%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE142+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 : n003.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 7.71s 1.56s
% Output : Proof 7.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 17
% Syntax : Number of formulae : 291 ( 282 unt; 0 def)
% Number of atoms : 304 ( 288 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 : 406 ( 100 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(t14,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t26,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t14]) ).
fof(f15,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f15_nnf,plain,
! [A,B,C] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [C,A,B] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t18,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(t86,plain,
ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
inference(orient,[status(thm)],[t18]) ).
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(t6,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t42,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t46,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t26,t42]) ).
cnf(t3137,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t46]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t13,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t76,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t13]) ).
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(t12,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t47,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
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(t23,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t50,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t47,t23]) ).
cnf(t144,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t50]) ).
cnf(t153,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t76,t144]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t25,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t15342,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t153,t25]) ).
cnf(t167,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t15342]) ).
cnf(t172,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t167,t42]) ).
cnf(t178,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t172]) ).
cnf(t183,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t178,t47]) ).
cnf(t350,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t183]) ).
cnf(t352,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t350,t42]) ).
cnf(t15347,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t352,t47]) ).
cnf(t427,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t15347]) ).
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(t17,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t34,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
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(t4,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t22,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t36,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t34,t22]) ).
cnf(t228,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t36]) ).
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(t10,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t71,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t180,plain,
true = leq(multiplication(star(X1),X1),star(X1)),
inference(cp,[status(thm)],[t178,t71]) ).
cnf(t295,plain,
leq(multiplication(star(X1),X1),star(X1)) = true,
inference(orient,[status(thm)],[t180]) ).
cnf(t296,plain,
star(X1) = ifeq(true,true,addition(multiplication(star(X1),X1),star(X1)),star(X1)),
inference(cp,[status(thm)],[t26,t295]) ).
cnf(t15366,plain,
star(X1) = addition(multiplication(star(X1),X1),star(X1)),
inference(step,[status(thm)],[t296,t25]) ).
cnf(t15367,plain,
star(X1) = addition(star(X1),multiplication(star(X1),X1)),
inference(step,[status(thm)],[t15366,t42]) ).
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(t16,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t30,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
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(t3,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t21,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t31,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t30,t21]) ).
cnf(t216,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t31]) ).
cnf(t15368,plain,
star(X1) = multiplication(star(X1),addition(one,X1)),
inference(step,[status(thm)],[t15367,t216]) ).
cnf(t654,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(orient,[status(thm)],[t15368]) ).
cnf(t667,plain,
multiplication(addition(one,star(X1)),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(cp,[status(thm)],[t228,t654]) ).
cnf(t147,plain,
addition(one,multiplication(star(X1),X1)) = addition(one,star(X1)),
inference(cp,[status(thm)],[t144,t71]) ).
cnf(t15338,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t147,t71]) ).
cnf(t157,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t15338]) ).
cnf(t15369,plain,
multiplication(star(X1),addition(one,X1)) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t667,t157]) ).
cnf(t15370,plain,
star(X1) = addition(addition(one,X1),star(X1)),
inference(step,[status(thm)],[t15369,t654]) ).
cnf(t15371,plain,
star(X1) = addition(one,addition(X1,star(X1))),
inference(step,[status(thm)],[t15370,t47]) ).
cnf(t433,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t427,t157]) ).
cnf(t451,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t433]) ).
cnf(t454,plain,
addition(X1,star(X2)) = ifeq(true,true,addition(one,addition(X1,star(X2))),addition(X1,star(X2))),
inference(cp,[status(thm)],[t26,t451]) ).
cnf(t15354,plain,
addition(X1,star(X2)) = addition(one,addition(X1,star(X2))),
inference(step,[status(thm)],[t454,t25]) ).
cnf(t583,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(orient,[status(thm)],[t15354]) ).
cnf(t15372,plain,
star(X1) = addition(X1,star(X1)),
inference(step,[status(thm)],[t15371,t583]) ).
cnf(t682,plain,
addition(X1,star(X1)) = star(X1),
inference(orient,[status(thm)],[t15372]) ).
cnf(t692,plain,
true = leq(X1,addition(X2,star(X1))),
inference(cp,[status(thm)],[t427,t682]) ).
cnf(t709,plain,
leq(X1,addition(X2,star(X1))) = true,
inference(orient,[status(thm)],[t692]) ).
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(t11,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t62,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t146,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = addition(star(X1),strong_iteration(X1)),
inference(cp,[status(thm)],[t144,t62]) ).
cnf(t15343,plain,
strong_iteration(X1) = addition(star(X1),strong_iteration(X1)),
inference(step,[status(thm)],[t146,t62]) ).
cnf(t15344,plain,
strong_iteration(X1) = addition(strong_iteration(X1),star(X1)),
inference(step,[status(thm)],[t15343,t42]) ).
cnf(t191,plain,
addition(strong_iteration(X1),star(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t15344]) ).
cnf(t710,plain,
true = leq(X1,strong_iteration(X1)),
inference(cp,[status(thm)],[t709,t191]) ).
cnf(t718,plain,
leq(X1,strong_iteration(X1)) = true,
inference(orient,[status(thm)],[t710]) ).
cnf(t719,plain,
strong_iteration(X1) = ifeq(true,true,addition(X1,strong_iteration(X1)),strong_iteration(X1)),
inference(cp,[status(thm)],[t26,t718]) ).
cnf(t15373,plain,
strong_iteration(X1) = addition(X1,strong_iteration(X1)),
inference(step,[status(thm)],[t719,t25]) ).
cnf(t723,plain,
addition(X1,strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t15373]) ).
cnf(t730,plain,
true = leq(X1,addition(X2,strong_iteration(X1))),
inference(cp,[status(thm)],[t427,t723]) ).
cnf(t785,plain,
leq(X1,addition(X2,strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t730]) ).
cnf(t787,plain,
true = leq(X1,addition(strong_iteration(X1),X2)),
inference(cp,[status(thm)],[t785,t42]) ).
cnf(t803,plain,
leq(X1,addition(strong_iteration(X1),X2)) = true,
inference(orient,[status(thm)],[t787]) ).
cnf(t809,plain,
true = leq(X1,multiplication(addition(one,X2),strong_iteration(X1))),
inference(cp,[status(thm)],[t803,t228]) ).
cnf(t2720,plain,
leq(X1,multiplication(addition(one,X2),strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t809]) ).
cnf(t2725,plain,
true = leq(X1,multiplication(star(X2),strong_iteration(X1))),
inference(cp,[status(thm)],[t2720,t157]) ).
cnf(t2747,plain,
leq(X1,multiplication(star(X2),strong_iteration(X1))) = true,
inference(orient,[status(thm)],[t2725]) ).
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(t15,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t29,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
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(t24,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t43,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t42,t24]) ).
cnf(t130,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t43]) ).
cnf(t230,plain,
multiplication(addition(one,X1),zero) = multiplication(X1,zero),
inference(cp,[status(thm)],[t228,t130]) ).
cnf(t243,plain,
multiplication(addition(one,X1),zero) = multiplication(X1,zero),
inference(orient,[status(thm)],[t230]) ).
cnf(t244,plain,
multiplication(multiplication(star(X1),X1),zero) = multiplication(star(X1),zero),
inference(cp,[status(thm)],[t243,t71]) ).
cnf(t15350,plain,
multiplication(star(X1),multiplication(X1,zero)) = multiplication(star(X1),zero),
inference(step,[status(thm)],[t244,t29]) ).
cnf(t522,plain,
multiplication(star(X1),multiplication(X1,zero)) = multiplication(star(X1),zero),
inference(orient,[status(thm)],[t15350]) ).
cnf(t527,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = addition(star(X1),multiplication(star(X1),zero)),
inference(cp,[status(thm)],[t216,t522]) ).
cnf(t15446,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = multiplication(star(X1),addition(one,zero)),
inference(step,[status(thm)],[t527,t216]) ).
cnf(t15447,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = multiplication(star(X1),one),
inference(step,[status(thm)],[t15446,t24]) ).
cnf(t15448,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = star(X1),
inference(step,[status(thm)],[t15447,t21]) ).
cnf(t5719,plain,
multiplication(star(X1),addition(one,multiplication(X1,zero))) = star(X1),
inference(orient,[status(thm)],[t15448]) ).
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(t8,plain,
addition(multiplication(X1,strong_iteration(X1)),one) = strong_iteration(X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t15332,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(step,[status(thm)],[t8,t42]) ).
cnf(t56,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(orient,[status(thm)],[t15332]) ).
cnf(t58,plain,
strong_iteration(multiplication(X1,X2)) = addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))),
inference(cp,[status(thm)],[t56,t29]) ).
cnf(t11092,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(orient,[status(thm)],[t58]) ).
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(t5,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t40,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t11094,plain,
strong_iteration(multiplication(X1,zero)) = addition(one,multiplication(X1,zero)),
inference(cp,[status(thm)],[t11092,t40]) ).
cnf(t11207,plain,
addition(one,multiplication(X1,zero)) = strong_iteration(multiplication(X1,zero)),
inference(orient,[status(thm)],[t11094]) ).
cnf(t15516,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(step,[status(thm)],[t5719,t11207]) ).
cnf(t11254,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(rw,[status(thm)],[t15516]) ).
cnf(t11365,plain,
multiplication(star(X1),strong_iteration(multiplication(X1,zero))) = star(X1),
inference(orient,[status(thm)],[t11254]) ).
cnf(t429,plain,
true = leq(X1,addition(X2,multiplication(X1,addition(one,X3)))),
inference(cp,[status(thm)],[t427,t216]) ).
cnf(t12810,plain,
leq(X1,addition(X2,multiplication(X1,addition(one,X3)))) = true,
inference(orient,[status(thm)],[t429]) ).
cnf(t148,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = addition(one,strong_iteration(X1)),
inference(cp,[status(thm)],[t144,t56]) ).
cnf(t15340,plain,
strong_iteration(X1) = addition(one,strong_iteration(X1)),
inference(step,[status(thm)],[t148,t56]) ).
cnf(t162,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(orient,[status(thm)],[t15340]) ).
cnf(t12827,plain,
true = leq(X1,addition(X2,multiplication(X1,strong_iteration(X3)))),
inference(cp,[status(thm)],[t12810,t162]) ).
cnf(t12907,plain,
leq(X1,addition(X2,multiplication(X1,strong_iteration(X3)))) = true,
inference(orient,[status(thm)],[t12827]) ).
cnf(t12912,plain,
true = leq(X1,addition(multiplication(X1,strong_iteration(X2)),X3)),
inference(cp,[status(thm)],[t12907,t42]) ).
cnf(t13015,plain,
leq(X1,addition(multiplication(X1,strong_iteration(X2)),X3)) = true,
inference(orient,[status(thm)],[t12912]) ).
cnf(t13096,plain,
true = ifeq(true,true,leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)),true),
inference(cp,[status(thm)],[t86,t13015]) ).
cnf(t15560,plain,
true = leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)),
inference(step,[status(thm)],[t13096,t25]) ).
cnf(t13629,plain,
leq(strong_iteration(X1),multiplication(strong_iteration(strong_iteration(X1)),X2)) = true,
inference(orient,[status(thm)],[t15560]) ).
cnf(t57,plain,
strong_iteration(zero) = addition(one,zero),
inference(cp,[status(thm)],[t56,t40]) ).
cnf(t15333,plain,
strong_iteration(zero) = one,
inference(step,[status(thm)],[t57,t24]) ).
cnf(t124,plain,
strong_iteration(zero) = one,
inference(orient,[status(thm)],[t15333]) ).
cnf(t13630,plain,
true = leq(one,multiplication(strong_iteration(strong_iteration(zero)),X1)),
inference(cp,[status(thm)],[t13629,t124]) ).
cnf(t15561,plain,
true = leq(one,multiplication(strong_iteration(one),X1)),
inference(step,[status(thm)],[t13630,t124]) ).
cnf(t13638,plain,
leq(one,multiplication(strong_iteration(one),X1)) = true,
inference(orient,[status(thm)],[t15561]) ).
cnf(t13641,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)],[t26,t13638]) ).
cnf(t15562,plain,
multiplication(strong_iteration(one),X1) = addition(one,multiplication(strong_iteration(one),X1)),
inference(step,[status(thm)],[t13641,t25]) ).
cnf(t13655,plain,
addition(one,multiplication(strong_iteration(one),X1)) = multiplication(strong_iteration(one),X1),
inference(orient,[status(thm)],[t15562]) ).
cnf(t13656,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(multiplication(strong_iteration(one),zero)),
inference(cp,[status(thm)],[t13655,t11207]) ).
cnf(t13701,plain,
strong_iteration(multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(orient,[status(thm)],[t13656]) ).
cnf(t13716,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),multiplication(strong_iteration(one),zero)),
inference(cp,[status(thm)],[t11365,t13701]) ).
cnf(t15563,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),zero),
inference(step,[status(thm)],[t13716,t522]) ).
cnf(t13783,plain,
multiplication(star(strong_iteration(one)),zero) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t15563]) ).
cnf(t13793,plain,
multiplication(star(strong_iteration(one)),multiplication(zero,X1)) = multiplication(star(strong_iteration(one)),X1),
inference(cp,[status(thm)],[t29,t13783]) ).
cnf(t15568,plain,
multiplication(star(strong_iteration(one)),zero) = multiplication(star(strong_iteration(one)),X1),
inference(step,[status(thm)],[t13793,t40]) ).
cnf(t15569,plain,
star(strong_iteration(one)) = multiplication(star(strong_iteration(one)),X1),
inference(step,[status(thm)],[t15568,t13783]) ).
cnf(t13930,plain,
multiplication(star(strong_iteration(one)),X1) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t15569]) ).
cnf(t13943,plain,
true = leq(X1,star(strong_iteration(one))),
inference(cp,[status(thm)],[t2747,t13930]) ).
cnf(t13965,plain,
leq(X1,star(strong_iteration(one))) = true,
inference(orient,[status(thm)],[t13943]) ).
cnf(t13931,plain,
multiplication(addition(one,star(strong_iteration(one))),X1) = addition(X1,star(strong_iteration(one))),
inference(cp,[status(thm)],[t228,t13930]) ).
cnf(t15570,plain,
multiplication(star(strong_iteration(one)),X1) = addition(X1,star(strong_iteration(one))),
inference(step,[status(thm)],[t13931,t157]) ).
cnf(t15571,plain,
star(strong_iteration(one)) = addition(X1,star(strong_iteration(one))),
inference(step,[status(thm)],[t15570,t13930]) ).
cnf(t13971,plain,
addition(X1,star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t15571]) ).
cnf(t13972,plain,
star(strong_iteration(one)) = strong_iteration(strong_iteration(one)),
inference(cp,[status(thm)],[t13971,t191]) ).
cnf(t13993,plain,
star(strong_iteration(one)) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t13972]) ).
cnf(t15574,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(step,[status(thm)],[t13965,t13993]) ).
cnf(t14015,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(rw,[status(thm)],[t15574]) ).
cnf(t14102,plain,
leq(X1,strong_iteration(strong_iteration(one))) = true,
inference(orient,[status(thm)],[t14015]) ).
cnf(t14105,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)],[t3137,t14102]) ).
cnf(t15581,plain,
strong_iteration(strong_iteration(one)) = addition(strong_iteration(strong_iteration(one)),X1),
inference(step,[status(thm)],[t14105,t25]) ).
cnf(t14150,plain,
addition(strong_iteration(strong_iteration(one)),X1) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t15581]) ).
cnf(t712,plain,
true = leq(X1,addition(star(X1),X2)),
inference(cp,[status(thm)],[t709,t42]) ).
cnf(t737,plain,
leq(X1,addition(star(X1),X2)) = true,
inference(orient,[status(thm)],[t712]) ).
cnf(t741,plain,
true = leq(X1,multiplication(addition(one,X2),star(X1))),
inference(cp,[status(thm)],[t737,t228]) ).
cnf(t2626,plain,
leq(X1,multiplication(addition(one,X2),star(X1))) = true,
inference(orient,[status(thm)],[t741]) ).
cnf(t2631,plain,
true = leq(X1,multiplication(star(X2),star(X1))),
inference(cp,[status(thm)],[t2626,t157]) ).
cnf(t2653,plain,
leq(X1,multiplication(star(X2),star(X1))) = true,
inference(orient,[status(thm)],[t2631]) ).
cnf(t2654,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)],[t26,t2653]) ).
cnf(t15482,plain,
multiplication(star(X1),star(X2)) = addition(X2,multiplication(star(X1),star(X2))),
inference(step,[status(thm)],[t2654,t25]) ).
cnf(t8837,plain,
addition(X1,multiplication(star(X2),star(X1))) = multiplication(star(X2),star(X1)),
inference(orient,[status(thm)],[t15482]) ).
cnf(t14151,plain,
strong_iteration(strong_iteration(one)) = multiplication(star(X1),star(strong_iteration(strong_iteration(one)))),
inference(cp,[status(thm)],[t14150,t8837]) ).
cnf(t13784,plain,
strong_iteration(multiplication(star(strong_iteration(one)),zero)) = addition(one,star(strong_iteration(one))),
inference(cp,[status(thm)],[t11207,t13783]) ).
cnf(t15564,plain,
strong_iteration(star(strong_iteration(one))) = addition(one,star(strong_iteration(one))),
inference(step,[status(thm)],[t13784,t13783]) ).
cnf(t15565,plain,
strong_iteration(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t15564,t157]) ).
cnf(t13834,plain,
strong_iteration(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t15565]) ).
cnf(t13838,plain,
strong_iteration(star(strong_iteration(one))) = addition(star(strong_iteration(one)),star(star(strong_iteration(one)))),
inference(cp,[status(thm)],[t191,t13834]) ).
cnf(t15566,plain,
star(strong_iteration(one)) = addition(star(strong_iteration(one)),star(star(strong_iteration(one)))),
inference(step,[status(thm)],[t13838,t13834]) ).
cnf(t15567,plain,
star(strong_iteration(one)) = star(star(strong_iteration(one))),
inference(step,[status(thm)],[t15566,t682]) ).
cnf(t13886,plain,
star(star(strong_iteration(one))) = star(strong_iteration(one)),
inference(orient,[status(thm)],[t15567]) ).
cnf(t15577,plain,
star(strong_iteration(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t13886,t13993]) ).
cnf(t15578,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t15577,t13993]) ).
cnf(t14017,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(rw,[status(thm)],[t15578]) ).
cnf(t14019,plain,
star(strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14017]) ).
cnf(t15586,plain,
strong_iteration(strong_iteration(one)) = multiplication(star(X1),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t14151,t14019]) ).
cnf(t14216,plain,
multiplication(star(X1),strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t15586]) ).
cnf(t13703,plain,
strong_iteration(multiplication(strong_iteration(one),zero)) = addition(multiplication(strong_iteration(one),zero),star(multiplication(strong_iteration(one),zero))),
inference(cp,[status(thm)],[t191,t13701]) ).
cnf(t15584,plain,
multiplication(strong_iteration(one),zero) = addition(multiplication(strong_iteration(one),zero),star(multiplication(strong_iteration(one),zero))),
inference(step,[status(thm)],[t13703,t13701]) ).
cnf(t15585,plain,
multiplication(strong_iteration(one),zero) = star(multiplication(strong_iteration(one),zero)),
inference(step,[status(thm)],[t15584,t682]) ).
cnf(t14173,plain,
star(multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(orient,[status(thm)],[t15585]) ).
cnf(t14217,plain,
strong_iteration(strong_iteration(one)) = multiplication(multiplication(strong_iteration(one),zero),strong_iteration(strong_iteration(one))),
inference(cp,[status(thm)],[t14216,t14173]) ).
cnf(t15587,plain,
strong_iteration(strong_iteration(one)) = multiplication(strong_iteration(one),multiplication(zero,strong_iteration(strong_iteration(one)))),
inference(step,[status(thm)],[t14217,t29]) ).
cnf(t15588,plain,
strong_iteration(strong_iteration(one)) = multiplication(strong_iteration(one),zero),
inference(step,[status(thm)],[t15587,t40]) ).
cnf(t14233,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t15588]) ).
cnf(t14238,plain,
multiplication(strong_iteration(one),addition(one,zero)) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(cp,[status(thm)],[t216,t14233]) ).
cnf(t15589,plain,
multiplication(strong_iteration(one),one) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t14238,t24]) ).
cnf(t15590,plain,
strong_iteration(one) = addition(strong_iteration(one),strong_iteration(strong_iteration(one))),
inference(step,[status(thm)],[t15589,t21]) ).
cnf(t15572,plain,
addition(X1,strong_iteration(strong_iteration(one))) = star(strong_iteration(one)),
inference(step,[status(thm)],[t13971,t13993]) ).
cnf(t15573,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t15572,t13993]) ).
cnf(t14014,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(rw,[status(thm)],[t15573]) ).
cnf(t14108,plain,
addition(X1,strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)),
inference(orient,[status(thm)],[t14014]) ).
cnf(t15591,plain,
strong_iteration(one) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t15590,t14108]) ).
cnf(t14277,plain,
strong_iteration(strong_iteration(one)) = strong_iteration(one),
inference(orient,[status(thm)],[t15591]) ).
cnf(t15598,plain,
addition(strong_iteration(one),X1) = strong_iteration(strong_iteration(one)),
inference(step,[status(thm)],[t14150,t14277]) ).
cnf(t15599,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(step,[status(thm)],[t15598,t14277]) ).
cnf(t14313,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(rw,[status(thm)],[t15599]) ).
cnf(t14323,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(orient,[status(thm)],[t14313]) ).
cnf(t715,plain,
true = ifeq(true,true,leq(X1,multiplication(strong_iteration(X2),star(X1))),true),
inference(cp,[status(thm)],[t86,t709]) ).
cnf(t15380,plain,
true = leq(X1,multiplication(strong_iteration(X2),star(X1))),
inference(step,[status(thm)],[t715,t25]) ).
cnf(t984,plain,
leq(X1,multiplication(strong_iteration(X2),star(X1))) = true,
inference(orient,[status(thm)],[t15380]) ).
cnf(t985,plain,
multiplication(strong_iteration(X1),star(X2)) = ifeq(true,true,addition(X2,multiplication(strong_iteration(X1),star(X2))),multiplication(strong_iteration(X1),star(X2))),
inference(cp,[status(thm)],[t26,t984]) ).
cnf(t15456,plain,
multiplication(strong_iteration(X1),star(X2)) = addition(X2,multiplication(strong_iteration(X1),star(X2))),
inference(step,[status(thm)],[t985,t25]) ).
cnf(t6821,plain,
addition(X1,multiplication(strong_iteration(X2),star(X1))) = multiplication(strong_iteration(X2),star(X1)),
inference(orient,[status(thm)],[t15456]) ).
cnf(t14332,plain,
strong_iteration(one) = multiplication(strong_iteration(X1),star(strong_iteration(one))),
inference(cp,[status(thm)],[t14323,t6821]) ).
cnf(t15592,plain,
star(strong_iteration(one)) = strong_iteration(one),
inference(step,[status(thm)],[t13993,t14277]) ).
cnf(t14278,plain,
star(strong_iteration(one)) = strong_iteration(one),
inference(orient,[status(thm)],[t15592]) ).
cnf(t15605,plain,
strong_iteration(one) = multiplication(strong_iteration(X1),strong_iteration(one)),
inference(step,[status(thm)],[t14332,t14278]) ).
cnf(t14418,plain,
multiplication(strong_iteration(X1),strong_iteration(one)) = strong_iteration(one),
inference(orient,[status(thm)],[t15605]) ).
cnf(t14431,plain,
true = ifeq(leq(strong_iteration(one),addition(strong_iteration(one),X1)),true,leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X2)),X1)),true),
inference(cp,[status(thm)],[t86,t14418]) ).
cnf(t15615,plain,
true = ifeq(true,true,leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X2)),X1)),true),
inference(step,[status(thm)],[t14431,t167]) ).
cnf(t15616,plain,
true = leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X2)),X1)),
inference(step,[status(thm)],[t15615,t25]) ).
cnf(t15224,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),X2)) = true,
inference(orient,[status(thm)],[t15616]) ).
cnf(t15230,plain,
multiplication(strong_iteration(strong_iteration(X1)),X2) = ifeq(true,true,addition(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),X2)),multiplication(strong_iteration(strong_iteration(X1)),X2)),
inference(cp,[status(thm)],[t26,t15224]) ).
cnf(t15617,plain,
multiplication(strong_iteration(strong_iteration(X1)),X2) = addition(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),X2)),
inference(step,[status(thm)],[t15230,t25]) ).
cnf(t15618,plain,
multiplication(strong_iteration(strong_iteration(X1)),X2) = strong_iteration(one),
inference(step,[status(thm)],[t15617,t14323]) ).
cnf(t15234,plain,
multiplication(strong_iteration(strong_iteration(X1)),X2) = strong_iteration(one),
inference(orient,[status(thm)],[t15618]) ).
cnf(t15238,plain,
strong_iteration(one) = strong_iteration(strong_iteration(X1)),
inference(cp,[status(thm)],[t15234,t21]) ).
cnf(t15330,plain,
strong_iteration(strong_iteration(X1)) = strong_iteration(one),
inference(orient,[status(thm)],[t15238]) ).
fof(f18,conjecture,
! [X0] : strong_iteration(strong_iteration(X0)) = strong_iteration(one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0] : strong_iteration(strong_iteration(X0)) = strong_iteration(one),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0] : strong_iteration(strong_iteration(X0)) != strong_iteration(one),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
strong_iteration(strong_iteration(sk0)) != strong_iteration(one),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c19,plain,
strong_iteration(strong_iteration(sk0)) != strong_iteration(one),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
strong_iteration(strong_iteration(sk0)) != strong_iteration(one),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
strong_iteration(one) != strong_iteration(one),
inference(rw,[status(thm)],[goal_0,t15330]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE142+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 19:05:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.71/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.71/1.56 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------