%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE071+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 01:51:32 PM UTC 2026
% Result : Theorem 48.65s 7.52s
% Output : Proof 48.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 15
% Syntax : Number of formulae : 298 ( 293 unt; 0 def)
% Number of atoms : 307 ( 299 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 6 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 629 ( 108 sgn 81 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain5) ).
fof(f16_nnf,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c17,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t15,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t59,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t15]) ).
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(t21,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t66,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t21]) ).
fof(f12,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f12_nnf,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t17,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t42,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(orient,[status(thm)],[t17]) ).
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',left_distributivity) ).
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(t23,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t47,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t23]) ).
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(t8,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t27,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t49,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t47,t27]) ).
cnf(t224,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t49]) ).
cnf(t114748,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t42,t224]) ).
fof(f14,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f14_nnf,plain,
! [X0] : addition(domain(X0),one) = one,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0] : addition(domain(X0),one) = one,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t10,plain,
addition(domain(X1),one) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
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(t12,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t32,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t114734,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t10,t32]) ).
cnf(t63,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t114734]) ).
cnf(t114749,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t114748,t63]) ).
cnf(t114750,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t114749,t27]) ).
cnf(t235,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t114750]) ).
cnf(t236,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t235]) ).
cnf(t243,plain,
multiplication(domain(X1),multiplication(X1,X2)) = multiplication(X1,X2),
inference(cp,[status(thm)],[t66,t236]) ).
cnf(t293,plain,
multiplication(domain(X1),multiplication(X1,X2)) = multiplication(X1,X2),
inference(orient,[status(thm)],[t243]) ).
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',right_distributivity) ).
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(t22,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t53,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t22]) ).
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(t6,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t26,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t55,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t53,t26]) ).
cnf(t254,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t55]) ).
cnf(t258,plain,
multiplication(domain(X1),addition(one,X1)) = addition(domain(X1),X1),
inference(cp,[status(thm)],[t254,t236]) ).
cnf(t114756,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(step,[status(thm)],[t258,t32]) ).
cnf(t454,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(orient,[status(thm)],[t114756]) ).
cnf(t469,plain,
multiplication(domain(X1),multiplication(addition(one,X1),X2)) = multiplication(addition(X1,domain(X1)),X2),
inference(cp,[status(thm)],[t66,t454]) ).
cnf(t12479,plain,
multiplication(domain(X1),multiplication(addition(one,X1),X2)) = multiplication(addition(X1,domain(X1)),X2),
inference(orient,[status(thm)],[t469]) ).
cnf(t12551,plain,
multiplication(domain(X1),multiplication(addition(one,X1),X2)) = multiplication(domain(domain(X1)),multiplication(addition(X1,domain(X1)),X2)),
inference(cp,[status(thm)],[t293,t12479]) ).
cnf(t115120,plain,
multiplication(addition(X1,domain(X1)),X2) = multiplication(domain(domain(X1)),multiplication(addition(X1,domain(X1)),X2)),
inference(step,[status(thm)],[t12551,t12479]) ).
fof(f13,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f13_nnf,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t16,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t76,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t16]) ).
cnf(t78,plain,
domain(multiplication(one,X1)) = domain(domain(X1)),
inference(cp,[status(thm)],[t76,t27]) ).
cnf(t114736,plain,
domain(X1) = domain(domain(X1)),
inference(step,[status(thm)],[t78,t27]) ).
cnf(t104,plain,
domain(domain(X1)) = domain(X1),
inference(orient,[status(thm)],[t114736]) ).
cnf(t115121,plain,
multiplication(addition(X1,domain(X1)),X2) = multiplication(domain(X1),multiplication(addition(X1,domain(X1)),X2)),
inference(step,[status(thm)],[t115120,t104]) ).
cnf(t71932,plain,
multiplication(domain(X1),multiplication(addition(X1,domain(X1)),X2)) = multiplication(addition(X1,domain(X1)),X2),
inference(orient,[status(thm)],[t115121]) ).
cnf(t67,plain,
multiplication(addition(multiplication(X1,X2),X3),Y3) = addition(multiplication(X1,multiplication(X2,Y3)),multiplication(X3,Y3)),
inference(cp,[status(thm)],[t47,t66]) ).
cnf(t31511,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(Y3,X3)) = multiplication(addition(multiplication(X1,X2),Y3),X3),
inference(orient,[status(thm)],[t67]) ).
cnf(t246,plain,
multiplication(addition(domain(X1),X2),X1) = addition(X1,multiplication(X2,X1)),
inference(cp,[status(thm)],[t47,t236]) ).
cnf(t114759,plain,
multiplication(addition(domain(X1),X2),X1) = multiplication(addition(one,X2),X1),
inference(step,[status(thm)],[t246,t224]) ).
cnf(t510,plain,
multiplication(addition(domain(X1),X2),X1) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t114759]) ).
cnf(t511,plain,
multiplication(addition(one,domain(X1)),X2) = multiplication(domain(addition(X2,X1)),X2),
inference(cp,[status(thm)],[t510,t59]) ).
cnf(t114760,plain,
multiplication(one,X2) = multiplication(domain(addition(X2,X1)),X2),
inference(step,[status(thm)],[t511,t63]) ).
cnf(t114761,plain,
X2 = multiplication(domain(addition(X2,X1)),X2),
inference(step,[status(thm)],[t114760,t27]) ).
cnf(t530,plain,
multiplication(domain(addition(X1,X2)),X1) = X1,
inference(orient,[status(thm)],[t114761]) ).
cnf(t537,plain,
X1 = multiplication(domain(addition(X2,X1)),X1),
inference(cp,[status(thm)],[t530,t32]) ).
cnf(t544,plain,
multiplication(domain(addition(X1,X2)),X2) = X2,
inference(orient,[status(thm)],[t537]) ).
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(t18,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t35,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(t552,plain,
X1 = multiplication(domain(addition(X2,addition(X3,X1))),X1),
inference(cp,[status(thm)],[t544,t35]) ).
cnf(t695,plain,
multiplication(domain(addition(X1,addition(X2,X3))),X3) = X3,
inference(orient,[status(thm)],[t552]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_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(t1,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t24,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t38,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t35,t24]) ).
cnf(t126,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t38]) ).
cnf(t129,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t126,t32]) ).
cnf(t145,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t129]) ).
cnf(t548,plain,
addition(X1,X2) = multiplication(domain(addition(X2,X1)),addition(X1,X2)),
inference(cp,[status(thm)],[t544,t145]) ).
cnf(t1512,plain,
multiplication(domain(addition(X1,X2)),addition(X2,X1)) = addition(X2,X1),
inference(orient,[status(thm)],[t548]) ).
cnf(t106,plain,
domain(addition(X1,domain(X2))) = addition(domain(X1),domain(X2)),
inference(cp,[status(thm)],[t59,t104]) ).
cnf(t114745,plain,
domain(addition(X1,domain(X2))) = domain(addition(X1,X2)),
inference(step,[status(thm)],[t106,t59]) ).
cnf(t190,plain,
domain(addition(X1,domain(X2))) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t114745]) ).
cnf(t1516,plain,
addition(domain(X1),X2) = multiplication(domain(addition(X2,X1)),addition(domain(X1),X2)),
inference(cp,[status(thm)],[t1512,t190]) ).
cnf(t16497,plain,
multiplication(domain(addition(X1,X2)),addition(domain(X2),X1)) = addition(domain(X2),X1),
inference(orient,[status(thm)],[t1516]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t20,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t29,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t19,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t90,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t131,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t90,t126]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t114740,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t131,t28]) ).
cnf(t132,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t114740]) ).
cnf(t137,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t132,t32]) ).
cnf(t138,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t137]) ).
cnf(t140,plain,
true = leq(multiplication(X1,X2),multiplication(addition(X3,X1),X2)),
inference(cp,[status(thm)],[t138,t47]) ).
cnf(t1725,plain,
leq(multiplication(X1,X2),multiplication(addition(X3,X1),X2)) = true,
inference(orient,[status(thm)],[t140]) ).
cnf(t65,plain,
addition(one,addition(domain(X1),X2)) = addition(one,X2),
inference(cp,[status(thm)],[t35,t63]) ).
cnf(t284,plain,
addition(one,addition(domain(X1),X2)) = addition(one,X2),
inference(orient,[status(thm)],[t65]) ).
cnf(t285,plain,
addition(one,multiplication(X1,domain(X2))) = addition(one,multiplication(addition(one,X1),domain(X2))),
inference(cp,[status(thm)],[t284,t224]) ).
cnf(t10995,plain,
addition(one,multiplication(addition(one,X1),domain(X2))) = addition(one,multiplication(X1,domain(X2))),
inference(orient,[status(thm)],[t285]) ).
cnf(t10999,plain,
addition(one,multiplication(domain(X1),domain(X2))) = addition(one,multiplication(one,domain(X2))),
inference(cp,[status(thm)],[t10995,t63]) ).
cnf(t114882,plain,
addition(one,multiplication(domain(X1),domain(X2))) = multiplication(one,addition(one,domain(X2))),
inference(step,[status(thm)],[t10999,t254]) ).
cnf(t114883,plain,
addition(one,multiplication(domain(X1),domain(X2))) = addition(one,domain(X2)),
inference(step,[status(thm)],[t114882,t27]) ).
cnf(t114884,plain,
addition(one,multiplication(domain(X1),domain(X2))) = one,
inference(step,[status(thm)],[t114883,t63]) ).
cnf(t11076,plain,
addition(one,multiplication(domain(X1),domain(X2))) = one,
inference(orient,[status(thm)],[t114884]) ).
cnf(t11104,plain,
true = leq(multiplication(multiplication(domain(X1),domain(X2)),X3),multiplication(one,X3)),
inference(cp,[status(thm)],[t1725,t11076]) ).
cnf(t114889,plain,
true = leq(multiplication(domain(X1),multiplication(domain(X2),X3)),multiplication(one,X3)),
inference(step,[status(thm)],[t11104,t66]) ).
cnf(t114890,plain,
true = leq(multiplication(domain(X1),multiplication(domain(X2),X3)),X3),
inference(step,[status(thm)],[t114889,t27]) ).
cnf(t11176,plain,
leq(multiplication(domain(X1),multiplication(domain(X2),X3)),X3) = true,
inference(orient,[status(thm)],[t114890]) ).
cnf(t244,plain,
multiplication(domain(X1),addition(X1,X2)) = addition(X1,multiplication(domain(X1),X2)),
inference(cp,[status(thm)],[t53,t236]) ).
cnf(t754,plain,
addition(X1,multiplication(domain(X1),X2)) = multiplication(domain(X1),addition(X1,X2)),
inference(orient,[status(thm)],[t244]) ).
cnf(t764,plain,
multiplication(domain(domain(X1)),addition(domain(X1),X2)) = addition(domain(X1),multiplication(domain(X1),X2)),
inference(cp,[status(thm)],[t754,t104]) ).
cnf(t114803,plain,
multiplication(domain(X1),addition(domain(X1),X2)) = addition(domain(X1),multiplication(domain(X1),X2)),
inference(step,[status(thm)],[t764,t104]) ).
cnf(t114804,plain,
multiplication(domain(X1),addition(domain(X1),X2)) = multiplication(domain(X1),addition(one,X2)),
inference(step,[status(thm)],[t114803,t254]) ).
cnf(t3686,plain,
multiplication(domain(X1),addition(domain(X1),X2)) = multiplication(domain(X1),addition(one,X2)),
inference(orient,[status(thm)],[t114804]) ).
cnf(t3687,plain,
multiplication(domain(X1),addition(one,domain(X2))) = multiplication(domain(X1),domain(addition(X1,X2))),
inference(cp,[status(thm)],[t3686,t59]) ).
cnf(t114805,plain,
multiplication(domain(X1),one) = multiplication(domain(X1),domain(addition(X1,X2))),
inference(step,[status(thm)],[t3687,t63]) ).
cnf(t114806,plain,
domain(X1) = multiplication(domain(X1),domain(addition(X1,X2))),
inference(step,[status(thm)],[t114805,t26]) ).
cnf(t3709,plain,
multiplication(domain(X1),domain(addition(X1,X2))) = domain(X1),
inference(orient,[status(thm)],[t114806]) ).
cnf(t3730,plain,
domain(X1) = multiplication(domain(X1),domain(addition(X2,X1))),
inference(cp,[status(thm)],[t3709,t32]) ).
cnf(t3747,plain,
multiplication(domain(X1),domain(addition(X2,X1))) = domain(X1),
inference(orient,[status(thm)],[t3730]) ).
cnf(t3765,plain,
domain(multiplication(X1,X2)) = multiplication(domain(multiplication(X1,X2)),domain(multiplication(X1,addition(one,X2)))),
inference(cp,[status(thm)],[t3747,t254]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(hi13,axiom,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t14,plain,
leq(X1,multiplication(domain(X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi13]) ).
cnf(t84,plain,
leq(X1,multiplication(domain(X1),X1)) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t85,plain,
true = leq(one,domain(one)),
inference(cp,[status(thm)],[t84,t26]) ).
cnf(t109,plain,
leq(one,domain(one)) = true,
inference(orient,[status(thm)],[t85]) ).
cnf(t110,plain,
domain(one) = ifeq(true,true,addition(one,domain(one)),domain(one)),
inference(cp,[status(thm)],[t29,t109]) ).
cnf(t114737,plain,
domain(one) = addition(one,domain(one)),
inference(step,[status(thm)],[t110,t28]) ).
cnf(t114738,plain,
domain(one) = one,
inference(step,[status(thm)],[t114737,t63]) ).
cnf(t112,plain,
domain(one) = one,
inference(orient,[status(thm)],[t114738]) ).
cnf(t113,plain,
domain(addition(one,X1)) = addition(one,domain(X1)),
inference(cp,[status(thm)],[t59,t112]) ).
cnf(t114739,plain,
domain(addition(one,X1)) = one,
inference(step,[status(thm)],[t113,t63]) ).
cnf(t115,plain,
domain(addition(one,X1)) = one,
inference(orient,[status(thm)],[t114739]) ).
cnf(t119,plain,
domain(multiplication(X1,addition(one,X2))) = domain(multiplication(X1,one)),
inference(cp,[status(thm)],[t76,t115]) ).
cnf(t114746,plain,
domain(multiplication(X1,addition(one,X2))) = domain(X1),
inference(step,[status(thm)],[t119,t26]) ).
cnf(t204,plain,
domain(multiplication(X1,addition(one,X2))) = domain(X1),
inference(orient,[status(thm)],[t114746]) ).
cnf(t114807,plain,
domain(multiplication(X1,X2)) = multiplication(domain(multiplication(X1,X2)),domain(X1)),
inference(step,[status(thm)],[t3765,t204]) ).
cnf(t3788,plain,
multiplication(domain(multiplication(X1,X2)),domain(X1)) = domain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t114807]) ).
cnf(t11188,plain,
true = leq(multiplication(domain(X1),domain(multiplication(X2,X3))),domain(X2)),
inference(cp,[status(thm)],[t11176,t3788]) ).
cnf(t12171,plain,
leq(multiplication(domain(X1),domain(multiplication(X2,X3))),domain(X2)) = true,
inference(orient,[status(thm)],[t11188]) ).
cnf(t12239,plain,
domain(X1) = ifeq(true,true,addition(multiplication(domain(X2),domain(multiplication(X1,X3))),domain(X1)),domain(X1)),
inference(cp,[status(thm)],[t29,t12171]) ).
cnf(t114948,plain,
domain(X1) = addition(multiplication(domain(X2),domain(multiplication(X1,X3))),domain(X1)),
inference(step,[status(thm)],[t12239,t28]) ).
cnf(t114949,plain,
domain(X1) = addition(domain(X1),multiplication(domain(X2),domain(multiplication(X1,X3)))),
inference(step,[status(thm)],[t114948,t32]) ).
cnf(t19549,plain,
addition(domain(X1),multiplication(domain(X2),domain(multiplication(X1,X3)))) = domain(X1),
inference(orient,[status(thm)],[t114949]) ).
cnf(t19665,plain,
addition(domain(multiplication(domain(X1),domain(multiplication(X2,X3)))),domain(X2)) = multiplication(domain(domain(X2)),addition(domain(multiplication(domain(X1),domain(multiplication(X2,X3)))),domain(X2))),
inference(cp,[status(thm)],[t16497,t19549]) ).
cnf(t114950,plain,
domain(addition(multiplication(domain(X1),domain(multiplication(X2,X3))),X2)) = multiplication(domain(domain(X2)),addition(domain(multiplication(domain(X1),domain(multiplication(X2,X3)))),domain(X2))),
inference(step,[status(thm)],[t19665,t59]) ).
cnf(t79,plain,
domain(addition(multiplication(X1,domain(X2)),X3)) = addition(domain(multiplication(X1,X2)),domain(X3)),
inference(cp,[status(thm)],[t59,t76]) ).
cnf(t114792,plain,
domain(addition(multiplication(X1,domain(X2)),X3)) = domain(addition(multiplication(X1,X2),X3)),
inference(step,[status(thm)],[t79,t59]) ).
cnf(t3071,plain,
domain(addition(multiplication(X1,domain(X2)),X3)) = domain(addition(multiplication(X1,X2),X3)),
inference(orient,[status(thm)],[t114792]) ).
cnf(t114951,plain,
domain(addition(multiplication(domain(X1),multiplication(X2,X3)),X2)) = multiplication(domain(domain(X2)),addition(domain(multiplication(domain(X1),domain(multiplication(X2,X3)))),domain(X2))),
inference(step,[status(thm)],[t114950,t3071]) ).
cnf(t114952,plain,
domain(addition(X2,multiplication(domain(X1),multiplication(X2,X3)))) = multiplication(domain(domain(X2)),addition(domain(multiplication(domain(X1),domain(multiplication(X2,X3)))),domain(X2))),
inference(step,[status(thm)],[t114951,t32]) ).
cnf(t114953,plain,
domain(addition(X2,multiplication(domain(X1),multiplication(X2,X3)))) = multiplication(domain(X2),addition(domain(multiplication(domain(X1),domain(multiplication(X2,X3)))),domain(X2))),
inference(step,[status(thm)],[t114952,t104]) ).
cnf(t3694,plain,
multiplication(domain(X1),addition(one,X2)) = multiplication(domain(X1),addition(X2,domain(X1))),
inference(cp,[status(thm)],[t3686,t32]) ).
cnf(t4025,plain,
multiplication(domain(X1),addition(X2,domain(X1))) = multiplication(domain(X1),addition(one,X2)),
inference(orient,[status(thm)],[t3694]) ).
cnf(t114954,plain,
domain(addition(X2,multiplication(domain(X1),multiplication(X2,X3)))) = multiplication(domain(X2),addition(one,domain(multiplication(domain(X1),domain(multiplication(X2,X3)))))),
inference(step,[status(thm)],[t114953,t4025]) ).
cnf(t114955,plain,
domain(addition(X2,multiplication(domain(X1),multiplication(X2,X3)))) = multiplication(domain(X2),one),
inference(step,[status(thm)],[t114954,t63]) ).
cnf(t114956,plain,
domain(addition(X2,multiplication(domain(X1),multiplication(X2,X3)))) = domain(X2),
inference(step,[status(thm)],[t114955,t26]) ).
cnf(t19744,plain,
domain(addition(X1,multiplication(domain(X2),multiplication(X1,X3)))) = domain(X1),
inference(orient,[status(thm)],[t114956]) ).
cnf(t19765,plain,
domain(domain(addition(X1,X2))) = domain(addition(domain(addition(X1,X2)),multiplication(domain(X3),X1))),
inference(cp,[status(thm)],[t19744,t530]) ).
cnf(t114961,plain,
domain(addition(X1,X2)) = domain(addition(domain(addition(X1,X2)),multiplication(domain(X3),X1))),
inference(step,[status(thm)],[t19765,t104]) ).
cnf(t105,plain,
domain(addition(domain(X1),X2)) = addition(domain(X1),domain(X2)),
inference(cp,[status(thm)],[t59,t104]) ).
cnf(t114743,plain,
domain(addition(domain(X1),X2)) = domain(addition(X1,X2)),
inference(step,[status(thm)],[t105,t59]) ).
cnf(t167,plain,
domain(addition(domain(X1),X2)) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t114743]) ).
cnf(t114962,plain,
domain(addition(X1,X2)) = domain(addition(addition(X1,X2),multiplication(domain(X3),X1))),
inference(step,[status(thm)],[t114961,t167]) ).
cnf(t114963,plain,
domain(addition(X1,X2)) = domain(addition(X1,addition(X2,multiplication(domain(X3),X1)))),
inference(step,[status(thm)],[t114962,t35]) ).
cnf(t20200,plain,
domain(addition(X1,addition(X2,multiplication(domain(X3),X1)))) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t114963]) ).
cnf(t20374,plain,
multiplication(domain(X1),X2) = multiplication(domain(addition(X2,X3)),multiplication(domain(X1),X2)),
inference(cp,[status(thm)],[t695,t20200]) ).
cnf(t20566,plain,
multiplication(domain(addition(X1,X2)),multiplication(domain(X3),X1)) = multiplication(domain(X3),X1),
inference(orient,[status(thm)],[t20374]) ).
cnf(t20567,plain,
multiplication(domain(X1),X2) = multiplication(domain(X2),multiplication(domain(X1),X2)),
inference(cp,[status(thm)],[t20566,t19744]) ).
cnf(t20665,plain,
multiplication(domain(X1),multiplication(domain(X2),X1)) = multiplication(domain(X2),X1),
inference(orient,[status(thm)],[t20567]) ).
cnf(t31559,plain,
multiplication(addition(multiplication(domain(X1),domain(X2)),X3),X1) = addition(multiplication(domain(X2),X1),multiplication(X3,X1)),
inference(cp,[status(thm)],[t31511,t20665]) ).
cnf(t115127,plain,
multiplication(addition(multiplication(domain(X1),domain(X2)),X3),X1) = multiplication(addition(domain(X2),X3),X1),
inference(step,[status(thm)],[t31559,t47]) ).
cnf(t74361,plain,
multiplication(addition(multiplication(domain(X1),domain(X2)),X3),X1) = multiplication(addition(domain(X2),X3),X1),
inference(orient,[status(thm)],[t115127]) ).
cnf(t74565,plain,
multiplication(addition(multiplication(domain(X1),domain(X2)),domain(multiplication(domain(X1),domain(X2)))),X1) = multiplication(domain(multiplication(domain(X1),domain(X2))),multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1)),
inference(cp,[status(thm)],[t71932,t74361]) ).
cnf(t115128,plain,
multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1) = multiplication(domain(multiplication(domain(X1),domain(X2))),multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1)),
inference(step,[status(thm)],[t74565,t74361]) ).
cnf(t115129,plain,
multiplication(domain(addition(X2,multiplication(domain(X1),domain(X2)))),X1) = multiplication(domain(multiplication(domain(X1),domain(X2))),multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1)),
inference(step,[status(thm)],[t115128,t59]) ).
cnf(t80,plain,
domain(addition(X1,multiplication(X2,domain(X3)))) = addition(domain(X1),domain(multiplication(X2,X3))),
inference(cp,[status(thm)],[t59,t76]) ).
cnf(t114795,plain,
domain(addition(X1,multiplication(X2,domain(X3)))) = domain(addition(X1,multiplication(X2,X3))),
inference(step,[status(thm)],[t80,t59]) ).
cnf(t3221,plain,
domain(addition(X1,multiplication(X2,domain(X3)))) = domain(addition(X1,multiplication(X2,X3))),
inference(orient,[status(thm)],[t114795]) ).
cnf(t115130,plain,
multiplication(domain(addition(X2,multiplication(domain(X1),X2))),X1) = multiplication(domain(multiplication(domain(X1),domain(X2))),multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1)),
inference(step,[status(thm)],[t115129,t3221]) ).
cnf(t115131,plain,
multiplication(domain(multiplication(addition(one,domain(X1)),X2)),X1) = multiplication(domain(multiplication(domain(X1),domain(X2))),multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1)),
inference(step,[status(thm)],[t115130,t224]) ).
cnf(t115132,plain,
multiplication(domain(multiplication(one,X2)),X1) = multiplication(domain(multiplication(domain(X1),domain(X2))),multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1)),
inference(step,[status(thm)],[t115131,t63]) ).
cnf(t115133,plain,
multiplication(domain(X2),X1) = multiplication(domain(multiplication(domain(X1),domain(X2))),multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1)),
inference(step,[status(thm)],[t115132,t27]) ).
cnf(t115134,plain,
multiplication(domain(X2),X1) = multiplication(domain(multiplication(domain(X1),X2)),multiplication(addition(domain(X2),domain(multiplication(domain(X1),domain(X2)))),X1)),
inference(step,[status(thm)],[t115133,t76]) ).
cnf(t115135,plain,
multiplication(domain(X2),X1) = multiplication(domain(multiplication(domain(X1),X2)),multiplication(domain(addition(X2,multiplication(domain(X1),domain(X2)))),X1)),
inference(step,[status(thm)],[t115134,t59]) ).
cnf(t115136,plain,
multiplication(domain(X2),X1) = multiplication(domain(multiplication(domain(X1),X2)),multiplication(domain(addition(X2,multiplication(domain(X1),X2))),X1)),
inference(step,[status(thm)],[t115135,t3221]) ).
cnf(t3775,plain,
multiplication(domain(X1),multiplication(domain(addition(X2,X1)),X3)) = multiplication(domain(X1),X3),
inference(cp,[status(thm)],[t66,t3747]) ).
cnf(t17202,plain,
multiplication(domain(X1),multiplication(domain(addition(X2,X1)),X3)) = multiplication(domain(X1),X3),
inference(orient,[status(thm)],[t3775]) ).
cnf(t115137,plain,
multiplication(domain(X2),X1) = multiplication(domain(multiplication(domain(X1),X2)),X1),
inference(step,[status(thm)],[t115136,t17202]) ).
cnf(t74684,plain,
multiplication(domain(multiplication(domain(X1),X2)),X1) = multiplication(domain(X2),X1),
inference(orient,[status(thm)],[t115137]) ).
cnf(t74757,plain,
multiplication(domain(X1),domain(X2)) = multiplication(domain(multiplication(domain(X2),X1)),domain(X2)),
inference(cp,[status(thm)],[t74684,t104]) ).
cnf(t3763,plain,
domain(multiplication(domain(X1),X2)) = multiplication(domain(multiplication(domain(X1),X2)),domain(multiplication(domain(X1),addition(X1,X2)))),
inference(cp,[status(thm)],[t3747,t754]) ).
cnf(t265,plain,
domain(addition(X1,multiplication(domain(X1),X2))) = domain(multiplication(domain(X1),addition(one,X2))),
inference(cp,[status(thm)],[t167,t254]) ).
cnf(t114757,plain,
domain(addition(X1,multiplication(domain(X1),X2))) = domain(domain(X1)),
inference(step,[status(thm)],[t265,t204]) ).
cnf(t114758,plain,
domain(addition(X1,multiplication(domain(X1),X2))) = domain(X1),
inference(step,[status(thm)],[t114757,t104]) ).
cnf(t489,plain,
domain(addition(X1,multiplication(domain(X1),X2))) = domain(X1),
inference(orient,[status(thm)],[t114758]) ).
cnf(t114768,plain,
domain(multiplication(domain(X1),addition(X1,X2))) = domain(X1),
inference(step,[status(thm)],[t489,t754]) ).
cnf(t792,plain,
domain(multiplication(domain(X1),addition(X1,X2))) = domain(X1),
inference(rw,[status(thm)],[t114768]) ).
cnf(t793,plain,
domain(multiplication(domain(X1),addition(X1,X2))) = domain(X1),
inference(orient,[status(thm)],[t792]) ).
cnf(t114865,plain,
domain(multiplication(domain(X1),X2)) = multiplication(domain(multiplication(domain(X1),X2)),domain(X1)),
inference(step,[status(thm)],[t3763,t793]) ).
cnf(t7745,plain,
multiplication(domain(multiplication(domain(X1),X2)),domain(X1)) = domain(multiplication(domain(X1),X2)),
inference(orient,[status(thm)],[t114865]) ).
cnf(t115139,plain,
multiplication(domain(X1),domain(X2)) = domain(multiplication(domain(X2),X1)),
inference(step,[status(thm)],[t74757,t7745]) ).
cnf(t74992,plain,
domain(multiplication(domain(X1),X2)) = multiplication(domain(X2),domain(X1)),
inference(orient,[status(thm)],[t115139]) ).
cnf(t75038,plain,
domain(addition(X1,multiplication(domain(X2),X3))) = addition(domain(X1),multiplication(domain(X3),domain(X2))),
inference(cp,[status(thm)],[t59,t74992]) ).
cnf(t76781,plain,
addition(domain(X1),multiplication(domain(X2),domain(X3))) = domain(addition(X1,multiplication(domain(X3),X2))),
inference(orient,[status(thm)],[t75038]) ).
cnf(t139,plain,
true = leq(domain(X1),domain(addition(X2,X1))),
inference(cp,[status(thm)],[t138,t59]) ).
cnf(t337,plain,
leq(domain(X1),domain(addition(X2,X1))) = true,
inference(orient,[status(thm)],[t139]) ).
cnf(t346,plain,
true = leq(domain(multiplication(X1,X2)),domain(multiplication(X1,addition(one,X2)))),
inference(cp,[status(thm)],[t337,t254]) ).
cnf(t114754,plain,
true = leq(domain(multiplication(X1,X2)),domain(X1)),
inference(step,[status(thm)],[t346,t204]) ).
cnf(t423,plain,
leq(domain(multiplication(X1,X2)),domain(X1)) = true,
inference(orient,[status(thm)],[t114754]) ).
cnf(t539,plain,
multiplication(domain(addition(X1,X2)),multiplication(X1,X3)) = multiplication(X1,X3),
inference(cp,[status(thm)],[t66,t530]) ).
cnf(t1480,plain,
multiplication(domain(addition(X1,X2)),multiplication(X1,X3)) = multiplication(X1,X3),
inference(orient,[status(thm)],[t539]) ).
cnf(t1510,plain,
true = leq(domain(multiplication(X1,X2)),domain(domain(addition(X1,X3)))),
inference(cp,[status(thm)],[t423,t1480]) ).
cnf(t114787,plain,
true = leq(domain(multiplication(X1,X2)),domain(addition(X1,X3))),
inference(step,[status(thm)],[t1510,t104]) ).
cnf(t2288,plain,
leq(domain(multiplication(X1,X2)),domain(addition(X1,X3))) = true,
inference(orient,[status(thm)],[t114787]) ).
cnf(t2308,plain,
domain(addition(X1,X2)) = ifeq(true,true,addition(domain(multiplication(X1,X3)),domain(addition(X1,X2))),domain(addition(X1,X2))),
inference(cp,[status(thm)],[t29,t2288]) ).
cnf(t114815,plain,
domain(addition(X1,X2)) = addition(domain(multiplication(X1,X3)),domain(addition(X1,X2))),
inference(step,[status(thm)],[t2308,t28]) ).
cnf(t114816,plain,
domain(addition(X1,X2)) = domain(addition(multiplication(X1,X3),addition(X1,X2))),
inference(step,[status(thm)],[t114815,t59]) ).
cnf(t142,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t138,t35]) ).
cnf(t353,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t142]) ).
cnf(t356,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t353,t32]) ).
cnf(t114755,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t356,t35]) ).
cnf(t431,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t114755]) ).
cnf(t441,plain,
addition(X1,addition(X2,X3)) = ifeq(true,true,addition(X2,addition(X1,addition(X2,X3))),addition(X1,addition(X2,X3))),
inference(cp,[status(thm)],[t29,t431]) ).
cnf(t114780,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,addition(X2,X3))),
inference(step,[status(thm)],[t441,t28]) ).
cnf(t152,plain,
addition(X1,addition(addition(X2,X1),X3)) = addition(addition(X1,X2),X3),
inference(cp,[status(thm)],[t35,t145]) ).
cnf(t114778,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(addition(X1,X2),X3),
inference(step,[status(thm)],[t152,t35]) ).
cnf(t114779,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X1,addition(X2,X3)),
inference(step,[status(thm)],[t114778,t35]) ).
cnf(t1361,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t114779]) ).
cnf(t114781,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(step,[status(thm)],[t114780,t1361]) ).
cnf(t1409,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(orient,[status(thm)],[t114781]) ).
cnf(t114817,plain,
domain(addition(X1,X2)) = domain(addition(X1,addition(multiplication(X1,X3),X2))),
inference(step,[status(thm)],[t114816,t1409]) ).
cnf(t4407,plain,
domain(addition(X1,addition(multiplication(X1,X2),X3))) = domain(addition(X1,X3)),
inference(orient,[status(thm)],[t114817]) ).
cnf(t4413,plain,
domain(addition(X1,multiplication(X2,X3))) = domain(addition(X1,multiplication(addition(X1,X2),X3))),
inference(cp,[status(thm)],[t4407,t47]) ).
cnf(t13127,plain,
domain(addition(X1,multiplication(addition(X1,X2),X3))) = domain(addition(X1,multiplication(X2,X3))),
inference(orient,[status(thm)],[t4413]) ).
cnf(t13144,plain,
domain(addition(domain(X1),multiplication(domain(X2),X3))) = domain(addition(domain(X1),multiplication(domain(addition(X1,X2)),X3))),
inference(cp,[status(thm)],[t13127,t59]) ).
cnf(t115244,plain,
domain(addition(X1,multiplication(domain(X2),X3))) = domain(addition(domain(X1),multiplication(domain(addition(X1,X2)),X3))),
inference(step,[status(thm)],[t13144,t167]) ).
cnf(t115245,plain,
domain(addition(X1,multiplication(domain(X2),X3))) = domain(addition(X1,multiplication(domain(addition(X1,X2)),X3))),
inference(step,[status(thm)],[t115244,t167]) ).
cnf(t540,plain,
multiplication(domain(addition(X1,X2)),addition(X1,X3)) = addition(X1,multiplication(domain(addition(X1,X2)),X3)),
inference(cp,[status(thm)],[t53,t530]) ).
cnf(t24122,plain,
addition(X1,multiplication(domain(addition(X1,X2)),X3)) = multiplication(domain(addition(X1,X2)),addition(X1,X3)),
inference(orient,[status(thm)],[t540]) ).
cnf(t115246,plain,
domain(addition(X1,multiplication(domain(X2),X3))) = domain(multiplication(domain(addition(X1,X2)),addition(X1,X3))),
inference(step,[status(thm)],[t115245,t24122]) ).
cnf(t115247,plain,
domain(addition(X1,multiplication(domain(X2),X3))) = multiplication(domain(addition(X1,X3)),domain(addition(X1,X2))),
inference(step,[status(thm)],[t115246,t74992]) ).
cnf(t114313,plain,
multiplication(domain(addition(X1,X2)),domain(addition(X1,X3))) = domain(addition(X1,multiplication(domain(X3),X2))),
inference(orient,[status(thm)],[t115247]) ).
fof(f17,conjecture,
! [X0,X1,X2] : addition(domain(X0),multiplication(domain(X1),domain(X2))) = multiplication(addition(domain(X0),domain(X1)),addition(domain(X0),domain(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0,X1,X2] : addition(domain(X0),multiplication(domain(X1),domain(X2))) = multiplication(addition(domain(X0),domain(X1)),addition(domain(X0),domain(X2))),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0,X1,X2] : addition(domain(X0),multiplication(domain(X1),domain(X2))) != multiplication(addition(domain(X0),domain(X1)),addition(domain(X0),domain(X2))),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
addition(domain(sk0),multiplication(domain(sk1),domain(sk2))) != multiplication(addition(domain(sk0),domain(sk1)),addition(domain(sk0),domain(sk2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f17_nnf]) ).
cnf(c18,plain,
addition(domain(sk0),multiplication(domain(sk1),domain(sk2))) != multiplication(addition(domain(sk0),domain(sk1)),addition(domain(sk0),domain(sk2))),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(addition(domain(sk0),domain(sk1)),addition(domain(sk0),domain(sk2))) != addition(domain(sk0),multiplication(domain(sk1),domain(sk2))),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
domain(addition(sk0,multiplication(domain(sk2),sk1))) != addition(domain(sk0),multiplication(domain(sk1),domain(sk2))),
inference(rw,[status(thm)],[goal_0,t76781]) ).
cnf(g0_1,plain,
domain(addition(sk0,multiplication(domain(sk2),sk1))) != multiplication(addition(domain(sk0),domain(sk1)),domain(addition(sk0,sk2))),
inference(rw,[status(thm)],[g0_0,t59]) ).
cnf(g0_2,plain,
domain(addition(sk0,multiplication(domain(sk2),sk1))) != multiplication(domain(addition(sk0,sk1)),domain(addition(sk0,sk2))),
inference(rw,[status(thm)],[g0_1,t59]) ).
cnf(g0_3,plain,
domain(addition(sk0,multiplication(domain(sk2),sk1))) != domain(addition(sk0,multiplication(domain(sk2),sk1))),
inference(rw,[status(thm)],[g0_2,t114313]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE071+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 18:53:04 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 48.65/7.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.65/7.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------