%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE025+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 01:51:24 PM UTC 2026
% Result : Theorem 185.17s 40.76s
% Output : Proof 185.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 17
% Syntax : Number of formulae : 188 ( 165 unt; 0 def)
% Number of atoms : 249 ( 202 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 98 ( 37 ~; 30 |; 22 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 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 : 222 ( 6 sgn 83 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(t132,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t426,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t132]) ).
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(t158,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t406,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t158]) ).
fof(f18,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& test(X2)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( multiplication(sk2,sk1) != multiplication(multiplication(sk2,sk1),sk3)
& multiplication(multiplication(sk2,sk1),c(sk3)) = zero
& test(sk3)
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f18_nnf]) ).
cnf(c26,plain,
multiplication(multiplication(sk2,sk1),c(sk3)) = zero,
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t69,plain,
multiplication(multiplication(sk2,sk1),c(sk3)) = zero,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t58108,plain,
multiplication(sk2,multiplication(sk1,c(sk3))) = zero,
inference(step,[status(thm)],[t69,t426]) ).
cnf(t555,plain,
multiplication(sk2,multiplication(sk1,c(sk3))) = zero,
inference(orient,[status(thm)],[t58108]) ).
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(t7,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t260,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t408,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t406,t260]) ).
cnf(t1266,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t408]) ).
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(t159,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t388,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t159]) ).
fof(f12,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/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(hi13,axiom,
ifeq(test(X0),true,complement(sk0(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c25,plain,
test(sk3),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi25,negated_conjecture,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h12,plain,
complement(sk0(sk3),sk3) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi25]) ).
fof(f13,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/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(t22,plain,
multiplication(sk3,sk0(sk3)) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h12]) ).
cnf(t488,plain,
multiplication(sk3,sk0(sk3)) = zero,
inference(orient,[status(thm)],[t22]) ).
cnf(t493,plain,
multiplication(addition(X1,sk3),sk0(sk3)) = addition(multiplication(X1,sk0(sk3)),zero),
inference(cp,[status(thm)],[t388,t488]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f2_nnf,plain,
! [A] : addition(A,zero) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : addition(A,zero) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t259,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t58287,plain,
multiplication(addition(X1,sk3),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(step,[status(thm)],[t493,t259]) ).
cnf(t3101,plain,
multiplication(addition(X1,sk3),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(orient,[status(thm)],[t58287]) ).
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(t23,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t289,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t23]) ).
cnf(t3103,plain,
multiplication(X1,sk0(sk3)) = multiplication(addition(sk3,X1),sk0(sk3)),
inference(cp,[status(thm)],[t3101,t289]) ).
cnf(t3360,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(orient,[status(thm)],[t3103]) ).
fof(f14,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/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]) ).
cnf(hi31,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h23,plain,
complement(sk3,or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi25,hi31]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi17,axiom,
ifeq(complement(X0,X1),true,addition(X1,X0),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t45,plain,
addition(or(c(sk3),false),sk3) = one,
inference(hyper_resolution,[status(thm)],[hi17,h23]) ).
cnf(t58049,plain,
addition(sk3,or(c(sk3),false)) = one,
inference(step,[status(thm)],[t45,t289]) ).
cnf(t11,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t58050,plain,
addition(sk3,c(sk3)) = one,
inference(step,[status(thm)],[t58049,t256]) ).
cnf(t336,plain,
addition(sk3,c(sk3)) = one,
inference(orient,[status(thm)],[t58050]) ).
cnf(t3367,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(one,sk0(sk3)),
inference(cp,[status(thm)],[t3360,t336]) ).
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(t9,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t261,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t58301,plain,
multiplication(c(sk3),sk0(sk3)) = sk0(sk3),
inference(step,[status(thm)],[t3367,t261]) ).
cnf(t3393,plain,
multiplication(c(sk3),sk0(sk3)) = sk0(sk3),
inference(orient,[status(thm)],[t58301]) ).
cnf(t3394,plain,
multiplication(c(sk3),addition(one,sk0(sk3))) = addition(c(sk3),sk0(sk3)),
inference(cp,[status(thm)],[t1266,t3393]) ).
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(t130,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)],[t130]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t126,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t650,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t126]) ).
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(t124,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t301,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t124]) ).
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(t2,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t258,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t304,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t301,t258]) ).
cnf(t897,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t304]) ).
cnf(t910,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t650,t897]) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t24]) ).
cnf(t58167,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t910,t262]) ).
cnf(t930,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t58167]) ).
cnf(t937,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t930,t289]) ).
cnf(t944,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t937]) ).
cnf(t16,plain,
addition(sk3,sk0(sk3)) = one,
inference(hyper_resolution,[status(thm)],[hi17,h12]) ).
cnf(t330,plain,
addition(sk3,sk0(sk3)) = one,
inference(orient,[status(thm)],[t16]) ).
cnf(t948,plain,
true = leq(sk0(sk3),one),
inference(cp,[status(thm)],[t944,t330]) ).
cnf(t958,plain,
leq(sk0(sk3),one) = true,
inference(orient,[status(thm)],[t948]) ).
cnf(t959,plain,
one = ifeq(true,true,addition(sk0(sk3),one),one),
inference(cp,[status(thm)],[t264,t958]) ).
cnf(t58170,plain,
one = addition(sk0(sk3),one),
inference(step,[status(thm)],[t959,t262]) ).
cnf(t58171,plain,
one = addition(one,sk0(sk3)),
inference(step,[status(thm)],[t58170,t289]) ).
cnf(t968,plain,
addition(one,sk0(sk3)) = one,
inference(orient,[status(thm)],[t58171]) ).
cnf(t58302,plain,
multiplication(c(sk3),one) = addition(c(sk3),sk0(sk3)),
inference(step,[status(thm)],[t3394,t968]) ).
cnf(t58303,plain,
c(sk3) = addition(c(sk3),sk0(sk3)),
inference(step,[status(thm)],[t58302,t260]) ).
cnf(t58304,plain,
c(sk3) = addition(sk0(sk3),c(sk3)),
inference(step,[status(thm)],[t58303,t289]) ).
cnf(c16,plain,
( multiplication(X1,X0) = zero
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi16,axiom,
ifeq(complement(X0,X1),true,multiplication(X0,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t82,plain,
multiplication(sk3,or(c(sk3),false)) = zero,
inference(hyper_resolution,[status(thm)],[hi16,h23]) ).
cnf(t58094,plain,
multiplication(sk3,c(sk3)) = zero,
inference(step,[status(thm)],[t82,t256]) ).
cnf(t481,plain,
multiplication(sk3,c(sk3)) = zero,
inference(orient,[status(thm)],[t58094]) ).
cnf(t486,plain,
multiplication(addition(X1,sk3),c(sk3)) = addition(multiplication(X1,c(sk3)),zero),
inference(cp,[status(thm)],[t388,t481]) ).
cnf(t58286,plain,
multiplication(addition(X1,sk3),c(sk3)) = multiplication(X1,c(sk3)),
inference(step,[status(thm)],[t486,t259]) ).
cnf(t3086,plain,
multiplication(addition(X1,sk3),c(sk3)) = multiplication(X1,c(sk3)),
inference(orient,[status(thm)],[t58286]) ).
cnf(t3088,plain,
multiplication(X1,c(sk3)) = multiplication(addition(sk3,X1),c(sk3)),
inference(cp,[status(thm)],[t3086,t289]) ).
cnf(t3287,plain,
multiplication(addition(sk3,X1),c(sk3)) = multiplication(X1,c(sk3)),
inference(orient,[status(thm)],[t3088]) ).
cnf(t3293,plain,
multiplication(sk0(sk3),c(sk3)) = multiplication(one,c(sk3)),
inference(cp,[status(thm)],[t3287,t330]) ).
cnf(t58296,plain,
multiplication(sk0(sk3),c(sk3)) = c(sk3),
inference(step,[status(thm)],[t3293,t261]) ).
cnf(t3309,plain,
multiplication(sk0(sk3),c(sk3)) = c(sk3),
inference(orient,[status(thm)],[t58296]) ).
cnf(t3310,plain,
multiplication(sk0(sk3),addition(one,c(sk3))) = addition(sk0(sk3),c(sk3)),
inference(cp,[status(thm)],[t1266,t3309]) ).
cnf(hi3,axiom,
addition(X0,X0) = X0,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h14,plain,
complement(sk3,addition(c(sk3),c(sk3))) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi25,hi3]) ).
cnf(t87,plain,
addition(addition(c(sk3),c(sk3)),sk3) = one,
inference(hyper_resolution,[status(thm)],[hi17,h14]) ).
cnf(t58073,plain,
addition(c(sk3),addition(c(sk3),sk3)) = one,
inference(step,[status(thm)],[t87,t301]) ).
cnf(t58074,plain,
addition(c(sk3),addition(sk3,c(sk3))) = one,
inference(step,[status(thm)],[t58073,t289]) ).
cnf(t58075,plain,
addition(c(sk3),one) = one,
inference(step,[status(thm)],[t58074,t336]) ).
cnf(t58076,plain,
addition(one,c(sk3)) = one,
inference(step,[status(thm)],[t58075,t289]) ).
cnf(t364,plain,
addition(one,c(sk3)) = one,
inference(orient,[status(thm)],[t58076]) ).
cnf(t58298,plain,
multiplication(sk0(sk3),one) = addition(sk0(sk3),c(sk3)),
inference(step,[status(thm)],[t3310,t364]) ).
cnf(t58299,plain,
sk0(sk3) = addition(sk0(sk3),c(sk3)),
inference(step,[status(thm)],[t58298,t260]) ).
cnf(t3331,plain,
addition(sk0(sk3),c(sk3)) = sk0(sk3),
inference(orient,[status(thm)],[t58299]) ).
cnf(t58305,plain,
c(sk3) = sk0(sk3),
inference(step,[status(thm)],[t58304,t3331]) ).
cnf(t3405,plain,
c(sk3) = sk0(sk3),
inference(orient,[status(thm)],[t58305]) ).
cnf(t58339,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(step,[status(thm)],[t555,t3405]) ).
cnf(t3446,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(rw,[status(thm)],[t58339]) ).
cnf(t3567,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(orient,[status(thm)],[t3446]) ).
cnf(t3573,plain,
multiplication(sk2,addition(multiplication(sk1,sk0(sk3)),X1)) = addition(zero,multiplication(sk2,X1)),
inference(cp,[status(thm)],[t406,t3567]) ).
cnf(t296,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t289,t259]) ).
cnf(t843,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t296]) ).
cnf(t58632,plain,
multiplication(sk2,addition(multiplication(sk1,sk0(sk3)),X1)) = multiplication(sk2,X1),
inference(step,[status(thm)],[t3573,t843]) ).
cnf(t8036,plain,
multiplication(sk2,addition(multiplication(sk1,sk0(sk3)),X1)) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t58632]) ).
cnf(t8038,plain,
multiplication(sk2,multiplication(sk1,X1)) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),X1))),
inference(cp,[status(thm)],[t8036,t406]) ).
cnf(t57828,plain,
multiplication(sk2,multiplication(sk1,addition(sk0(sk3),X1))) = multiplication(sk2,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t8038]) ).
cnf(t3104,plain,
multiplication(addition(X1,sk3),addition(one,sk0(sk3))) = addition(addition(X1,sk3),multiplication(X1,sk0(sk3))),
inference(cp,[status(thm)],[t1266,t3101]) ).
cnf(t58579,plain,
multiplication(addition(X1,sk3),one) = addition(addition(X1,sk3),multiplication(X1,sk0(sk3))),
inference(step,[status(thm)],[t3104,t968]) ).
cnf(t58580,plain,
addition(X1,sk3) = addition(addition(X1,sk3),multiplication(X1,sk0(sk3))),
inference(step,[status(thm)],[t58579,t260]) ).
cnf(t58581,plain,
addition(X1,sk3) = addition(X1,addition(sk3,multiplication(X1,sk0(sk3)))),
inference(step,[status(thm)],[t58580,t301]) ).
cnf(t7242,plain,
addition(X1,addition(sk3,multiplication(X1,sk0(sk3)))) = addition(X1,sk3),
inference(orient,[status(thm)],[t58581]) ).
cnf(t57840,plain,
multiplication(sk2,multiplication(sk1,addition(sk3,multiplication(sk0(sk3),sk0(sk3))))) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),sk3))),
inference(cp,[status(thm)],[t57828,t7242]) ).
cnf(t3366,plain,
multiplication(sk0(sk3),sk0(sk3)) = multiplication(one,sk0(sk3)),
inference(cp,[status(thm)],[t3360,t330]) ).
cnf(t58300,plain,
multiplication(sk0(sk3),sk0(sk3)) = sk0(sk3),
inference(step,[status(thm)],[t3366,t261]) ).
cnf(t3382,plain,
multiplication(sk0(sk3),sk0(sk3)) = sk0(sk3),
inference(orient,[status(thm)],[t58300]) ).
cnf(t59412,plain,
multiplication(sk2,multiplication(sk1,addition(sk3,sk0(sk3)))) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),sk3))),
inference(step,[status(thm)],[t57840,t3382]) ).
cnf(t59413,plain,
multiplication(sk2,multiplication(sk1,one)) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),sk3))),
inference(step,[status(thm)],[t59412,t330]) ).
cnf(t59414,plain,
multiplication(sk2,sk1) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),sk3))),
inference(step,[status(thm)],[t59413,t260]) ).
cnf(t59415,plain,
multiplication(sk2,sk1) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t59414,t57828]) ).
cnf(t57939,plain,
multiplication(sk2,multiplication(sk1,sk3)) = multiplication(sk2,sk1),
inference(orient,[status(thm)],[t59415]) ).
cnf(c27,plain,
multiplication(sk2,sk1) != multiplication(multiplication(sk2,sk1),sk3),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(multiplication(sk2,sk1),sk3) != multiplication(sk2,sk1),
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
multiplication(sk2,multiplication(sk1,sk3)) != multiplication(sk2,sk1),
inference(rw,[status(thm)],[goal_0,t426]) ).
cnf(g0_1,plain,
multiplication(sk2,sk1) != multiplication(sk2,sk1),
inference(rw,[status(thm)],[g0_0,t57939]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE025+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/15.39 % Computer : n014.cluster.edu
% 0.10/15.39 % Model : x86_64 x86_64
% 0.10/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.39 % Memory : 8046.5625MB
% 0.10/15.39 % OS : Linux 6.8.0-71-generic
% 0.10/15.39 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Wed Sep 23 18:40:34 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 185.17/40.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 185.17/40.76 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------