%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE034+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:51:26 PM UTC 2026
% Result : Theorem 153.81s 27.71s
% Output : Proof 153.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 18
% Syntax : Number of formulae : 256 ( 234 unt; 0 def)
% Number of atoms : 324 ( 258 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 107 ( 39 ~; 29 |; 32 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 261 ( 11 sgn 90 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(t128,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t432,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t128]) ).
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(t155,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t384,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t155]) ).
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(f18,conjecture,
! [X0,X1,X2,X3,X4] :
( ( leq(multiplication(multiplication(X3,X1),c(X4)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X4)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( leq(multiplication(multiplication(X3,X1),c(X4)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X4)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0,X1,X2,X3,X4] :
( ~ leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X4)
& test(X2)
& test(X3) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( ~ leq(multiplication(multiplication(multiplication(sk3,sk1),sk2),c(sk5)),zero)
& leq(multiplication(multiplication(sk4,sk2),c(sk5)),zero)
& leq(multiplication(multiplication(sk3,sk1),c(sk4)),zero)
& test(sk5)
& test(sk3)
& test(sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4,sk5])],[f18_nnf]) ).
cnf(c26,plain,
test(sk5),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi26,negated_conjecture,
test(sk5) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(hi33,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h41,plain,
complement(sk5,or(c(sk5),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi26,hi33]) ).
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(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(t75,plain,
multiplication(sk5,or(c(sk5),false)) = zero,
inference(hyper_resolution,[status(thm)],[hi16,h41]) ).
cnf(t12,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t185125,plain,
multiplication(sk5,c(sk5)) = zero,
inference(step,[status(thm)],[t75,t256]) ).
cnf(t487,plain,
multiplication(sk5,c(sk5)) = zero,
inference(orient,[status(thm)],[t185125]) ).
cnf(t492,plain,
multiplication(addition(X1,sk5),c(sk5)) = addition(multiplication(X1,c(sk5)),zero),
inference(cp,[status(thm)],[t384,t487]) ).
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(t185373,plain,
multiplication(addition(X1,sk5),c(sk5)) = multiplication(X1,c(sk5)),
inference(step,[status(thm)],[t492,t259]) ).
cnf(t4043,plain,
multiplication(addition(X1,sk5),c(sk5)) = multiplication(X1,c(sk5)),
inference(orient,[status(thm)],[t185373]) ).
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(t16,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t291,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t16]) ).
cnf(t4045,plain,
multiplication(X1,c(sk5)) = multiplication(addition(sk5,X1),c(sk5)),
inference(cp,[status(thm)],[t4043,t291]) ).
cnf(t4530,plain,
multiplication(addition(sk5,X1),c(sk5)) = multiplication(X1,c(sk5)),
inference(orient,[status(thm)],[t4045]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t123,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t788,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t123]) ).
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(t127,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t726,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t127]) ).
cnf(t2,plain,
test(sk5) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t573,plain,
test(sk5) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t730,plain,
true = ifeq(true,true,complement(sk0(sk5),sk5),true),
inference(cp,[status(thm)],[t726,t573]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t185199,plain,
true = complement(sk0(sk5),sk5),
inference(step,[status(thm)],[t730,t262]) ).
cnf(t877,plain,
complement(sk0(sk5),sk5) = true,
inference(orient,[status(thm)],[t185199]) ).
cnf(t878,plain,
one = ifeq(true,true,addition(sk5,sk0(sk5)),one),
inference(cp,[status(thm)],[t788,t877]) ).
cnf(t185204,plain,
one = addition(sk5,sk0(sk5)),
inference(step,[status(thm)],[t878,t262]) ).
cnf(t919,plain,
addition(sk5,sk0(sk5)) = one,
inference(orient,[status(thm)],[t185204]) ).
cnf(t4538,plain,
multiplication(sk0(sk5),c(sk5)) = multiplication(one,c(sk5)),
inference(cp,[status(thm)],[t4530,t919]) ).
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(t154,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t402,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t154]) ).
cnf(t124,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t771,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t124]) ).
cnf(t879,plain,
zero = ifeq(true,true,multiplication(sk0(sk5),sk5),zero),
inference(cp,[status(thm)],[t771,t877]) ).
cnf(t185205,plain,
zero = multiplication(sk0(sk5),sk5),
inference(step,[status(thm)],[t879,t262]) ).
cnf(t925,plain,
multiplication(sk0(sk5),sk5) = zero,
inference(orient,[status(thm)],[t185205]) ).
cnf(t928,plain,
multiplication(sk0(sk5),addition(sk5,X1)) = addition(zero,multiplication(sk0(sk5),X1)),
inference(cp,[status(thm)],[t402,t925]) ).
cnf(t298,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t291,t259]) ).
cnf(t816,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t298]) ).
cnf(t185382,plain,
multiplication(sk0(sk5),addition(sk5,X1)) = multiplication(sk0(sk5),X1),
inference(step,[status(thm)],[t928,t816]) ).
cnf(t4183,plain,
multiplication(sk0(sk5),addition(sk5,X1)) = multiplication(sk0(sk5),X1),
inference(orient,[status(thm)],[t185382]) ).
cnf(hi17,axiom,
ifeq(complement(X0,X1),true,addition(X1,X0),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t39,plain,
addition(or(c(sk5),false),sk5) = one,
inference(hyper_resolution,[status(thm)],[hi17,h41]) ).
cnf(t185075,plain,
addition(sk5,or(c(sk5),false)) = one,
inference(step,[status(thm)],[t39,t291]) ).
cnf(t185076,plain,
addition(sk5,c(sk5)) = one,
inference(step,[status(thm)],[t185075,t256]) ).
cnf(t332,plain,
addition(sk5,c(sk5)) = one,
inference(orient,[status(thm)],[t185076]) ).
cnf(t4189,plain,
multiplication(sk0(sk5),c(sk5)) = multiplication(sk0(sk5),one),
inference(cp,[status(thm)],[t4183,t332]) ).
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(t8,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t260,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t185383,plain,
multiplication(sk0(sk5),c(sk5)) = sk0(sk5),
inference(step,[status(thm)],[t4189,t260]) ).
cnf(t4208,plain,
multiplication(sk0(sk5),c(sk5)) = sk0(sk5),
inference(orient,[status(thm)],[t185383]) ).
cnf(t185404,plain,
sk0(sk5) = multiplication(one,c(sk5)),
inference(step,[status(thm)],[t4538,t4208]) ).
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(t10,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t261,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t185405,plain,
sk0(sk5) = c(sk5),
inference(step,[status(thm)],[t185404,t261]) ).
cnf(t4553,plain,
c(sk5) = sk0(sk5),
inference(orient,[status(thm)],[t185405]) ).
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(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(c27,plain,
leq(multiplication(multiplication(sk3,sk1),c(sk4)),zero),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi27,negated_conjecture,
leq(multiplication(multiplication(sk3,sk1),c(sk4)),zero) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t92,plain,
addition(multiplication(multiplication(sk3,sk1),c(sk4)),zero) = zero,
inference(hyper_resolution,[status(thm)],[hi11,hi27]) ).
cnf(t185119,plain,
multiplication(multiplication(sk3,sk1),c(sk4)) = zero,
inference(step,[status(thm)],[t92,t259]) ).
cnf(t420,plain,
multiplication(multiplication(sk3,sk1),c(sk4)) = zero,
inference(orient,[status(thm)],[t185119]) ).
cnf(t185122,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(step,[status(thm)],[t420,t432]) ).
cnf(t443,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(rw,[status(thm)],[t185122]) ).
cnf(t1277,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(orient,[status(thm)],[t443]) ).
cnf(t217,plain,
ifeq(test(X1),true,ifeq(c(X1),X2,complement(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t732,plain,
ifeq(test(X1),true,ifeq(c(X1),X2,complement(X1,X2),true),true) = true,
inference(orient,[status(thm)],[t217]) ).
cnf(c24,plain,
test(sk4),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t1,plain,
test(sk4) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t609,plain,
test(sk4) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t733,plain,
true = ifeq(true,true,ifeq(c(sk4),X1,complement(sk4,X1),true),true),
inference(cp,[status(thm)],[t732,t609]) ).
cnf(t185526,plain,
true = ifeq(c(sk4),X1,complement(sk4,X1),true),
inference(step,[status(thm)],[t733,t262]) ).
cnf(t5753,plain,
ifeq(c(sk4),X1,complement(sk4,X1),true) = true,
inference(orient,[status(thm)],[t185526]) ).
cnf(t5754,plain,
true = complement(sk4,c(sk4)),
inference(cp,[status(thm)],[t5753,t262]) ).
cnf(t5755,plain,
complement(sk4,c(sk4)) = true,
inference(orient,[status(thm)],[t5754]) ).
cnf(t5757,plain,
zero = ifeq(true,true,multiplication(sk4,c(sk4)),zero),
inference(cp,[status(thm)],[t771,t5755]) ).
cnf(t185530,plain,
zero = multiplication(sk4,c(sk4)),
inference(step,[status(thm)],[t5757,t262]) ).
cnf(t5790,plain,
multiplication(sk4,c(sk4)) = zero,
inference(orient,[status(thm)],[t185530]) ).
cnf(t5796,plain,
multiplication(addition(sk4,X1),c(sk4)) = addition(zero,multiplication(X1,c(sk4))),
inference(cp,[status(thm)],[t384,t5790]) ).
cnf(t185577,plain,
multiplication(addition(sk4,X1),c(sk4)) = multiplication(X1,c(sk4)),
inference(step,[status(thm)],[t5796,t816]) ).
cnf(t6392,plain,
multiplication(addition(sk4,X1),c(sk4)) = multiplication(X1,c(sk4)),
inference(orient,[status(thm)],[t185577]) ).
cnf(t727,plain,
true = ifeq(true,true,complement(sk0(sk4),sk4),true),
inference(cp,[status(thm)],[t726,t609]) ).
cnf(t185198,plain,
true = complement(sk0(sk4),sk4),
inference(step,[status(thm)],[t727,t262]) ).
cnf(t870,plain,
complement(sk0(sk4),sk4) = true,
inference(orient,[status(thm)],[t185198]) ).
cnf(t871,plain,
one = ifeq(true,true,addition(sk4,sk0(sk4)),one),
inference(cp,[status(thm)],[t788,t870]) ).
cnf(t185201,plain,
one = addition(sk4,sk0(sk4)),
inference(step,[status(thm)],[t871,t262]) ).
cnf(t891,plain,
addition(sk4,sk0(sk4)) = one,
inference(orient,[status(thm)],[t185201]) ).
cnf(t6399,plain,
multiplication(sk0(sk4),c(sk4)) = multiplication(one,c(sk4)),
inference(cp,[status(thm)],[t6392,t891]) ).
cnf(t872,plain,
zero = ifeq(true,true,multiplication(sk0(sk4),sk4),zero),
inference(cp,[status(thm)],[t771,t870]) ).
cnf(t185202,plain,
zero = multiplication(sk0(sk4),sk4),
inference(step,[status(thm)],[t872,t262]) ).
cnf(t897,plain,
multiplication(sk0(sk4),sk4) = zero,
inference(orient,[status(thm)],[t185202]) ).
cnf(t900,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = addition(zero,multiplication(sk0(sk4),X1)),
inference(cp,[status(thm)],[t402,t897]) ).
cnf(t185377,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = multiplication(sk0(sk4),X1),
inference(step,[status(thm)],[t900,t816]) ).
cnf(t4103,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = multiplication(sk0(sk4),X1),
inference(orient,[status(thm)],[t185377]) ).
cnf(t5756,plain,
one = ifeq(true,true,addition(c(sk4),sk4),one),
inference(cp,[status(thm)],[t788,t5755]) ).
cnf(t185528,plain,
one = addition(c(sk4),sk4),
inference(step,[status(thm)],[t5756,t262]) ).
cnf(t185529,plain,
one = addition(sk4,c(sk4)),
inference(step,[status(thm)],[t185528,t291]) ).
cnf(t5770,plain,
addition(sk4,c(sk4)) = one,
inference(orient,[status(thm)],[t185529]) ).
cnf(t5773,plain,
multiplication(sk0(sk4),c(sk4)) = multiplication(sk0(sk4),one),
inference(cp,[status(thm)],[t4103,t5770]) ).
cnf(t185543,plain,
multiplication(sk0(sk4),c(sk4)) = sk0(sk4),
inference(step,[status(thm)],[t5773,t260]) ).
cnf(t5859,plain,
multiplication(sk0(sk4),c(sk4)) = sk0(sk4),
inference(orient,[status(thm)],[t185543]) ).
cnf(t185578,plain,
sk0(sk4) = multiplication(one,c(sk4)),
inference(step,[status(thm)],[t6399,t5859]) ).
cnf(t185579,plain,
sk0(sk4) = c(sk4),
inference(step,[status(thm)],[t185578,t261]) ).
cnf(t6416,plain,
c(sk4) = sk0(sk4),
inference(orient,[status(thm)],[t185579]) ).
cnf(t185605,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(step,[status(thm)],[t1277,t6416]) ).
cnf(t6445,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(rw,[status(thm)],[t185605]) ).
cnf(t6574,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(orient,[status(thm)],[t6445]) ).
cnf(t6580,plain,
multiplication(sk3,addition(multiplication(sk1,sk0(sk4)),X1)) = addition(zero,multiplication(sk3,X1)),
inference(cp,[status(thm)],[t402,t6574]) ).
cnf(t186056,plain,
multiplication(sk3,addition(multiplication(sk1,sk0(sk4)),X1)) = multiplication(sk3,X1),
inference(step,[status(thm)],[t6580,t816]) ).
cnf(t18541,plain,
multiplication(sk3,addition(multiplication(sk1,sk0(sk4)),X1)) = multiplication(sk3,X1),
inference(orient,[status(thm)],[t186056]) ).
cnf(t18545,plain,
multiplication(sk3,multiplication(sk1,X1)) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),X1))),
inference(cp,[status(thm)],[t18541,t402]) ).
cnf(t183594,plain,
multiplication(sk3,multiplication(sk1,addition(sk0(sk4),X1))) = multiplication(sk3,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t18545]) ).
cnf(t392,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t384,t261]) ).
cnf(t1431,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t392]) ).
cnf(t901,plain,
multiplication(sk0(sk4),addition(X1,sk4)) = addition(multiplication(sk0(sk4),X1),zero),
inference(cp,[status(thm)],[t402,t897]) ).
cnf(t185379,plain,
multiplication(sk0(sk4),addition(X1,sk4)) = multiplication(sk0(sk4),X1),
inference(step,[status(thm)],[t901,t259]) ).
cnf(t4135,plain,
multiplication(sk0(sk4),addition(X1,sk4)) = multiplication(sk0(sk4),X1),
inference(orient,[status(thm)],[t185379]) ).
cnf(t4138,plain,
multiplication(addition(one,sk0(sk4)),addition(X1,sk4)) = addition(addition(X1,sk4),multiplication(sk0(sk4),X1)),
inference(cp,[status(thm)],[t1431,t4135]) ).
cnf(t126,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)],[t126]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t122,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t630,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t122]) ).
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(t121,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t303,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t121]) ).
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(t306,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t303,t258]) ).
cnf(t969,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t306]) ).
cnf(t983,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t630,t969]) ).
cnf(t185216,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t983,t262]) ).
cnf(t1010,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t185216]) ).
cnf(t1017,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t1010,t291]) ).
cnf(t1024,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t1017]) ).
cnf(t1025,plain,
true = leq(sk0(sk4),one),
inference(cp,[status(thm)],[t1024,t891]) ).
cnf(t1036,plain,
leq(sk0(sk4),one) = true,
inference(orient,[status(thm)],[t1025]) ).
cnf(t1037,plain,
one = ifeq(true,true,addition(sk0(sk4),one),one),
inference(cp,[status(thm)],[t264,t1036]) ).
cnf(t185217,plain,
one = addition(sk0(sk4),one),
inference(step,[status(thm)],[t1037,t262]) ).
cnf(t185218,plain,
one = addition(one,sk0(sk4)),
inference(step,[status(thm)],[t185217,t291]) ).
cnf(t1045,plain,
addition(one,sk0(sk4)) = one,
inference(orient,[status(thm)],[t185218]) ).
cnf(t185868,plain,
multiplication(one,addition(X1,sk4)) = addition(addition(X1,sk4),multiplication(sk0(sk4),X1)),
inference(step,[status(thm)],[t4138,t1045]) ).
cnf(t185869,plain,
addition(X1,sk4) = addition(addition(X1,sk4),multiplication(sk0(sk4),X1)),
inference(step,[status(thm)],[t185868,t261]) ).
cnf(t185870,plain,
addition(X1,sk4) = addition(X1,addition(sk4,multiplication(sk0(sk4),X1))),
inference(step,[status(thm)],[t185869,t303]) ).
cnf(t14203,plain,
addition(X1,addition(sk4,multiplication(sk0(sk4),X1))) = addition(X1,sk4),
inference(orient,[status(thm)],[t185870]) ).
cnf(t183615,plain,
multiplication(sk3,multiplication(sk1,addition(sk4,multiplication(sk0(sk4),sk0(sk4))))) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),sk4))),
inference(cp,[status(thm)],[t183594,t14203]) ).
cnf(t4107,plain,
multiplication(sk0(sk4),sk0(sk4)) = multiplication(sk0(sk4),one),
inference(cp,[status(thm)],[t4103,t891]) ).
cnf(t185378,plain,
multiplication(sk0(sk4),sk0(sk4)) = sk0(sk4),
inference(step,[status(thm)],[t4107,t260]) ).
cnf(t4124,plain,
multiplication(sk0(sk4),sk0(sk4)) = sk0(sk4),
inference(orient,[status(thm)],[t185378]) ).
cnf(t188187,plain,
multiplication(sk3,multiplication(sk1,addition(sk4,sk0(sk4)))) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),sk4))),
inference(step,[status(thm)],[t183615,t4124]) ).
cnf(t188188,plain,
multiplication(sk3,multiplication(sk1,one)) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),sk4))),
inference(step,[status(thm)],[t188187,t891]) ).
cnf(t188189,plain,
multiplication(sk3,sk1) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),sk4))),
inference(step,[status(thm)],[t188188,t260]) ).
cnf(t188190,plain,
multiplication(sk3,sk1) = multiplication(sk3,multiplication(sk1,sk4)),
inference(step,[status(thm)],[t188189,t183594]) ).
cnf(t183770,plain,
multiplication(sk3,multiplication(sk1,sk4)) = multiplication(sk3,sk1),
inference(orient,[status(thm)],[t188190]) ).
cnf(t183783,plain,
multiplication(sk3,multiplication(multiplication(sk1,sk4),X1)) = multiplication(multiplication(sk3,sk1),X1),
inference(cp,[status(thm)],[t432,t183770]) ).
cnf(t188199,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk4,X1))) = multiplication(multiplication(sk3,sk1),X1),
inference(step,[status(thm)],[t183783,t432]) ).
cnf(t188200,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk4,X1))) = multiplication(sk3,multiplication(sk1,X1)),
inference(step,[status(thm)],[t188199,t432]) ).
cnf(t184418,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk4,X1))) = multiplication(sk3,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t188200]) ).
cnf(c28,plain,
leq(multiplication(multiplication(sk4,sk2),c(sk5)),zero),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi28,negated_conjecture,
leq(multiplication(multiplication(sk4,sk2),c(sk5)),zero) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t93,plain,
addition(multiplication(multiplication(sk4,sk2),c(sk5)),zero) = zero,
inference(hyper_resolution,[status(thm)],[hi11,hi28]) ).
cnf(t185120,plain,
multiplication(multiplication(sk4,sk2),c(sk5)) = zero,
inference(step,[status(thm)],[t93,t259]) ).
cnf(t426,plain,
multiplication(multiplication(sk4,sk2),c(sk5)) = zero,
inference(orient,[status(thm)],[t185120]) ).
cnf(t185121,plain,
multiplication(sk4,multiplication(sk2,c(sk5))) = zero,
inference(step,[status(thm)],[t426,t432]) ).
cnf(t442,plain,
multiplication(sk4,multiplication(sk2,c(sk5))) = zero,
inference(rw,[status(thm)],[t185121]) ).
cnf(t1266,plain,
multiplication(sk4,multiplication(sk2,c(sk5))) = zero,
inference(orient,[status(thm)],[t442]) ).
cnf(t185432,plain,
multiplication(sk4,multiplication(sk2,sk0(sk5))) = zero,
inference(step,[status(thm)],[t1266,t4553]) ).
cnf(t4589,plain,
multiplication(sk4,multiplication(sk2,sk0(sk5))) = zero,
inference(rw,[status(thm)],[t185432]) ).
cnf(t4809,plain,
multiplication(sk4,multiplication(sk2,sk0(sk5))) = zero,
inference(orient,[status(thm)],[t4589]) ).
cnf(t184512,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))) = multiplication(sk3,multiplication(sk1,zero)),
inference(cp,[status(thm)],[t184418,t4809]) ).
fof(f9,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f9_nnf,plain,
! [A] : multiplication(A,zero) = zero,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : multiplication(A,zero) = zero,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t9,plain,
multiplication(X1,zero) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t445,plain,
multiplication(X1,zero) = zero,
inference(orient,[status(thm)],[t9]) ).
cnf(t188203,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))) = multiplication(sk3,zero),
inference(step,[status(thm)],[t184512,t445]) ).
cnf(t188204,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))) = zero,
inference(step,[status(thm)],[t188203,t445]) ).
cnf(t184947,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))) = zero,
inference(orient,[status(thm)],[t188204]) ).
cnf(t819,plain,
true = ifeq(X1,X1,leq(zero,X1),true),
inference(cp,[status(thm)],[t630,t816]) ).
cnf(t185171,plain,
true = leq(zero,X1),
inference(step,[status(thm)],[t819,t262]) ).
cnf(t826,plain,
leq(zero,X1) = true,
inference(orient,[status(thm)],[t185171]) ).
cnf(c29,plain,
~ leq(multiplication(multiplication(multiplication(sk3,sk1),sk2),c(sk5)),zero),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
leq(multiplication(multiplication(multiplication(sk3,sk1),sk2),c(sk5)),zero) != true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(g0_0,plain,
leq(multiplication(multiplication(sk3,sk1),multiplication(sk2,c(sk5))),zero) != true,
inference(rw,[status(thm)],[goal_0,t432]) ).
cnf(g0_1,plain,
leq(multiplication(sk3,multiplication(sk1,multiplication(sk2,c(sk5)))),zero) != true,
inference(rw,[status(thm)],[g0_0,t432]) ).
cnf(g0_2,plain,
leq(multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))),zero) != true,
inference(rw,[status(thm)],[g0_1,t4553]) ).
cnf(g0_3,plain,
leq(zero,zero) != true,
inference(rw,[status(thm)],[g0_2,t184947]) ).
cnf(g0_4,plain,
true != true,
inference(rw,[status(thm)],[g0_3,t826]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE034+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.39 % Computer : n008.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Wed Sep 23 18:43:45 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 153.81/27.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 153.81/27.71 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------