%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE034+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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:51:26 PM UTC 2026
% Result : Theorem 184.14s 27.61s
% Output : Proof 184.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 18
% Syntax : Number of formulae : 259 ( 236 unt; 0 def)
% Number of atoms : 328 ( 261 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 109 ( 40 ~; 30 |; 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 : 267 ( 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(t125,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t578,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t125]) ).
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(t155,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t337,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
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(f16,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(f16_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)],[f16]) ).
fof(f16_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)],[f16_neg]) ).
fof(f16_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])],[f16_nnf]) ).
cnf(c24,plain,
test(sk5),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi24,negated_conjecture,
test(sk5) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(hi31,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h23,plain,
complement(sk5,or(c(sk5),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi24,hi31]) ).
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(t67,plain,
multiplication(or(c(sk5),false),sk5) = 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(t173539,plain,
multiplication(c(sk5),sk5) = zero,
inference(step,[status(thm)],[t67,t256]) ).
cnf(t494,plain,
multiplication(c(sk5),sk5) = zero,
inference(orient,[status(thm)],[t173539]) ).
cnf(t496,plain,
multiplication(c(sk5),addition(X1,sk5)) = addition(multiplication(c(sk5),X1),zero),
inference(cp,[status(thm)],[t337,t494]) ).
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(t173730,plain,
multiplication(c(sk5),addition(X1,sk5)) = multiplication(c(sk5),X1),
inference(step,[status(thm)],[t496,t259]) ).
cnf(t3361,plain,
multiplication(c(sk5),addition(X1,sk5)) = multiplication(c(sk5),X1),
inference(orient,[status(thm)],[t173730]) ).
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(t273,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t14]) ).
cnf(t3363,plain,
multiplication(c(sk5),X1) = multiplication(c(sk5),addition(sk5,X1)),
inference(cp,[status(thm)],[t3361,t273]) ).
cnf(t3972,plain,
multiplication(c(sk5),addition(sk5,X1)) = multiplication(c(sk5),X1),
inference(orient,[status(thm)],[t3363]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t120,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t599,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t120]) ).
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(t124,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t443,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t124]) ).
cnf(t2,plain,
test(sk5) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t363,plain,
test(sk5) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t445,plain,
true = ifeq(true,true,complement(sk0(sk5),sk5),true),
inference(cp,[status(thm)],[t443,t363]) ).
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(t173565,plain,
true = complement(sk0(sk5),sk5),
inference(step,[status(thm)],[t445,t262]) ).
cnf(t642,plain,
complement(sk0(sk5),sk5) = true,
inference(orient,[status(thm)],[t173565]) ).
cnf(t643,plain,
one = ifeq(true,true,addition(sk5,sk0(sk5)),one),
inference(cp,[status(thm)],[t599,t642]) ).
cnf(t173588,plain,
one = addition(sk5,sk0(sk5)),
inference(step,[status(thm)],[t643,t262]) ).
cnf(t692,plain,
addition(sk5,sk0(sk5)) = one,
inference(orient,[status(thm)],[t173588]) ).
cnf(t3979,plain,
multiplication(c(sk5),sk0(sk5)) = multiplication(c(sk5),one),
inference(cp,[status(thm)],[t3972,t692]) ).
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(t156,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t331,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t156]) ).
cnf(t122,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t552,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(orient,[status(thm)],[t122]) ).
cnf(t645,plain,
zero = ifeq(true,true,multiplication(sk5,sk0(sk5)),zero),
inference(cp,[status(thm)],[t552,t642]) ).
cnf(t173590,plain,
zero = multiplication(sk5,sk0(sk5)),
inference(step,[status(thm)],[t645,t262]) ).
cnf(t706,plain,
multiplication(sk5,sk0(sk5)) = zero,
inference(orient,[status(thm)],[t173590]) ).
cnf(t711,plain,
multiplication(addition(sk5,X1),sk0(sk5)) = addition(zero,multiplication(X1,sk0(sk5))),
inference(cp,[status(thm)],[t331,t706]) ).
cnf(t274,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t273,t259]) ).
cnf(t624,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t274]) ).
cnf(t173745,plain,
multiplication(addition(sk5,X1),sk0(sk5)) = multiplication(X1,sk0(sk5)),
inference(step,[status(thm)],[t711,t624]) ).
cnf(t3568,plain,
multiplication(addition(sk5,X1),sk0(sk5)) = multiplication(X1,sk0(sk5)),
inference(orient,[status(thm)],[t173745]) ).
cnf(hi17,axiom,
ifeq(complement(X0,X1),true,addition(X1,X0),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t47,plain,
addition(or(c(sk5),false),sk5) = one,
inference(hyper_resolution,[status(thm)],[hi17,h23]) ).
cnf(t173468,plain,
addition(sk5,or(c(sk5),false)) = one,
inference(step,[status(thm)],[t47,t273]) ).
cnf(t173469,plain,
addition(sk5,c(sk5)) = one,
inference(step,[status(thm)],[t173468,t256]) ).
cnf(t295,plain,
addition(sk5,c(sk5)) = one,
inference(orient,[status(thm)],[t173469]) ).
cnf(t3574,plain,
multiplication(c(sk5),sk0(sk5)) = multiplication(one,sk0(sk5)),
inference(cp,[status(thm)],[t3568,t295]) ).
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(t173746,plain,
multiplication(c(sk5),sk0(sk5)) = sk0(sk5),
inference(step,[status(thm)],[t3574,t261]) ).
cnf(t3590,plain,
multiplication(c(sk5),sk0(sk5)) = sk0(sk5),
inference(orient,[status(thm)],[t173746]) ).
cnf(t173783,plain,
sk0(sk5) = multiplication(c(sk5),one),
inference(step,[status(thm)],[t3979,t3590]) ).
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(t173784,plain,
sk0(sk5) = c(sk5),
inference(step,[status(thm)],[t173783,t260]) ).
cnf(t3993,plain,
c(sk5) = sk0(sk5),
inference(orient,[status(thm)],[t173784]) ).
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(c25,plain,
leq(multiplication(multiplication(sk3,sk1),c(sk4)),zero),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi25,negated_conjecture,
leq(multiplication(multiplication(sk3,sk1),c(sk4)),zero) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t92,plain,
addition(multiplication(multiplication(sk3,sk1),c(sk4)),zero) = zero,
inference(hyper_resolution,[status(thm)],[hi11,hi25]) ).
cnf(t173500,plain,
multiplication(multiplication(sk3,sk1),c(sk4)) = zero,
inference(step,[status(thm)],[t92,t259]) ).
cnf(t343,plain,
multiplication(multiplication(sk3,sk1),c(sk4)) = zero,
inference(orient,[status(thm)],[t173500]) ).
cnf(t173555,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(step,[status(thm)],[t343,t578]) ).
cnf(t597,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(rw,[status(thm)],[t173555]) ).
cnf(t1054,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(orient,[status(thm)],[t597]) ).
cnf(c16,plain,
( multiplication(X1,X0) = zero
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t121,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t566,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t121]) ).
cnf(t227,plain,
ifeq(test(X1),true,ifeq(c(X1),X2,complement(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t449,plain,
ifeq(test(X1),true,ifeq(c(X1),X2,complement(X1,X2),true),true) = true,
inference(orient,[status(thm)],[t227]) ).
cnf(c22,plain,
test(sk4),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t1,plain,
test(sk4) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t365,plain,
test(sk4) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t450,plain,
true = ifeq(true,true,ifeq(c(sk4),X1,complement(sk4,X1),true),true),
inference(cp,[status(thm)],[t449,t365]) ).
cnf(t173817,plain,
true = ifeq(c(sk4),X1,complement(sk4,X1),true),
inference(step,[status(thm)],[t450,t262]) ).
cnf(t4705,plain,
ifeq(c(sk4),X1,complement(sk4,X1),true) = true,
inference(orient,[status(thm)],[t173817]) ).
cnf(t4706,plain,
true = complement(sk4,c(sk4)),
inference(cp,[status(thm)],[t4705,t262]) ).
cnf(t4707,plain,
complement(sk4,c(sk4)) = true,
inference(orient,[status(thm)],[t4706]) ).
cnf(t4709,plain,
zero = ifeq(true,true,multiplication(sk4,c(sk4)),zero),
inference(cp,[status(thm)],[t566,t4707]) ).
cnf(t173821,plain,
zero = multiplication(sk4,c(sk4)),
inference(step,[status(thm)],[t4709,t262]) ).
cnf(t4738,plain,
multiplication(sk4,c(sk4)) = zero,
inference(orient,[status(thm)],[t173821]) ).
cnf(t4744,plain,
multiplication(addition(sk4,X1),c(sk4)) = addition(zero,multiplication(X1,c(sk4))),
inference(cp,[status(thm)],[t331,t4738]) ).
cnf(t173862,plain,
multiplication(addition(sk4,X1),c(sk4)) = multiplication(X1,c(sk4)),
inference(step,[status(thm)],[t4744,t624]) ).
cnf(t5589,plain,
multiplication(addition(sk4,X1),c(sk4)) = multiplication(X1,c(sk4)),
inference(orient,[status(thm)],[t173862]) ).
cnf(t444,plain,
true = ifeq(true,true,complement(sk0(sk4),sk4),true),
inference(cp,[status(thm)],[t443,t365]) ).
cnf(t173564,plain,
true = complement(sk0(sk4),sk4),
inference(step,[status(thm)],[t444,t262]) ).
cnf(t635,plain,
complement(sk0(sk4),sk4) = true,
inference(orient,[status(thm)],[t173564]) ).
cnf(t636,plain,
one = ifeq(true,true,addition(sk4,sk0(sk4)),one),
inference(cp,[status(thm)],[t599,t635]) ).
cnf(t173585,plain,
one = addition(sk4,sk0(sk4)),
inference(step,[status(thm)],[t636,t262]) ).
cnf(t670,plain,
addition(sk4,sk0(sk4)) = one,
inference(orient,[status(thm)],[t173585]) ).
cnf(t5596,plain,
multiplication(sk0(sk4),c(sk4)) = multiplication(one,c(sk4)),
inference(cp,[status(thm)],[t5589,t670]) ).
cnf(t637,plain,
zero = ifeq(true,true,multiplication(sk0(sk4),sk4),zero),
inference(cp,[status(thm)],[t566,t635]) ).
cnf(t173586,plain,
zero = multiplication(sk0(sk4),sk4),
inference(step,[status(thm)],[t637,t262]) ).
cnf(t675,plain,
multiplication(sk0(sk4),sk4) = zero,
inference(orient,[status(thm)],[t173586]) ).
cnf(t678,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = addition(zero,multiplication(sk0(sk4),X1)),
inference(cp,[status(thm)],[t337,t675]) ).
cnf(t173733,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = multiplication(sk0(sk4),X1),
inference(step,[status(thm)],[t678,t624]) ).
cnf(t3403,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = multiplication(sk0(sk4),X1),
inference(orient,[status(thm)],[t173733]) ).
cnf(t4708,plain,
one = ifeq(true,true,addition(c(sk4),sk4),one),
inference(cp,[status(thm)],[t599,t4707]) ).
cnf(t173819,plain,
one = addition(c(sk4),sk4),
inference(step,[status(thm)],[t4708,t262]) ).
cnf(t173820,plain,
one = addition(sk4,c(sk4)),
inference(step,[status(thm)],[t173819,t273]) ).
cnf(t4718,plain,
addition(sk4,c(sk4)) = one,
inference(orient,[status(thm)],[t173820]) ).
cnf(t4721,plain,
multiplication(sk0(sk4),c(sk4)) = multiplication(sk0(sk4),one),
inference(cp,[status(thm)],[t3403,t4718]) ).
cnf(t173834,plain,
multiplication(sk0(sk4),c(sk4)) = sk0(sk4),
inference(step,[status(thm)],[t4721,t260]) ).
cnf(t4806,plain,
multiplication(sk0(sk4),c(sk4)) = sk0(sk4),
inference(orient,[status(thm)],[t173834]) ).
cnf(t173863,plain,
sk0(sk4) = multiplication(one,c(sk4)),
inference(step,[status(thm)],[t5596,t4806]) ).
cnf(t173864,plain,
sk0(sk4) = c(sk4),
inference(step,[status(thm)],[t173863,t261]) ).
cnf(t5615,plain,
c(sk4) = sk0(sk4),
inference(orient,[status(thm)],[t173864]) ).
cnf(t173888,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(step,[status(thm)],[t1054,t5615]) ).
cnf(t5635,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(rw,[status(thm)],[t173888]) ).
cnf(t5764,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(orient,[status(thm)],[t5635]) ).
cnf(t5770,plain,
multiplication(sk3,addition(multiplication(sk1,sk0(sk4)),X1)) = addition(zero,multiplication(sk3,X1)),
inference(cp,[status(thm)],[t337,t5764]) ).
cnf(t174282,plain,
multiplication(sk3,addition(multiplication(sk1,sk0(sk4)),X1)) = multiplication(sk3,X1),
inference(step,[status(thm)],[t5770,t624]) ).
cnf(t16002,plain,
multiplication(sk3,addition(multiplication(sk1,sk0(sk4)),X1)) = multiplication(sk3,X1),
inference(orient,[status(thm)],[t174282]) ).
cnf(t16006,plain,
multiplication(sk3,multiplication(sk1,X1)) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),X1))),
inference(cp,[status(thm)],[t16002,t337]) ).
cnf(t172459,plain,
multiplication(sk3,multiplication(sk1,addition(sk0(sk4),X1))) = multiplication(sk3,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t16006]) ).
cnf(t333,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t331,t261]) ).
cnf(t1118,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t333]) ).
cnf(t679,plain,
multiplication(sk0(sk4),addition(X1,sk4)) = addition(multiplication(sk0(sk4),X1),zero),
inference(cp,[status(thm)],[t337,t675]) ).
cnf(t173735,plain,
multiplication(sk0(sk4),addition(X1,sk4)) = multiplication(sk0(sk4),X1),
inference(step,[status(thm)],[t679,t259]) ).
cnf(t3433,plain,
multiplication(sk0(sk4),addition(X1,sk4)) = multiplication(sk0(sk4),X1),
inference(orient,[status(thm)],[t173735]) ).
cnf(t3436,plain,
multiplication(addition(one,sk0(sk4)),addition(X1,sk4)) = addition(addition(X1,sk4),multiplication(sk0(sk4),X1)),
inference(cp,[status(thm)],[t1118,t3433]) ).
cnf(t123,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)],[t123]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t119,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t382,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t119]) ).
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(t118,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t276,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t118]) ).
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(t279,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t276,t258]) ).
cnf(t736,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t279]) ).
cnf(t749,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t382,t736]) ).
cnf(t173600,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t749,t262]) ).
cnf(t773,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t173600]) ).
cnf(t779,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t773,t273]) ).
cnf(t786,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t779]) ).
cnf(t787,plain,
true = leq(sk0(sk4),one),
inference(cp,[status(thm)],[t786,t670]) ).
cnf(t797,plain,
leq(sk0(sk4),one) = true,
inference(orient,[status(thm)],[t787]) ).
cnf(t798,plain,
one = ifeq(true,true,addition(sk0(sk4),one),one),
inference(cp,[status(thm)],[t264,t797]) ).
cnf(t173601,plain,
one = addition(sk0(sk4),one),
inference(step,[status(thm)],[t798,t262]) ).
cnf(t173602,plain,
one = addition(one,sk0(sk4)),
inference(step,[status(thm)],[t173601,t273]) ).
cnf(t806,plain,
addition(one,sk0(sk4)) = one,
inference(orient,[status(thm)],[t173602]) ).
cnf(t174121,plain,
multiplication(one,addition(X1,sk4)) = addition(addition(X1,sk4),multiplication(sk0(sk4),X1)),
inference(step,[status(thm)],[t3436,t806]) ).
cnf(t174122,plain,
addition(X1,sk4) = addition(addition(X1,sk4),multiplication(sk0(sk4),X1)),
inference(step,[status(thm)],[t174121,t261]) ).
cnf(t174123,plain,
addition(X1,sk4) = addition(X1,addition(sk4,multiplication(sk0(sk4),X1))),
inference(step,[status(thm)],[t174122,t276]) ).
cnf(t13077,plain,
addition(X1,addition(sk4,multiplication(sk0(sk4),X1))) = addition(X1,sk4),
inference(orient,[status(thm)],[t174123]) ).
cnf(t172476,plain,
multiplication(sk3,multiplication(sk1,addition(sk4,multiplication(sk0(sk4),sk0(sk4))))) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),sk4))),
inference(cp,[status(thm)],[t172459,t13077]) ).
cnf(t3407,plain,
multiplication(sk0(sk4),sk0(sk4)) = multiplication(sk0(sk4),one),
inference(cp,[status(thm)],[t3403,t670]) ).
cnf(t173734,plain,
multiplication(sk0(sk4),sk0(sk4)) = sk0(sk4),
inference(step,[status(thm)],[t3407,t260]) ).
cnf(t3423,plain,
multiplication(sk0(sk4),sk0(sk4)) = sk0(sk4),
inference(orient,[status(thm)],[t173734]) ).
cnf(t176453,plain,
multiplication(sk3,multiplication(sk1,addition(sk4,sk0(sk4)))) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),sk4))),
inference(step,[status(thm)],[t172476,t3423]) ).
cnf(t176454,plain,
multiplication(sk3,multiplication(sk1,one)) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),sk4))),
inference(step,[status(thm)],[t176453,t670]) ).
cnf(t176455,plain,
multiplication(sk3,sk1) = multiplication(sk3,multiplication(sk1,addition(sk0(sk4),sk4))),
inference(step,[status(thm)],[t176454,t260]) ).
cnf(t176456,plain,
multiplication(sk3,sk1) = multiplication(sk3,multiplication(sk1,sk4)),
inference(step,[status(thm)],[t176455,t172459]) ).
cnf(t172607,plain,
multiplication(sk3,multiplication(sk1,sk4)) = multiplication(sk3,sk1),
inference(orient,[status(thm)],[t176456]) ).
cnf(t172615,plain,
multiplication(sk3,multiplication(multiplication(sk1,sk4),X1)) = multiplication(multiplication(sk3,sk1),X1),
inference(cp,[status(thm)],[t578,t172607]) ).
cnf(t176461,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk4,X1))) = multiplication(multiplication(sk3,sk1),X1),
inference(step,[status(thm)],[t172615,t578]) ).
cnf(t176462,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk4,X1))) = multiplication(sk3,multiplication(sk1,X1)),
inference(step,[status(thm)],[t176461,t578]) ).
cnf(t172928,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk4,X1))) = multiplication(sk3,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t176462]) ).
cnf(c26,plain,
leq(multiplication(multiplication(sk4,sk2),c(sk5)),zero),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi26,negated_conjecture,
leq(multiplication(multiplication(sk4,sk2),c(sk5)),zero) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t93,plain,
addition(multiplication(multiplication(sk4,sk2),c(sk5)),zero) = zero,
inference(hyper_resolution,[status(thm)],[hi11,hi26]) ).
cnf(t173501,plain,
multiplication(multiplication(sk4,sk2),c(sk5)) = zero,
inference(step,[status(thm)],[t93,t259]) ).
cnf(t348,plain,
multiplication(multiplication(sk4,sk2),c(sk5)) = zero,
inference(orient,[status(thm)],[t173501]) ).
cnf(t173554,plain,
multiplication(sk4,multiplication(sk2,c(sk5))) = zero,
inference(step,[status(thm)],[t348,t578]) ).
cnf(t596,plain,
multiplication(sk4,multiplication(sk2,c(sk5))) = zero,
inference(rw,[status(thm)],[t173554]) ).
cnf(t1044,plain,
multiplication(sk4,multiplication(sk2,c(sk5))) = zero,
inference(orient,[status(thm)],[t596]) ).
cnf(t173795,plain,
multiplication(sk4,multiplication(sk2,sk0(sk5))) = zero,
inference(step,[status(thm)],[t1044,t3993]) ).
cnf(t4004,plain,
multiplication(sk4,multiplication(sk2,sk0(sk5))) = zero,
inference(rw,[status(thm)],[t173795]) ).
cnf(t4077,plain,
multiplication(sk4,multiplication(sk2,sk0(sk5))) = zero,
inference(orient,[status(thm)],[t4004]) ).
cnf(t173013,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))) = multiplication(sk3,multiplication(sk1,zero)),
inference(cp,[status(thm)],[t172928,t4077]) ).
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(t7,plain,
multiplication(X1,zero) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t469,plain,
multiplication(X1,zero) = zero,
inference(orient,[status(thm)],[t7]) ).
cnf(t176465,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))) = multiplication(sk3,zero),
inference(step,[status(thm)],[t173013,t469]) ).
cnf(t176466,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))) = zero,
inference(step,[status(thm)],[t176465,t469]) ).
cnf(t173378,plain,
multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))) = zero,
inference(orient,[status(thm)],[t176466]) ).
cnf(t627,plain,
true = ifeq(X1,X1,leq(zero,X1),true),
inference(cp,[status(thm)],[t382,t624]) ).
cnf(t173563,plain,
true = leq(zero,X1),
inference(step,[status(thm)],[t627,t262]) ).
cnf(t634,plain,
leq(zero,X1) = true,
inference(orient,[status(thm)],[t173563]) ).
cnf(c27,plain,
~ leq(multiplication(multiplication(multiplication(sk3,sk1),sk2),c(sk5)),zero),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
leq(multiplication(multiplication(multiplication(sk3,sk1),sk2),c(sk5)),zero) != true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
leq(multiplication(multiplication(sk3,sk1),multiplication(sk2,c(sk5))),zero) != true,
inference(rw,[status(thm)],[goal_0,t578]) ).
cnf(g0_1,plain,
leq(multiplication(sk3,multiplication(sk1,multiplication(sk2,c(sk5)))),zero) != true,
inference(rw,[status(thm)],[g0_0,t578]) ).
cnf(g0_2,plain,
leq(multiplication(sk3,multiplication(sk1,multiplication(sk2,sk0(sk5)))),zero) != true,
inference(rw,[status(thm)],[g0_1,t3993]) ).
cnf(g0_3,plain,
leq(zero,zero) != true,
inference(rw,[status(thm)],[g0_2,t173378]) ).
cnf(g0_4,plain,
true != true,
inference(rw,[status(thm)],[g0_3,t634]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE034+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 18:44:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 184.14/27.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 184.14/27.61 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------