t27]) ).
cnf(t14360,plain,
star(X1) = addition(star(X1),multiplication(star(X1),X1)),
inference(step,[status(thm)],[t14359,t44]) ).
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]) ).
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(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(t14361,plain,
star(X1) = multiplication(star(X1),addition(one,X1)),
inference(step,[status(thm)],[t14360,t218]) ).
cnf(t656,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t14361]) ).
cnf(t669,plain,
multiplication(addition(one,star(X1)),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t230,t656]) ).
cnf(t149,plain,
addition(one,multiplication(star(X1),X1)) = addition(one,star(X1)),
inference(cp,[status(thm)],[t146,t73]) ).
cnf(t14331,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)],[t14331]) ).
cnf(t14362,plain,
multiplication(star(X1),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t669,t159]) ).
cnf(t14363,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t14362,t656]) ).
cnf(t14364,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t14363,t49]) ).
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(t14347,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)],[t14347]) ).
cnf(t14365,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t14364,t585]) ).
cnf(t684,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t14365]) ).
cnf(t694,plain,
true = leq(X1,addition(X2,star(X1))),
inference(cp,[status(thm)],[t429,t684]) ).
cnf(t711,plain,
leq(X1,addition(X2,star(X1))) = true,
inference(orient,[status(thm)],[t694]) ).
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(t148,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = addition(star(X1),strong_iteration(X1)),
inference(cp,[status(thm)],[t146,t64]) ).
cnf(t14336,plain,
strong_iteration(X1) = addition(star(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t148,t64]) ).
cnf(t14337,plain,
strong_iteration(X1) = addition(strong_iteration(X1),star(X1)),
inference(step,[status(thm)],[t14336,t44]) ).
cnf(t193,plain,
addition(strong_iteration(X1),star(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t14337]) ).
cnf(t712,plain,
true = leq(X1,strong_iteration(X1)),
inference(cp,[status(thm)],[t711,t193]) ).
cnf(t720,plain,
leq(X1,strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t712]) ).
cnf(t721,plain,
strong_iteration(X1) = ifeq(true,true,addition(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t28,t720]) ).
cnf(t14366,plain,
strong_iteration(X1) = addition(X1,strong_iteration(X1)),
inference(step,[status(thm)],[t721,t27]) ).
cnf(t725,plain,
addition(X1,strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t14366]) ).
cnf(t732,plain,
true = leq(X1,addition(X2,strong_iteration(X1))),
inference(cp,[status(thm)],[t429,t725]) ).
cnf(t787,plain,
leq(X1,addition(X2,strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t732]) ).
cnf(t789,plain,
true = leq(X1,addition(strong_iteration(X1),X2)),
inference(cp,[status(thm)],[t787,t44]) ).
cnf(t805,plain,
leq(X1,addition(strong_iteration(X1),X2)) = true,
inference(orient,[status(thm)],[t789]) ).
cnf(t811,plain,
true = leq(X1,multiplication(addition(one,X2),strong_iteration(X1))),
inference(cp,[status(thm)],[t805,t230]) ).
cnf(t2722,plain,
leq(X1,multiplication(addition(one,X2),strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t811]) ).
cnf(t2727,plain,
true = leq(X1,multiplication(star(X2),strong_iteration(X1))),
inference(cp,[status(thm)],[t2722,t159]) ).
cnf(t2749,plain,
leq(X1,multiplication(star(X2),strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t2727]) ).
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]) ).
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(t232,plain,
multiplication(addition(one,X1),zero) = multiplication(X1,zero),
inference(cp,[status(thm)],[t230,t132]) ).
cnf(t245,plain,
multiplication(addition(one,X1),zero) = multiplication(X1,zero),
inference(orient,[status(thm)],[t232]) ).
cnf(t246,plain,
multiplication(multiplication(star(X1),X1),zero) = multiplication(star(X1),zero),
inference(cp,[status(thm)],[t245,t73]) ).
cnf(t14343,plain,
multiplication(star(X1),multiplication(X1,zero)) = multiplication(star(X1),zero),
inference(step,[status(thm)],[t246,t31]) ).
cnf(t524,plain,
multiplication(star(X1),multiplication(X1,zero)) = multiplication(star(X1),zero),
inference(orient,[status(thm)],[t14343]) ).
cnf(t529,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = addition(star(X1),multiplication(star(X1),zero)),
inference(cp,[status(thm)],[t218,t524]) ).
cnf(t14439,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = multiplication(star(X1),addition(one,zero)),
inference(step,[status(thm)],[t529,t218]) ).
cnf(t14440,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = multiplication(star(X1),one),
inference(step,[status(thm)],[t14439,t26]) ).
cnf(t14441,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = star(X1),
inference(step,[status(thm)],[t14440,t23]) ).
cnf(t5721,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = star(X1),
inference(orient,[status(thm)],[t14441]) ).
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(t14325,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)],[t14325]) ).
cnf(t60,plain,
strong_iteration(multiplication(X1,X2)) = addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))),
inference(cp,[status(thm)],[t58,t31]) ).
cnf(t11094,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(orient,[status(thm)],[t60]) ).
fof(f9,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/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(t11096,plain,
strong_iteration(multiplication(X1,zero)) = addition(one,multiplication(X1,zero)),
inference(cp,[status(thm)],[t11094,t42]) ).
cnf(t11209,plain,
addition(one,multiplication(X1,zero)) = strong_iteration(multiplication(X1,zero)),
inference(orient,[status(thm)],[t11096]) ).
cnf(t14509,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(step,[status(thm)],[t5721,t11209]) ).
cnf(t11256,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(rw,[status(thm)],[t14509]) ).
cnf(t11367,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(orient,[status(thm)],[t11256]) ).
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(t431,plain,
true = leq(X1,addition(X2,multiplication(X1,addition(one,X3)))),
inference(cp,[status(thm)],[t429,t218]) ).
cnf(t12812,plain,
leq(X1,addition(X2,multiplication(X1,addition(one,X3)))) = true,
inference(orient,[status(thm)],[t431]) ).
cnf(t150,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = addition(one,strong_iteration(X1)),
inference(cp,[status(thm)],[t146,t58]) ).
cnf(t14333,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)],[t14333]) ).
cnf(t12829,plain,
true = leq(X1,addition(X2,multiplication(X1,strong_iteration(X3)))),
inference(cp,[status(thm)],[t12812,t164]) ).
cnf(t12909,plain,
leq(X1,addition(X2,multiplication(X1,strong_iteration(X3)))) = true,
inference(orient,[status(thm)],[t12829]) ).
cnf(t12914,plain,
true = leq(X1,addition(multiplication(X1,strong_iteration(X2)),X3)),
inference(cp,[status(thm)],[t12909,t44]) ).
cnf(t13017,plain,
leq(X1,addition(multiplication(X1,strong_iteration(X2)),X3)) = true,
inference(orient,[status(thm)],[t12914]) ).
cnf(t13098,plain,
true = ifeq(true,true,leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)),true),
inference(cp,[status(thm)],[t88,t13017]) ).
cnf(t14553,plain,
true = leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)),
inference(step,[status(thm)],[t13098,t27]) ).
cnf(t13631,plain,
leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)) = true,
inference(orient,[status(thm)],[t14553]) ).
cnf(t59,plain,
strong_iteration(zero) = addition(one,zero),
inference(cp,[status(thm)],[t58,t42]) ).
cnf(t14326,plain,
strong_iteration(zero) = one,
inference(step,[status(thm)],[t59,t26]) ).
cnf(t126,plain,
strong_iteration(zero) = one,
inference(orient,[status(thm)],[t14326]) ).
cnf(t13632,plain,
true = leq(one,multiplication(strong_iteration(strong_iteration(zero)),X1)),
inference(cp,[status(thm)],[t13631,t126]) ).
cnf(t14554,plain,
true = leq(one,multiplication(strong_iteration(one),X1)),
inference(step,[status(thm)],[t13632,t126]) ).
cnf(t13640,plain,
leq(one,multiplication(strong_iteration(one),X1)) = true,
inference(orient,[status(thm)],[t14554]) ).
cnf(t13643,plain,
multiplication(strong_iteration(one),X1) = ifeq(true,true,addition(one,multiplication(strong_iteration(one),X1)),multiplication(strong_iteration(one),X1)),
inference(cp,[status(thm)],[t28,t13640]) ).
cnf(t14555,plain,
multiplication(strong_iteration(one),X1) = addition(one,multiplication(strong_iteration(one),X1)),
inference(step,[status(thm)],[t13643,t27]) ).
cnf(t13657,plain,
addition(one,multiplication(strong_iteration(one),X1)) = multiplication(strong_iteration(one),X1),
inference(orient,[status(thm)],[t14555]) ).
cnf(t13658,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(multiplication(strong_iteration(one),zero)),
inference(cp,[status(thm)],[t13657,t11209]) ).
cnf(t13703,plain,
strong_iteration(multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(orient,[status(thm)],[t13658]) ).
cnf(t13718,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),multiplication(strong_iteration(one),zero)),
inference(cp,[status(thm)],[t11367,t13703]) ).
cnf(t14556,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),zero),
inference(step,[status(thm)],[t13718,t524]) ).
cnf(t13785,plain,
multiplication(star(strong_iteration(one)),zero) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t14556]) ).
cnf(t13795,plain,
multiplication(star(strong_iteration(one)),multiplication(zero,X1)) = multiplication(star(strong_iteration(one)),X1),
inference(cp,[status(thm)],[t31,t13785]) ).
cnf(t14561,plain,
multiplication(star(strong_iteration(one)),zero) = multiplication(star(strong_iteration(one)),X1),
inference(step,[status(thm)],[t13795,t42]) ).
cnf(t14562,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),X1),
inference(step,[status(thm)],[t14561,t13785]) ).
cnf(t13932,plain,
multiplication(star(strong_iteration(one)),X1) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t14562]) ).
cnf(t13945,plain,
true = leq(X1,star(strong_iteration(one))),
inference(cp,[status(thm)],[t2749,t13932]) ).
cnf(t13967,plain,
leq(X1,star(strong_iteration(one))) = true,
inference(orient,[status(thm)],[t13945]) ).
cnf(t13933,plain,
multiplication(addition(one,star(strong_iteration(one))),X1) = addition(X1,star(strong_iteration(one))),
inference(cp,[status(thm)],[t230,t13932]) ).
cnf(t14563,plain,
multiplication(star(strong_iteration(one)),X1) = addition(X1,star(strong_iteration(one))),
inference(step,[status(thm)],[t13933,t159]) ).
cnf(t14564,plain,
star(strong_iteration(one)) = addition(X1,star(strong_iteration(one))),
inference(step,[status(thm)],[t14563,t13932]) ).
cnf(t13973,plain,
addition(X1,star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t14564]) ).
cnf(t13974,plain,
star(strong_iteration(one)) = strong_iteration(strong_iteration(one)),
inference(cp,[status(thm)],[t13973,t193]) ).
cnf(t13995,plain,
star(strong_iteration(one)) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t13974]) ).
cnf(t14567,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(step,[status(thm)],[t13967,t13995]) ).
cnf(t14017,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(rw,[status(thm)],[t14567]) ).
cnf(t14104,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(orient,[status(thm)],[t14017]) ).
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]) ).
cnf(t14107,plain,
strong_iteration(strong_iteration(one)) = ifeq(true,true,addition(strong_iteration(strong_iteration(one)),X1),strong_iteration(strong_iteration(one))),
inference(cp,[status(thm)],[t3139,t14104]) ).
cnf(t14574,plain,
strong_iteration(strong_iteration(one)) = addition(strong_iteration(strong_iteration(one)),X1),
inference(step,[status(thm)],[t14107,t27]) ).
cnf(t14152,plain,
addition(strong_iteration(strong_iteration(one)),X1) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14574]) ).
cnf(t714,plain,
true = leq(X1,addition(star(X1),X2)),
inference(cp,[status(thm)],[t711,t44]) ).
cnf(t739,plain,
leq(X1,addition(star(X1),X2)) = true,
inference(orient,[status(thm)],[t714]) ).
cnf(t743,plain,
true = leq(X1,multiplication(addition(one,X2),star(X1))),
inference(cp,[status(thm)],[t739,t230]) ).
cnf(t2628,plain,
leq(X1,multiplication(addition(one,X2),star(X1))) = true,
inference(orient,[status(thm)],[t743]) ).
cnf(t2633,plain,
true = leq(X1,multiplication(star(X2),star(X1))),
inference(cp,[status(thm)],[t2628,t159]) ).
cnf(t2655,plain,
leq(X1,multiplication(star(X2),star(X1))) = true,
inference(orient,[status(thm)],[t2633]) ).
cnf(t2656,plain,
multiplication(star(X1),star(X2)) = ifeq(true,true,addition(X2,multiplication(star(X1),star(X2))),multiplication(star(X1),star(X2))),
inference(cp,[status(thm)],[t28,t2655]) ).
cnf(t14475,plain,
multiplication(star(X1),star(X2)) = addition(X2,multiplication(star(X1),star(X2))),
inference(step,[status(thm)],[t2656,t27]) ).
cnf(t8839,plain,
addition(X1,multiplication(star(X2),star(X1))) = multiplication(star(X2),star(X1)),
inference(orient,[status(thm)],[t14475]) ).
cnf(t14153,plain,
strong_iteration(strong_iteration(one)) = multiplication(star(X1),star(strong_iteration(strong_iteration(one)))),
inference(cp,[status(thm)],[t14152,t8839]) ).
cnf(t13786,plain,
strong_iteration(multiplication(star(strong_iteration(one)),zero)) = addition(one,star(strong_iteration(one))),
inference(cp,[status(thm)],[t11209,t13785]) ).
cnf(t14557,plain,
strong_iteration(star(strong_iteration(one))) = addition(one,star(strong_iteration(one))),
inference(step,[status(thm)],[t13786,t13785]) ).
cnf(t14558,plain,
strong_iteration(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t14557,t159]) ).
cnf(t13836,plain,
strong_iteration(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t14558]) ).
cnf(t13840,plain,
strong_iteration(star(strong_iteration(one))) = addition(star(strong_iteration(one)),star(star(strong_iteration(one)))),
inference(cp,[status(thm)],[t193,t13836]) ).
cnf(t14559,plain,
star(strong_iteration(one)) = addition(star(strong_iteration(one)),star(star(strong_iteration(one)))),
inference(step,[status(thm)],[t13840,t13836]) ).
cnf(t14560,plain,
star(strong_iteration(one)) = star(star(strong_iteration(one))),
inference(step,[status(thm)],[t14559,t684]) ).
cnf(t13888,plain,
star(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t14560]) ).
cnf(t14570,plain,
star(strong_iteration(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t13888,t13995]) ).
cnf(t14571,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t14570,t13995]) ).
cnf(t14019,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(rw,[status(thm)],[t14571]) ).
cnf(t14021,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14019]) ).
cnf(t14579,plain,
strong_iteration(strong_iteration(one)) = multiplication(star(X1),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t14153,t14021]) ).
cnf(t14218,plain,
multiplication(star(X1),strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14579]) ).
cnf(t13705,plain,
strong_iteration(multiplication(strong_iteration(one),zero)) = addition(multiplication(strong_iteration(one),zero),star(multiplication(strong_iteration(one),zero))),
inference(cp,[status(thm)],[t193,t13703]) ).
cnf(t14577,plain,
multiplication(strong_iteration(one),zero) = addition(multiplication(strong_iteration(one),zero),star(multiplication(strong_iteration(one),zero))),
inference(step,[status(thm)],[t13705,t13703]) ).
cnf(t14578,plain,
multiplication(strong_iteration(one),zero) = star(multiplication(strong_iteration(one),zero)),
inference(step,[status(thm)],[t14577,t684]) ).
cnf(t14175,plain,
star(multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(orient,[status(thm)],[t14578]) ).
cnf(t14219,plain,
strong_iteration(strong_iteration(one)) = multiplication(multiplication(strong_iteration(one),zero),strong_iteration(strong_iteration(one))),
inference(cp,[status(thm)],[t14218,t14175]) ).
cnf(t14580,plain,
strong_iteration(strong_iteration(one)) = multiplication(strong_iteration(one),multiplication(zero,strong_iteration(strong_iteration(one)))),
inference(step,[status(thm)],[t14219,t31]) ).
cnf(t14581,plain,
strong_iteration(strong_iteration(one)) = multiplication(strong_iteration(one),zero),
inference(step,[status(thm)],[t14580,t42]) ).
cnf(t14235,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14581]) ).
cnf(t14240,plain,
multiplication(strong_iteration(one),addition(one,zero)) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(cp,[status(thm)],[t218,t14235]) ).
cnf(t14582,plain,
multiplication(strong_iteration(one),one) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t14240,t26]) ).
cnf(t14583,plain,
strong_iteration(one) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t14582,t23]) ).
cnf(t14565,plain,
addition(X1,strong_iteration(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t13973,t13995]) ).
cnf(t14566,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t14565,t13995]) ).
cnf(t14016,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(rw,[status(thm)],[t14566]) ).
cnf(t14110,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14016]) ).
cnf(t14584,plain,
strong_iteration(one) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t14583,t14110]) ).
cnf(t14279,plain,
strong_iteration(strong_iteration(one)) = strong_iteration(one),
inference(orient,[status(thm)],[t14584]) ).
cnf(t14597,plain,
leq(X1,strong_iteration(one)) = true,
inference(step,[status(thm)],[t14104,t14279]) ).
cnf(t14318,plain,
leq(X1,strong_iteration(one)) = true,
inference(rw,[status(thm)],[t14597]) ).
cnf(t14319,plain,
leq(X1,strong_iteration(one)) = true,
inference(orient,[status(thm)],[t14318]) ).
fof(f18,conjecture,
! [X0] : leq(X0,strong_iteration(one)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0] : leq(X0,strong_iteration(one)),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0] : ~ leq(X0,strong_iteration(one)),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
~ leq(sk0,strong_iteration(one)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c19,plain,
~ leq(sk0,strong_iteration(one)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
leq(sk0,strong_iteration(one)) != true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t14319]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE137+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.41 % Computer : n018.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8046.5625MB
% 0.09/0.41 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Wed Sep 23 19:05:03 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.29/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.29/1.90 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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