%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE019+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 : n007.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 01:51:22 PM UTC 2026
% Result : Theorem 98.39s 14.52s
% Output : Proof 98.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 17
% Syntax : Number of formulae : 385 ( 362 unt; 0 def)
% Number of atoms : 450 ( 387 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 102 ( 37 ~; 30 |; 26 &)
% ( 4 <=>; 3 =>; 2 <=; 0 <~>)
% Maximal formula depth : 9 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 352 ( 26 sgn 83 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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',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(t180,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t470,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t180]) ).
fof(f14,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f14_nnf,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c19,plain,
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi19,axiom,
ifeq(test(X0),true,ifeq(c(X0),X1,complement(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> ( leq(multiplication(X0,c(X1)),X2)
<= leq(X0,addition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> ( leq(multiplication(X0,c(X1)),X2)
<= leq(X0,addition(X1,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X0,c(X1)),X2)
& leq(X0,addition(X1,X2))
& test(X2)
& test(X1)
& test(X0) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( ~ leq(multiplication(sk1,c(sk2)),sk3)
& leq(sk1,addition(sk2,sk3))
& test(sk3)
& test(sk2)
& test(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f16_nnf]) ).
cnf(c23,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi23,negated_conjecture,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(hi30,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h23,plain,
complement(sk2,or(c(sk2),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi30]) ).
fof(f13,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f13_nnf,plain,
! [X0,X1] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X1,X0] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c15,plain,
( multiplication(X0,X1) = zero
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi15,axiom,
ifeq(complement(X0,X1),true,multiplication(X1,X0),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t94,plain,
multiplication(or(c(sk2),false),sk2) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h23]) ).
cnf(t10,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t66438,plain,
multiplication(c(sk2),sk2) = zero,
inference(step,[status(thm)],[t94,t256]) ).
cnf(t496,plain,
multiplication(c(sk2),sk2) = zero,
inference(orient,[status(thm)],[t66438]) ).
cnf(t499,plain,
multiplication(c(sk2),addition(X1,sk2)) = addition(multiplication(c(sk2),X1),zero),
inference(cp,[status(thm)],[t470,t496]) ).
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(t4,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t259,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t66710,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(step,[status(thm)],[t499,t259]) ).
cnf(t3594,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t66710]) ).
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(t14,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t367,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t14]) ).
cnf(t3596,plain,
multiplication(c(sk2),X1) = multiplication(c(sk2),addition(sk2,X1)),
inference(cp,[status(thm)],[t3594,t367]) ).
cnf(t4226,plain,
multiplication(c(sk2),addition(sk2,X1)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t3596]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t154,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t578,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t154]) ).
fof(f12,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
fof(f12_nnf,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| test(X0) )
& ( complement(sk0(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f12_nnf]) ).
cnf(c13,plain,
( complement(sk0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t158,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t335,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t158]) ).
cnf(t1,plain,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t287,plain,
test(sk2) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t337,plain,
true = ifeq(true,true,complement(sk0(sk2),sk2),true),
inference(cp,[status(thm)],[t335,t287]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(t66451,plain,
true = complement(sk0(sk2),sk2),
inference(step,[status(thm)],[t337,t262]) ).
cnf(t621,plain,
complement(sk0(sk2),sk2) = true,
inference(orient,[status(thm)],[t66451]) ).
cnf(t622,plain,
one = ifeq(true,true,addition(sk2,sk0(sk2)),one),
inference(cp,[status(thm)],[t578,t621]) ).
cnf(t66483,plain,
one = addition(sk2,sk0(sk2)),
inference(step,[status(thm)],[t622,t262]) ).
cnf(t678,plain,
addition(sk2,sk0(sk2)) = one,
inference(orient,[status(thm)],[t66483]) ).
cnf(t4234,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(c(sk2),one),
inference(cp,[status(thm)],[t4226,t678]) ).
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',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(t181,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t462,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t181]) ).
cnf(t156,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t548,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(orient,[status(thm)],[t156]) ).
cnf(t624,plain,
zero = ifeq(true,true,multiplication(sk2,sk0(sk2)),zero),
inference(cp,[status(thm)],[t548,t621]) ).
cnf(t66485,plain,
zero = multiplication(sk2,sk0(sk2)),
inference(step,[status(thm)],[t624,t262]) ).
cnf(t692,plain,
multiplication(sk2,sk0(sk2)) = zero,
inference(orient,[status(thm)],[t66485]) ).
cnf(t697,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = addition(zero,multiplication(X1,sk0(sk2))),
inference(cp,[status(thm)],[t462,t692]) ).
cnf(t368,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t367,t259]) ).
cnf(t605,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t368]) ).
cnf(t66732,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(step,[status(thm)],[t697,t605]) ).
cnf(t3849,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(orient,[status(thm)],[t66732]) ).
cnf(hi17,axiom,
ifeq(complement(X0,X1),true,addition(X1,X0),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t63,plain,
addition(or(c(sk2),false),sk2) = one,
inference(hyper_resolution,[status(thm)],[hi17,h23]) ).
cnf(t66412,plain,
addition(sk2,or(c(sk2),false)) = one,
inference(step,[status(thm)],[t63,t367]) ).
cnf(t66413,plain,
addition(sk2,c(sk2)) = one,
inference(step,[status(thm)],[t66412,t256]) ).
cnf(t407,plain,
addition(sk2,c(sk2)) = one,
inference(orient,[status(thm)],[t66413]) ).
cnf(t3856,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(one,sk0(sk2)),
inference(cp,[status(thm)],[t3849,t407]) ).
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(t8,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t261,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t66733,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(step,[status(thm)],[t3856,t261]) ).
cnf(t3868,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(orient,[status(thm)],[t66733]) ).
cnf(t66776,plain,
sk0(sk2) = multiplication(c(sk2),one),
inference(step,[status(thm)],[t4234,t3868]) ).
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(t6,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t260,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t66777,plain,
sk0(sk2) = c(sk2),
inference(step,[status(thm)],[t66776,t260]) ).
cnf(t4244,plain,
c(sk2) = sk0(sk2),
inference(orient,[status(thm)],[t66777]) ).
cnf(c26,plain,
~ leq(multiplication(sk1,c(sk2)),sk3),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t83,plain,
leq(multiplication(sk1,c(sk2)),sk3) = false,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t271,plain,
leq(multiplication(sk1,c(sk2)),sk3) = false,
inference(orient,[status(thm)],[t83]) ).
cnf(t66797,plain,
leq(multiplication(sk1,sk0(sk2)),sk3) = false,
inference(step,[status(thm)],[t271,t4244]) ).
cnf(t4262,plain,
leq(multiplication(sk1,sk0(sk2)),sk3) = false,
inference(rw,[status(thm)],[t66797]) ).
cnf(t4371,plain,
leq(multiplication(sk1,sk0(sk2)),sk3) = false,
inference(orient,[status(thm)],[t4262]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/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(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t153,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t314,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t153]) ).
cnf(t370,plain,
true = ifeq(addition(X1,X2),X1,leq(X2,X1),true),
inference(cp,[status(thm)],[t314,t367]) ).
cnf(t8036,plain,
ifeq(addition(X1,X2),X1,leq(X2,X1),true) = true,
inference(orient,[status(thm)],[t370]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t157,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t264,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t157]) ).
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(t152,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t373,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t152]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/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(t3,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t258,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t376,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t373,t258]) ).
cnf(t724,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t376]) ).
cnf(t739,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t314,t724]) ).
cnf(t66496,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t739,t262]) ).
cnf(t762,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t66496]) ).
cnf(t769,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t762,t367]) ).
cnf(t779,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t769]) ).
cnf(t788,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t779,t373]) ).
cnf(t2562,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t788]) ).
cnf(t780,plain,
true = leq(multiplication(X1,X2),multiplication(addition(X3,X1),X2)),
inference(cp,[status(thm)],[t779,t462]) ).
cnf(t26369,plain,
leq(multiplication(X1,X2),multiplication(addition(X3,X1),X2)) = true,
inference(orient,[status(thm)],[t780]) ).
cnf(t736,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t724,t367]) ).
cnf(t845,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t736]) ).
cnf(c24,plain,
test(sk3),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi24,negated_conjecture,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h22,plain,
complement(sk3,or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi24,hi30]) ).
cnf(t64,plain,
addition(or(c(sk3),false),sk3) = one,
inference(hyper_resolution,[status(thm)],[hi17,h22]) ).
cnf(t66416,plain,
addition(sk3,or(c(sk3),false)) = one,
inference(step,[status(thm)],[t64,t367]) ).
cnf(t66417,plain,
addition(sk3,c(sk3)) = one,
inference(step,[status(thm)],[t66416,t256]) ).
cnf(t417,plain,
addition(sk3,c(sk3)) = one,
inference(orient,[status(thm)],[t66417]) ).
cnf(t726,plain,
addition(sk3,c(sk3)) = addition(sk3,one),
inference(cp,[status(thm)],[t724,t417]) ).
cnf(t66490,plain,
one = addition(sk3,one),
inference(step,[status(thm)],[t726,t417]) ).
cnf(t741,plain,
addition(sk3,one) = one,
inference(orient,[status(thm)],[t66490]) ).
cnf(t744,plain,
addition(sk3,addition(one,X1)) = addition(one,X1),
inference(cp,[status(thm)],[t373,t741]) ).
cnf(t867,plain,
addition(sk3,addition(one,X1)) = addition(one,X1),
inference(orient,[status(thm)],[t744]) ).
cnf(t871,plain,
addition(addition(one,X1),sk3) = addition(addition(one,X1),addition(one,X1)),
inference(cp,[status(thm)],[t845,t867]) ).
cnf(t66514,plain,
addition(one,addition(X1,sk3)) = addition(addition(one,X1),addition(one,X1)),
inference(step,[status(thm)],[t871,t373]) ).
cnf(t66515,plain,
addition(one,addition(X1,sk3)) = addition(one,addition(X1,addition(one,X1))),
inference(step,[status(thm)],[t66514,t373]) ).
cnf(t66516,plain,
addition(one,addition(X1,sk3)) = addition(one,addition(X1,one)),
inference(step,[status(thm)],[t66515,t845]) ).
cnf(t66517,plain,
addition(one,addition(X1,sk3)) = addition(one,X1),
inference(step,[status(thm)],[t66516,t845]) ).
cnf(t933,plain,
addition(one,addition(X1,sk3)) = addition(one,X1),
inference(orient,[status(thm)],[t66517]) ).
cnf(t937,plain,
addition(one,X1) = addition(one,addition(sk3,X1)),
inference(cp,[status(thm)],[t933,t367]) ).
cnf(t1001,plain,
addition(one,addition(sk3,X1)) = addition(one,X1),
inference(orient,[status(thm)],[t937]) ).
cnf(t464,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t462,t261]) ).
cnf(t1129,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t464]) ).
cnf(t1145,plain,
addition(one,multiplication(X1,sk3)) = addition(one,multiplication(addition(one,X1),sk3)),
inference(cp,[status(thm)],[t1001,t1129]) ).
cnf(t95,plain,
multiplication(or(c(sk3),false),sk3) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h22]) ).
cnf(t66439,plain,
multiplication(c(sk3),sk3) = zero,
inference(step,[status(thm)],[t95,t256]) ).
cnf(t504,plain,
multiplication(c(sk3),sk3) = zero,
inference(orient,[status(thm)],[t66439]) ).
cnf(t509,plain,
multiplication(addition(X1,c(sk3)),sk3) = addition(multiplication(X1,sk3),zero),
inference(cp,[status(thm)],[t462,t504]) ).
cnf(t66571,plain,
multiplication(addition(X1,c(sk3)),sk3) = multiplication(X1,sk3),
inference(step,[status(thm)],[t509,t259]) ).
cnf(t1674,plain,
multiplication(addition(X1,c(sk3)),sk3) = multiplication(X1,sk3),
inference(orient,[status(thm)],[t66571]) ).
cnf(t1675,plain,
multiplication(sk3,sk3) = multiplication(one,sk3),
inference(cp,[status(thm)],[t1674,t417]) ).
cnf(t66572,plain,
multiplication(sk3,sk3) = sk3,
inference(step,[status(thm)],[t1675,t261]) ).
cnf(t1689,plain,
multiplication(sk3,sk3) = sk3,
inference(orient,[status(thm)],[t66572]) ).
cnf(t1697,plain,
multiplication(addition(sk3,X1),sk3) = addition(sk3,multiplication(X1,sk3)),
inference(cp,[status(thm)],[t462,t1689]) ).
cnf(t66580,plain,
multiplication(addition(sk3,X1),sk3) = multiplication(addition(one,X1),sk3),
inference(step,[status(thm)],[t1697,t1129]) ).
cnf(t1781,plain,
multiplication(addition(one,X1),sk3) = multiplication(addition(sk3,X1),sk3),
inference(orient,[status(thm)],[t66580]) ).
cnf(t67062,plain,
addition(one,multiplication(X1,sk3)) = addition(one,multiplication(addition(sk3,X1),sk3)),
inference(step,[status(thm)],[t1145,t1781]) ).
cnf(t8545,plain,
addition(one,multiplication(addition(sk3,X1),sk3)) = addition(one,multiplication(X1,sk3)),
inference(orient,[status(thm)],[t67062]) ).
cnf(c16,plain,
( multiplication(X1,X0) = zero
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t155,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t564,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t155]) ).
cnf(t2,plain,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t289,plain,
test(sk3) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t336,plain,
true = ifeq(true,true,complement(sk0(sk3),sk3),true),
inference(cp,[status(thm)],[t335,t289]) ).
cnf(t66450,plain,
true = complement(sk0(sk3),sk3),
inference(step,[status(thm)],[t336,t262]) ).
cnf(t614,plain,
complement(sk0(sk3),sk3) = true,
inference(orient,[status(thm)],[t66450]) ).
cnf(t616,plain,
zero = ifeq(true,true,multiplication(sk0(sk3),sk3),zero),
inference(cp,[status(thm)],[t564,t614]) ).
cnf(t66481,plain,
zero = multiplication(sk0(sk3),sk3),
inference(step,[status(thm)],[t616,t262]) ).
cnf(t661,plain,
multiplication(sk0(sk3),sk3) = zero,
inference(orient,[status(thm)],[t66481]) ).
cnf(t666,plain,
multiplication(addition(sk0(sk3),X1),sk3) = addition(zero,multiplication(X1,sk3)),
inference(cp,[status(thm)],[t462,t661]) ).
cnf(t66591,plain,
multiplication(addition(sk0(sk3),X1),sk3) = multiplication(X1,sk3),
inference(step,[status(thm)],[t666,t605]) ).
cnf(t1938,plain,
multiplication(addition(sk0(sk3),X1),sk3) = multiplication(X1,sk3),
inference(orient,[status(thm)],[t66591]) ).
cnf(t615,plain,
one = ifeq(true,true,addition(sk3,sk0(sk3)),one),
inference(cp,[status(thm)],[t578,t614]) ).
cnf(t66480,plain,
one = addition(sk3,sk0(sk3)),
inference(step,[status(thm)],[t615,t262]) ).
cnf(t656,plain,
addition(sk3,sk0(sk3)) = one,
inference(orient,[status(thm)],[t66480]) ).
cnf(t658,plain,
addition(sk3,addition(sk0(sk3),X1)) = addition(one,X1),
inference(cp,[status(thm)],[t373,t656]) ).
cnf(t1924,plain,
addition(sk3,addition(sk0(sk3),X1)) = addition(one,X1),
inference(orient,[status(thm)],[t658]) ).
cnf(t1933,plain,
addition(addition(sk0(sk3),X1),sk3) = addition(addition(sk0(sk3),X1),addition(one,X1)),
inference(cp,[status(thm)],[t845,t1924]) ).
cnf(t66881,plain,
addition(sk0(sk3),addition(X1,sk3)) = addition(addition(sk0(sk3),X1),addition(one,X1)),
inference(step,[status(thm)],[t1933,t373]) ).
cnf(t66882,plain,
addition(sk0(sk3),addition(X1,sk3)) = addition(sk0(sk3),addition(X1,addition(one,X1))),
inference(step,[status(thm)],[t66881,t373]) ).
cnf(t66883,plain,
addition(sk0(sk3),addition(X1,sk3)) = addition(sk0(sk3),addition(X1,one)),
inference(step,[status(thm)],[t66882,t845]) ).
cnf(t782,plain,
true = leq(sk0(sk3),one),
inference(cp,[status(thm)],[t779,t656]) ).
cnf(t791,plain,
leq(sk0(sk3),one) = true,
inference(orient,[status(thm)],[t782]) ).
cnf(t792,plain,
one = ifeq(true,true,addition(sk0(sk3),one),one),
inference(cp,[status(thm)],[t264,t791]) ).
cnf(t66497,plain,
one = addition(sk0(sk3),one),
inference(step,[status(thm)],[t792,t262]) ).
cnf(t66498,plain,
one = addition(one,sk0(sk3)),
inference(step,[status(thm)],[t66497,t367]) ).
cnf(t800,plain,
addition(one,sk0(sk3)) = one,
inference(orient,[status(thm)],[t66498]) ).
cnf(t2604,plain,
true = leq(sk0(sk3),addition(X1,one)),
inference(cp,[status(thm)],[t2562,t800]) ).
cnf(t2667,plain,
leq(sk0(sk3),addition(X1,one)) = true,
inference(orient,[status(thm)],[t2604]) ).
cnf(t2669,plain,
addition(X1,one) = ifeq(true,true,addition(sk0(sk3),addition(X1,one)),addition(X1,one)),
inference(cp,[status(thm)],[t264,t2667]) ).
cnf(t66644,plain,
addition(X1,one) = addition(sk0(sk3),addition(X1,one)),
inference(step,[status(thm)],[t2669,t262]) ).
cnf(t2795,plain,
addition(sk0(sk3),addition(X1,one)) = addition(X1,one),
inference(orient,[status(thm)],[t66644]) ).
cnf(t66884,plain,
addition(sk0(sk3),addition(X1,sk3)) = addition(X1,one),
inference(step,[status(thm)],[t66883,t2795]) ).
cnf(t5414,plain,
addition(sk0(sk3),addition(X1,sk3)) = addition(X1,one),
inference(orient,[status(thm)],[t66884]) ).
cnf(t5427,plain,
multiplication(addition(X1,sk3),sk3) = multiplication(addition(X1,one),sk3),
inference(cp,[status(thm)],[t1938,t5414]) ).
cnf(t5486,plain,
multiplication(addition(X1,one),sk3) = multiplication(addition(X1,sk3),sk3),
inference(orient,[status(thm)],[t5427]) ).
cnf(c22,plain,
test(sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t0,plain,
test(sk1) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t285,plain,
test(sk1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t338,plain,
true = ifeq(true,true,complement(sk0(sk1),sk1),true),
inference(cp,[status(thm)],[t335,t285]) ).
cnf(t66452,plain,
true = complement(sk0(sk1),sk1),
inference(step,[status(thm)],[t338,t262]) ).
cnf(t628,plain,
complement(sk0(sk1),sk1) = true,
inference(orient,[status(thm)],[t66452]) ).
cnf(t629,plain,
one = ifeq(true,true,addition(sk1,sk0(sk1)),one),
inference(cp,[status(thm)],[t578,t628]) ).
cnf(t66486,plain,
one = addition(sk1,sk0(sk1)),
inference(step,[status(thm)],[t629,t262]) ).
cnf(t700,plain,
addition(sk1,sk0(sk1)) = one,
inference(orient,[status(thm)],[t66486]) ).
cnf(t730,plain,
addition(sk1,sk0(sk1)) = addition(sk1,one),
inference(cp,[status(thm)],[t724,t700]) ).
cnf(t66492,plain,
one = addition(sk1,one),
inference(step,[status(thm)],[t730,t700]) ).
cnf(t753,plain,
addition(sk1,one) = one,
inference(orient,[status(thm)],[t66492]) ).
cnf(t5488,plain,
multiplication(addition(sk1,sk3),sk3) = multiplication(one,sk3),
inference(cp,[status(thm)],[t5486,t753]) ).
cnf(t66891,plain,
multiplication(addition(sk3,sk1),sk3) = multiplication(one,sk3),
inference(step,[status(thm)],[t5488,t367]) ).
cnf(t66892,plain,
multiplication(addition(sk3,sk1),sk3) = sk3,
inference(step,[status(thm)],[t66891,t261]) ).
cnf(t5512,plain,
multiplication(addition(sk3,sk1),sk3) = sk3,
inference(orient,[status(thm)],[t66892]) ).
cnf(t8551,plain,
addition(one,multiplication(sk1,sk3)) = addition(one,sk3),
inference(cp,[status(thm)],[t8545,t5512]) ).
cnf(t67063,plain,
addition(one,multiplication(sk1,sk3)) = addition(sk3,one),
inference(step,[status(thm)],[t8551,t367]) ).
cnf(t67064,plain,
addition(one,multiplication(sk1,sk3)) = one,
inference(step,[status(thm)],[t67063,t741]) ).
cnf(t8607,plain,
addition(one,multiplication(sk1,sk3)) = one,
inference(orient,[status(thm)],[t67064]) ).
cnf(t26771,plain,
true = leq(multiplication(multiplication(sk1,sk3),X1),multiplication(one,X1)),
inference(cp,[status(thm)],[t26369,t8607]) ).
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(t159,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t478,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t159]) ).
cnf(t67620,plain,
true = leq(multiplication(sk1,multiplication(sk3,X1)),multiplication(one,X1)),
inference(step,[status(thm)],[t26771,t478]) ).
cnf(t67621,plain,
true = leq(multiplication(sk1,multiplication(sk3,X1)),X1),
inference(step,[status(thm)],[t67620,t261]) ).
cnf(t27092,plain,
leq(multiplication(sk1,multiplication(sk3,X1)),X1) = true,
inference(orient,[status(thm)],[t67621]) ).
cnf(t27123,plain,
X1 = ifeq(true,true,addition(multiplication(sk1,multiplication(sk3,X1)),X1),X1),
inference(cp,[status(thm)],[t264,t27092]) ).
cnf(t67645,plain,
X1 = addition(multiplication(sk1,multiplication(sk3,X1)),X1),
inference(step,[status(thm)],[t27123,t262]) ).
cnf(t67646,plain,
X1 = addition(X1,multiplication(sk1,multiplication(sk3,X1))),
inference(step,[status(thm)],[t67645,t367]) ).
cnf(t28921,plain,
addition(X1,multiplication(sk1,multiplication(sk3,X1))) = X1,
inference(orient,[status(thm)],[t67646]) ).
cnf(t29012,plain,
true = leq(multiplication(sk1,multiplication(sk3,X1)),addition(X2,X1)),
inference(cp,[status(thm)],[t2562,t28921]) ).
cnf(t65671,plain,
leq(multiplication(sk1,multiplication(sk3,X1)),addition(X2,X1)) = true,
inference(orient,[status(thm)],[t29012]) ).
cnf(t65710,plain,
true = leq(multiplication(sk1,sk3),addition(X1,sk3)),
inference(cp,[status(thm)],[t65671,t1689]) ).
cnf(t65936,plain,
leq(multiplication(sk1,sk3),addition(X1,sk3)) = true,
inference(orient,[status(thm)],[t65710]) ).
cnf(t65939,plain,
addition(X1,sk3) = ifeq(true,true,addition(multiplication(sk1,sk3),addition(X1,sk3)),addition(X1,sk3)),
inference(cp,[status(thm)],[t264,t65936]) ).
cnf(t68152,plain,
addition(X1,sk3) = addition(multiplication(sk1,sk3),addition(X1,sk3)),
inference(step,[status(thm)],[t65939,t262]) ).
cnf(t375,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(cp,[status(thm)],[t373,t367]) ).
cnf(t10302,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(orient,[status(thm)],[t375]) ).
cnf(t68153,plain,
addition(X1,sk3) = addition(sk3,addition(multiplication(sk1,sk3),X1)),
inference(step,[status(thm)],[t68152,t10302]) ).
cnf(t65950,plain,
addition(sk3,addition(multiplication(sk1,sk3),X1)) = addition(X1,sk3),
inference(orient,[status(thm)],[t68153]) ).
cnf(t65966,plain,
addition(multiplication(sk1,X1),sk3) = addition(sk3,multiplication(sk1,addition(sk3,X1))),
inference(cp,[status(thm)],[t65950,t470]) ).
cnf(t68156,plain,
addition(sk3,multiplication(sk1,X1)) = addition(sk3,multiplication(sk1,addition(sk3,X1))),
inference(step,[status(thm)],[t65966,t367]) ).
cnf(t66173,plain,
addition(sk3,multiplication(sk1,addition(sk3,X1))) = addition(sk3,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t68156]) ).
cnf(t631,plain,
zero = ifeq(true,true,multiplication(sk1,sk0(sk1)),zero),
inference(cp,[status(thm)],[t548,t628]) ).
cnf(t66488,plain,
zero = multiplication(sk1,sk0(sk1)),
inference(step,[status(thm)],[t631,t262]) ).
cnf(t714,plain,
multiplication(sk1,sk0(sk1)) = zero,
inference(orient,[status(thm)],[t66488]) ).
cnf(t717,plain,
multiplication(sk1,addition(sk0(sk1),X1)) = addition(zero,multiplication(sk1,X1)),
inference(cp,[status(thm)],[t470,t714]) ).
cnf(t66601,plain,
multiplication(sk1,addition(sk0(sk1),X1)) = multiplication(sk1,X1),
inference(step,[status(thm)],[t717,t605]) ).
cnf(t2096,plain,
multiplication(sk1,addition(sk0(sk1),X1)) = multiplication(sk1,X1),
inference(orient,[status(thm)],[t66601]) ).
cnf(t860,plain,
addition(X1,addition(X2,X3)) = addition(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t845,t373]) ).
cnf(t6450,plain,
addition(X1,addition(X2,addition(X3,X1))) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t860]) ).
cnf(t2576,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t2562,t367]) ).
cnf(t66687,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t2576,t373]) ).
cnf(t3358,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t66687]) ).
cnf(t472,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t470,t260]) ).
cnf(t1153,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t472]) ).
cnf(t702,plain,
addition(sk1,addition(sk0(sk1),X1)) = addition(one,X1),
inference(cp,[status(thm)],[t373,t700]) ).
cnf(t2056,plain,
addition(sk1,addition(sk0(sk1),X1)) = addition(one,X1),
inference(orient,[status(thm)],[t702]) ).
cnf(t2065,plain,
addition(addition(sk0(sk1),X1),sk1) = addition(addition(sk0(sk1),X1),addition(one,X1)),
inference(cp,[status(thm)],[t845,t2056]) ).
cnf(t66923,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(addition(sk0(sk1),X1),addition(one,X1)),
inference(step,[status(thm)],[t2065,t373]) ).
cnf(t66924,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(sk0(sk1),addition(X1,addition(one,X1))),
inference(step,[status(thm)],[t66923,t373]) ).
cnf(t66925,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(sk0(sk1),addition(X1,one)),
inference(step,[status(thm)],[t66924,t845]) ).
cnf(t784,plain,
true = leq(sk0(sk1),one),
inference(cp,[status(thm)],[t779,t700]) ).
cnf(t797,plain,
leq(sk0(sk1),one) = true,
inference(orient,[status(thm)],[t784]) ).
cnf(t798,plain,
one = ifeq(true,true,addition(sk0(sk1),one),one),
inference(cp,[status(thm)],[t264,t797]) ).
cnf(t66501,plain,
one = addition(sk0(sk1),one),
inference(step,[status(thm)],[t798,t262]) ).
cnf(t66502,plain,
one = addition(one,sk0(sk1)),
inference(step,[status(thm)],[t66501,t367]) ).
cnf(t812,plain,
addition(one,sk0(sk1)) = one,
inference(orient,[status(thm)],[t66502]) ).
cnf(t2603,plain,
true = leq(sk0(sk1),addition(X1,one)),
inference(cp,[status(thm)],[t2562,t812]) ).
cnf(t2663,plain,
leq(sk0(sk1),addition(X1,one)) = true,
inference(orient,[status(thm)],[t2603]) ).
cnf(t2665,plain,
addition(X1,one) = ifeq(true,true,addition(sk0(sk1),addition(X1,one)),addition(X1,one)),
inference(cp,[status(thm)],[t264,t2663]) ).
cnf(t66643,plain,
addition(X1,one) = addition(sk0(sk1),addition(X1,one)),
inference(step,[status(thm)],[t2665,t262]) ).
cnf(t2784,plain,
addition(sk0(sk1),addition(X1,one)) = addition(X1,one),
inference(orient,[status(thm)],[t66643]) ).
cnf(t66926,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(X1,one),
inference(step,[status(thm)],[t66925,t2784]) ).
cnf(t5882,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(X1,one),
inference(orient,[status(thm)],[t66926]) ).
cnf(t5888,plain,
addition(X1,one) = addition(sk0(sk1),addition(sk1,X1)),
inference(cp,[status(thm)],[t5882,t367]) ).
cnf(t5975,plain,
addition(sk0(sk1),addition(sk1,X1)) = addition(X1,one),
inference(orient,[status(thm)],[t5888]) ).
cnf(hi11,axiom,
ifeq(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(c25,plain,
leq(sk1,addition(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi25,negated_conjecture,
leq(sk1,addition(sk2,sk3)) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t120,plain,
addition(sk1,addition(sk2,sk3)) = addition(sk2,sk3),
inference(hyper_resolution,[status(thm)],[hi11,hi25]) ).
cnf(t66420,plain,
addition(sk1,addition(sk3,sk2)) = addition(sk2,sk3),
inference(step,[status(thm)],[t120,t367]) ).
cnf(t66421,plain,
addition(sk1,addition(sk3,sk2)) = addition(sk3,sk2),
inference(step,[status(thm)],[t66420,t367]) ).
cnf(t427,plain,
addition(sk1,addition(sk3,sk2)) = addition(sk3,sk2),
inference(orient,[status(thm)],[t66421]) ).
cnf(t5981,plain,
addition(addition(sk3,sk2),one) = addition(sk0(sk1),addition(sk3,sk2)),
inference(cp,[status(thm)],[t5975,t427]) ).
cnf(t66931,plain,
addition(sk3,addition(sk2,one)) = addition(sk0(sk1),addition(sk3,sk2)),
inference(step,[status(thm)],[t5981,t373]) ).
cnf(t869,plain,
addition(one,X1) = addition(sk3,addition(X1,one)),
inference(cp,[status(thm)],[t867,t367]) ).
cnf(t920,plain,
addition(sk3,addition(X1,one)) = addition(one,X1),
inference(orient,[status(thm)],[t869]) ).
cnf(t66932,plain,
addition(one,sk2) = addition(sk0(sk1),addition(sk3,sk2)),
inference(step,[status(thm)],[t66931,t920]) ).
cnf(t66933,plain,
addition(sk2,one) = addition(sk0(sk1),addition(sk3,sk2)),
inference(step,[status(thm)],[t66932,t367]) ).
cnf(t728,plain,
addition(sk2,c(sk2)) = addition(sk2,one),
inference(cp,[status(thm)],[t724,t407]) ).
cnf(t66491,plain,
one = addition(sk2,one),
inference(step,[status(thm)],[t728,t407]) ).
cnf(t747,plain,
addition(sk2,one) = one,
inference(orient,[status(thm)],[t66491]) ).
cnf(t66934,plain,
one = addition(sk0(sk1),addition(sk3,sk2)),
inference(step,[status(thm)],[t66933,t747]) ).
cnf(t5995,plain,
addition(sk0(sk1),addition(sk3,sk2)) = one,
inference(orient,[status(thm)],[t66934]) ).
cnf(t5999,plain,
addition(addition(sk3,sk2),sk0(sk1)) = addition(addition(sk3,sk2),one),
inference(cp,[status(thm)],[t845,t5995]) ).
cnf(t66937,plain,
addition(sk3,addition(sk2,sk0(sk1))) = addition(addition(sk3,sk2),one),
inference(step,[status(thm)],[t5999,t373]) ).
cnf(t66938,plain,
addition(sk3,addition(sk2,sk0(sk1))) = addition(sk3,addition(sk2,one)),
inference(step,[status(thm)],[t66937,t373]) ).
cnf(t66939,plain,
addition(sk3,addition(sk2,sk0(sk1))) = addition(one,sk2),
inference(step,[status(thm)],[t66938,t920]) ).
cnf(t66940,plain,
addition(sk3,addition(sk2,sk0(sk1))) = addition(sk2,one),
inference(step,[status(thm)],[t66939,t367]) ).
cnf(t66941,plain,
addition(sk3,addition(sk2,sk0(sk1))) = one,
inference(step,[status(thm)],[t66940,t747]) ).
cnf(t6032,plain,
addition(sk3,addition(sk2,sk0(sk1))) = one,
inference(orient,[status(thm)],[t66941]) ).
cnf(t6039,plain,
addition(addition(sk2,sk0(sk1)),sk3) = addition(addition(sk2,sk0(sk1)),one),
inference(cp,[status(thm)],[t845,t6032]) ).
cnf(t66942,plain,
addition(sk2,addition(sk0(sk1),sk3)) = addition(addition(sk2,sk0(sk1)),one),
inference(step,[status(thm)],[t6039,t373]) ).
cnf(t66943,plain,
addition(sk2,addition(sk3,sk0(sk1))) = addition(addition(sk2,sk0(sk1)),one),
inference(step,[status(thm)],[t66942,t367]) ).
cnf(t66944,plain,
addition(sk2,addition(sk3,sk0(sk1))) = addition(sk2,addition(sk0(sk1),one)),
inference(step,[status(thm)],[t66943,t373]) ).
cnf(t750,plain,
addition(sk2,addition(one,X1)) = addition(one,X1),
inference(cp,[status(thm)],[t373,t747]) ).
cnf(t882,plain,
addition(sk2,addition(one,X1)) = addition(one,X1),
inference(orient,[status(thm)],[t750]) ).
cnf(t884,plain,
addition(one,X1) = addition(sk2,addition(X1,one)),
inference(cp,[status(thm)],[t882,t367]) ).
cnf(t944,plain,
addition(sk2,addition(X1,one)) = addition(one,X1),
inference(orient,[status(thm)],[t884]) ).
cnf(t66945,plain,
addition(sk2,addition(sk3,sk0(sk1))) = addition(one,sk0(sk1)),
inference(step,[status(thm)],[t66944,t944]) ).
cnf(t66946,plain,
addition(sk2,addition(sk3,sk0(sk1))) = one,
inference(step,[status(thm)],[t66945,t812]) ).
cnf(t6045,plain,
addition(sk2,addition(sk3,sk0(sk1))) = one,
inference(orient,[status(thm)],[t66946]) ).
cnf(t6048,plain,
multiplication(addition(sk3,sk0(sk1)),sk0(sk2)) = multiplication(one,sk0(sk2)),
inference(cp,[status(thm)],[t3849,t6045]) ).
cnf(t66949,plain,
multiplication(addition(sk3,sk0(sk1)),sk0(sk2)) = sk0(sk2),
inference(step,[status(thm)],[t6048,t261]) ).
cnf(t6086,plain,
multiplication(addition(sk3,sk0(sk1)),sk0(sk2)) = sk0(sk2),
inference(orient,[status(thm)],[t66949]) ).
cnf(t6087,plain,
multiplication(addition(sk3,sk0(sk1)),addition(one,sk0(sk2))) = addition(addition(sk3,sk0(sk1)),sk0(sk2)),
inference(cp,[status(thm)],[t1153,t6086]) ).
cnf(t783,plain,
true = leq(sk0(sk2),one),
inference(cp,[status(thm)],[t779,t678]) ).
cnf(t794,plain,
leq(sk0(sk2),one) = true,
inference(orient,[status(thm)],[t783]) ).
cnf(t795,plain,
one = ifeq(true,true,addition(sk0(sk2),one),one),
inference(cp,[status(thm)],[t264,t794]) ).
cnf(t66499,plain,
one = addition(sk0(sk2),one),
inference(step,[status(thm)],[t795,t262]) ).
cnf(t66500,plain,
one = addition(one,sk0(sk2)),
inference(step,[status(thm)],[t66499,t367]) ).
cnf(t806,plain,
addition(one,sk0(sk2)) = one,
inference(orient,[status(thm)],[t66500]) ).
cnf(t66975,plain,
multiplication(addition(sk3,sk0(sk1)),one) = addition(addition(sk3,sk0(sk1)),sk0(sk2)),
inference(step,[status(thm)],[t6087,t806]) ).
cnf(t66976,plain,
addition(sk3,sk0(sk1)) = addition(addition(sk3,sk0(sk1)),sk0(sk2)),
inference(step,[status(thm)],[t66975,t260]) ).
cnf(t66977,plain,
addition(sk3,sk0(sk1)) = addition(sk3,addition(sk0(sk1),sk0(sk2))),
inference(step,[status(thm)],[t66976,t373]) ).
cnf(t66978,plain,
addition(sk3,sk0(sk1)) = addition(sk3,addition(sk0(sk2),sk0(sk1))),
inference(step,[status(thm)],[t66977,t367]) ).
cnf(t6375,plain,
addition(sk3,addition(sk0(sk2),sk0(sk1))) = addition(sk3,sk0(sk1)),
inference(orient,[status(thm)],[t66978]) ).
cnf(t6385,plain,
true = leq(sk0(sk2),addition(sk3,sk0(sk1))),
inference(cp,[status(thm)],[t3358,t6375]) ).
cnf(t6388,plain,
leq(sk0(sk2),addition(sk3,sk0(sk1))) = true,
inference(orient,[status(thm)],[t6385]) ).
cnf(t6389,plain,
addition(sk3,sk0(sk1)) = ifeq(true,true,addition(sk0(sk2),addition(sk3,sk0(sk1))),addition(sk3,sk0(sk1))),
inference(cp,[status(thm)],[t264,t6388]) ).
cnf(t66980,plain,
addition(sk3,sk0(sk1)) = addition(sk0(sk2),addition(sk3,sk0(sk1))),
inference(step,[status(thm)],[t6389,t262]) ).
cnf(t6398,plain,
addition(sk0(sk2),addition(sk3,sk0(sk1))) = addition(sk3,sk0(sk1)),
inference(orient,[status(thm)],[t66980]) ).
cnf(t6458,plain,
addition(sk0(sk1),addition(sk0(sk2),sk3)) = addition(sk0(sk1),addition(sk3,sk0(sk1))),
inference(cp,[status(thm)],[t6450,t6398]) ).
cnf(t66986,plain,
addition(sk0(sk1),addition(sk3,sk0(sk2))) = addition(sk0(sk1),addition(sk3,sk0(sk1))),
inference(step,[status(thm)],[t6458,t367]) ).
cnf(t66987,plain,
addition(sk0(sk1),addition(sk3,sk0(sk2))) = addition(sk0(sk1),sk3),
inference(step,[status(thm)],[t66986,t845]) ).
cnf(t66988,plain,
addition(sk0(sk1),addition(sk3,sk0(sk2))) = addition(sk3,sk0(sk1)),
inference(step,[status(thm)],[t66987,t367]) ).
cnf(t6601,plain,
addition(sk0(sk1),addition(sk3,sk0(sk2))) = addition(sk3,sk0(sk1)),
inference(orient,[status(thm)],[t66988]) ).
cnf(t6611,plain,
multiplication(sk1,addition(sk3,sk0(sk2))) = multiplication(sk1,addition(sk3,sk0(sk1))),
inference(cp,[status(thm)],[t2096,t6601]) ).
cnf(t718,plain,
multiplication(sk1,addition(X1,sk0(sk1))) = addition(multiplication(sk1,X1),zero),
inference(cp,[status(thm)],[t470,t714]) ).
cnf(t66602,plain,
multiplication(sk1,addition(X1,sk0(sk1))) = multiplication(sk1,X1),
inference(step,[status(thm)],[t718,t259]) ).
cnf(t2109,plain,
multiplication(sk1,addition(X1,sk0(sk1))) = multiplication(sk1,X1),
inference(orient,[status(thm)],[t66602]) ).
cnf(t66989,plain,
multiplication(sk1,addition(sk3,sk0(sk2))) = multiplication(sk1,sk3),
inference(step,[status(thm)],[t6611,t2109]) ).
cnf(t6615,plain,
multiplication(sk1,addition(sk3,sk0(sk2))) = multiplication(sk1,sk3),
inference(orient,[status(thm)],[t66989]) ).
cnf(t66177,plain,
addition(sk3,multiplication(sk1,sk0(sk2))) = addition(sk3,multiplication(sk1,sk3)),
inference(cp,[status(thm)],[t66173,t6615]) ).
cnf(t68157,plain,
addition(sk3,multiplication(sk1,sk0(sk2))) = multiplication(addition(one,sk1),sk3),
inference(step,[status(thm)],[t66177,t1129]) ).
cnf(t68158,plain,
addition(sk3,multiplication(sk1,sk0(sk2))) = multiplication(addition(sk3,sk1),sk3),
inference(step,[status(thm)],[t68157,t1781]) ).
cnf(t68159,plain,
addition(sk3,multiplication(sk1,sk0(sk2))) = sk3,
inference(step,[status(thm)],[t68158,t5512]) ).
cnf(t66296,plain,
addition(sk3,multiplication(sk1,sk0(sk2))) = sk3,
inference(orient,[status(thm)],[t68159]) ).
cnf(t66301,plain,
true = ifeq(sk3,sk3,leq(multiplication(sk1,sk0(sk2)),sk3),true),
inference(cp,[status(thm)],[t8036,t66296]) ).
cnf(t68160,plain,
true = leq(multiplication(sk1,sk0(sk2)),sk3),
inference(step,[status(thm)],[t66301,t262]) ).
cnf(t68161,plain,
true = false,
inference(step,[status(thm)],[t68160,t4371]) ).
cnf(t66346,plain,
false = true,
inference(orient,[status(thm)],[t68161]) ).
cnf(t68162,plain,
leq(multiplication(sk1,sk0(sk2)),sk3) = true,
inference(step,[status(thm)],[t4371,t66346]) ).
cnf(t66347,plain,
leq(multiplication(sk1,sk0(sk2)),sk3) = true,
inference(orient,[status(thm)],[t68162]) ).
cnf(goal_0,negated_conjecture,
leq(multiplication(sk1,c(sk2)),sk3) != true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(g0_0,plain,
leq(multiplication(sk1,sk0(sk2)),sk3) != true,
inference(rw,[status(thm)],[goal_0,t4244]) ).
cnf(g0_1,plain,
true != true,
inference(rw,[status(thm)],[g0_0,t66347]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE019+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n007.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 18:35:38 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 98.39/14.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 98.39/14.52 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------