%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE011+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:51:20 PM UTC 2026
% Result : Theorem 86.07s 11.26s
% Output : Proof 86.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 17
% Syntax : Number of formulae : 371 ( 347 unt; 0 def)
% Number of atoms : 429 ( 379 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 109 ( 51 ~; 31 |; 20 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 358 ( 29 sgn 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(t80,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t395,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t80]) ).
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(t85,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)],[t85]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t81,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t476,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t81]) ).
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(t260,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t398,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t395,t260]) ).
cnf(t621,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t398]) ).
cnf(t632,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t476,t621]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t40636,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t632,t262]) ).
cnf(t661,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t40636]) ).
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(t13,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t384,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t667,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t661,t384]) ).
cnf(t674,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t667]) ).
cnf(t677,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t674,t395]) ).
cnf(t1955,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t677]) ).
cnf(t2007,plain,
addition(X1,addition(X2,X3)) = ifeq(true,true,addition(X3,addition(X1,addition(X2,X3))),addition(X1,addition(X2,X3))),
inference(cp,[status(thm)],[t264,t1955]) ).
cnf(t40949,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,addition(X2,X3))),
inference(step,[status(thm)],[t2007,t262]) ).
cnf(t630,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t621,t384]) ).
cnf(t720,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t630]) ).
cnf(t728,plain,
addition(X1,addition(X2,X3)) = addition(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t720,t395]) ).
cnf(t4545,plain,
addition(X1,addition(X2,addition(X3,X1))) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t728]) ).
cnf(t40950,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(step,[status(thm)],[t40949,t4545]) ).
cnf(t6605,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(orient,[status(thm)],[t40950]) ).
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(t115,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t316,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t115]) ).
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(t7,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t257,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t328,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t316,t257]) ).
cnf(t889,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t328]) ).
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(t114,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t269,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t114]) ).
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(c16,plain,
( multiplication(X1,X0) = zero
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t83,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t520,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t83]) ).
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(t86,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t485,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t86]) ).
fof(f16,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1] :
( one != addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))
& test(X0)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( one != addition(addition(multiplication(addition(sk2,c(sk2)),sk1),multiplication(addition(sk1,c(sk1)),sk2)),multiplication(c(sk1),c(sk2)))
& test(sk1)
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f16_nnf]) ).
cnf(c23,plain,
test(sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t0,plain,
test(sk1) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t415,plain,
test(sk1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t487,plain,
true = ifeq(true,true,complement(sk0(sk1),sk1),true),
inference(cp,[status(thm)],[t485,t415]) ).
cnf(t40605,plain,
true = complement(sk0(sk1),sk1),
inference(step,[status(thm)],[t487,t262]) ).
cnf(t558,plain,
complement(sk0(sk1),sk1) = true,
inference(orient,[status(thm)],[t40605]) ).
cnf(t559,plain,
zero = ifeq(true,true,multiplication(sk0(sk1),sk1),zero),
inference(cp,[status(thm)],[t520,t558]) ).
cnf(t40625,plain,
zero = multiplication(sk0(sk1),sk1),
inference(step,[status(thm)],[t559,t262]) ).
cnf(t599,plain,
multiplication(sk0(sk1),sk1) = zero,
inference(orient,[status(thm)],[t40625]) ).
cnf(t603,plain,
multiplication(sk0(sk1),addition(sk1,X1)) = addition(zero,multiplication(sk0(sk1),X1)),
inference(cp,[status(thm)],[t269,t599]) ).
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(t261,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t385,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t384,t261]) ).
cnf(t532,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t385]) ).
cnf(t40770,plain,
multiplication(sk0(sk1),addition(sk1,X1)) = multiplication(sk0(sk1),X1),
inference(step,[status(thm)],[t603,t532]) ).
cnf(t2825,plain,
multiplication(sk0(sk1),addition(sk1,X1)) = multiplication(sk0(sk1),X1),
inference(orient,[status(thm)],[t40770]) ).
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(hi23,negated_conjecture,
test(sk1) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
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(hi5,axiom,
multiplication(X0,one) = X0,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h8,plain,
complement(sk1,multiplication(c(sk1),one)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi5]) ).
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(t25,plain,
addition(multiplication(c(sk1),one),sk1) = one,
inference(hyper_resolution,[status(thm)],[hi17,h8]) ).
cnf(t5,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t256,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t40558,plain,
addition(c(sk1),sk1) = one,
inference(step,[status(thm)],[t25,t256]) ).
cnf(t356,plain,
addition(c(sk1),sk1) = one,
inference(orient,[status(thm)],[t40558]) ).
cnf(t391,plain,
addition(c(sk1),sk1) = one,
inference(rw,[status(thm)],[t356]) ).
cnf(t40603,plain,
addition(sk1,c(sk1)) = one,
inference(step,[status(thm)],[t391,t384]) ).
cnf(t545,plain,
addition(sk1,c(sk1)) = one,
inference(orient,[status(thm)],[t40603]) ).
cnf(t2831,plain,
multiplication(sk0(sk1),c(sk1)) = multiplication(sk0(sk1),one),
inference(cp,[status(thm)],[t2825,t545]) ).
cnf(t40771,plain,
multiplication(sk0(sk1),c(sk1)) = sk0(sk1),
inference(step,[status(thm)],[t2831,t256]) ).
cnf(t2846,plain,
multiplication(sk0(sk1),c(sk1)) = sk0(sk1),
inference(orient,[status(thm)],[t40771]) ).
cnf(t2847,plain,
multiplication(addition(one,sk0(sk1)),c(sk1)) = addition(c(sk1),sk0(sk1)),
inference(cp,[status(thm)],[t889,t2846]) ).
cnf(t82,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t368,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t82]) ).
cnf(t561,plain,
one = ifeq(true,true,addition(sk1,sk0(sk1)),one),
inference(cp,[status(thm)],[t368,t558]) ).
cnf(t40627,plain,
one = addition(sk1,sk0(sk1)),
inference(step,[status(thm)],[t561,t262]) ).
cnf(t617,plain,
addition(sk1,sk0(sk1)) = one,
inference(orient,[status(thm)],[t40627]) ).
cnf(t675,plain,
true = leq(sk0(sk1),one),
inference(cp,[status(thm)],[t674,t617]) ).
cnf(t684,plain,
leq(sk0(sk1),one) = true,
inference(orient,[status(thm)],[t675]) ).
cnf(t685,plain,
one = ifeq(true,true,addition(sk0(sk1),one),one),
inference(cp,[status(thm)],[t264,t684]) ).
cnf(t40637,plain,
one = addition(sk0(sk1),one),
inference(step,[status(thm)],[t685,t262]) ).
cnf(t40638,plain,
one = addition(one,sk0(sk1)),
inference(step,[status(thm)],[t40637,t384]) ).
cnf(t690,plain,
addition(one,sk0(sk1)) = one,
inference(orient,[status(thm)],[t40638]) ).
cnf(t40773,plain,
multiplication(one,c(sk1)) = addition(c(sk1),sk0(sk1)),
inference(step,[status(thm)],[t2847,t690]) ).
cnf(t40774,plain,
c(sk1) = addition(c(sk1),sk0(sk1)),
inference(step,[status(thm)],[t40773,t257]) ).
cnf(t40775,plain,
c(sk1) = addition(sk0(sk1),c(sk1)),
inference(step,[status(thm)],[t40774,t384]) ).
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(t37,plain,
multiplication(multiplication(c(sk1),one),sk1) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h8]) ).
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(t87,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t268,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t87]) ).
cnf(t40528,plain,
multiplication(c(sk1),multiplication(one,sk1)) = zero,
inference(step,[status(thm)],[t37,t268]) ).
cnf(t40529,plain,
multiplication(c(sk1),sk1) = zero,
inference(step,[status(thm)],[t40528,t257]) ).
cnf(t276,plain,
multiplication(c(sk1),sk1) = zero,
inference(orient,[status(thm)],[t40529]) ).
cnf(t277,plain,
multiplication(c(sk1),addition(sk1,X1)) = addition(zero,multiplication(c(sk1),X1)),
inference(cp,[status(thm)],[t269,t276]) ).
cnf(t40713,plain,
multiplication(c(sk1),addition(sk1,X1)) = multiplication(c(sk1),X1),
inference(step,[status(thm)],[t277,t532]) ).
cnf(t2013,plain,
multiplication(c(sk1),addition(sk1,X1)) = multiplication(c(sk1),X1),
inference(orient,[status(thm)],[t40713]) ).
cnf(t2020,plain,
multiplication(c(sk1),sk0(sk1)) = multiplication(c(sk1),one),
inference(cp,[status(thm)],[t2013,t617]) ).
cnf(t40715,plain,
multiplication(c(sk1),sk0(sk1)) = c(sk1),
inference(step,[status(thm)],[t2020,t256]) ).
cnf(t2047,plain,
multiplication(c(sk1),sk0(sk1)) = c(sk1),
inference(orient,[status(thm)],[t40715]) ).
cnf(t2048,plain,
multiplication(addition(one,c(sk1)),sk0(sk1)) = addition(sk0(sk1),c(sk1)),
inference(cp,[status(thm)],[t889,t2047]) ).
cnf(hi28,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h15,plain,
complement(sk1,or(c(sk1),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi28]) ).
cnf(c14,plain,
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi14,axiom,
ifeq(complement(X0,X1),true,test(X1),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h89,plain,
test(or(c(sk1),false)) = true,
inference(hyper_resolution,[status(thm)],[hi14,h15]) ).
cnf(hi13,axiom,
ifeq(test(X0),true,complement(sk0(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h206,plain,
complement(sk0(or(c(sk1),false)),or(c(sk1),false)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h89]) ).
cnf(t94,plain,
addition(or(c(sk1),false),sk0(or(c(sk1),false))) = one,
inference(hyper_resolution,[status(thm)],[hi17,h206]) ).
cnf(t9,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t258,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t40563,plain,
addition(c(sk1),sk0(or(c(sk1),false))) = one,
inference(step,[status(thm)],[t94,t258]) ).
cnf(t40564,plain,
addition(c(sk1),sk0(c(sk1))) = one,
inference(step,[status(thm)],[t40563,t258]) ).
cnf(t362,plain,
addition(c(sk1),sk0(c(sk1))) = one,
inference(orient,[status(thm)],[t40564]) ).
cnf(t628,plain,
addition(c(sk1),sk0(c(sk1))) = addition(c(sk1),one),
inference(cp,[status(thm)],[t621,t362]) ).
cnf(t40632,plain,
one = addition(c(sk1),one),
inference(step,[status(thm)],[t628,t362]) ).
cnf(t40633,plain,
one = addition(one,c(sk1)),
inference(step,[status(thm)],[t40632,t384]) ).
cnf(t649,plain,
addition(one,c(sk1)) = one,
inference(orient,[status(thm)],[t40633]) ).
cnf(t40716,plain,
multiplication(one,sk0(sk1)) = addition(sk0(sk1),c(sk1)),
inference(step,[status(thm)],[t2048,t649]) ).
cnf(t40717,plain,
sk0(sk1) = addition(sk0(sk1),c(sk1)),
inference(step,[status(thm)],[t40716,t257]) ).
cnf(t2061,plain,
addition(sk0(sk1),c(sk1)) = sk0(sk1),
inference(orient,[status(thm)],[t40717]) ).
cnf(t40776,plain,
c(sk1) = sk0(sk1),
inference(step,[status(thm)],[t40775,t2061]) ).
cnf(t2873,plain,
c(sk1) = sk0(sk1),
inference(orient,[status(thm)],[t40776]) ).
cnf(c22,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi22,negated_conjecture,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h9,plain,
complement(sk2,multiplication(c(sk2),one)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi22,hi5]) ).
cnf(t38,plain,
multiplication(multiplication(c(sk2),one),sk2) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h9]) ).
cnf(t40533,plain,
multiplication(c(sk2),multiplication(one,sk2)) = zero,
inference(step,[status(thm)],[t38,t268]) ).
cnf(t40534,plain,
multiplication(c(sk2),sk2) = zero,
inference(step,[status(thm)],[t40533,t257]) ).
cnf(t284,plain,
multiplication(c(sk2),sk2) = zero,
inference(orient,[status(thm)],[t40534]) ).
cnf(t285,plain,
multiplication(c(sk2),addition(sk2,X1)) = addition(zero,multiplication(c(sk2),X1)),
inference(cp,[status(thm)],[t269,t284]) ).
cnf(t40804,plain,
multiplication(c(sk2),addition(sk2,X1)) = multiplication(c(sk2),X1),
inference(step,[status(thm)],[t285,t532]) ).
cnf(t2939,plain,
multiplication(c(sk2),addition(sk2,X1)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t40804]) ).
cnf(t1,plain,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t417,plain,
test(sk2) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t486,plain,
true = ifeq(true,true,complement(sk0(sk2),sk2),true),
inference(cp,[status(thm)],[t485,t417]) ).
cnf(t40604,plain,
true = complement(sk0(sk2),sk2),
inference(step,[status(thm)],[t486,t262]) ).
cnf(t551,plain,
complement(sk0(sk2),sk2) = true,
inference(orient,[status(thm)],[t40604]) ).
cnf(t554,plain,
one = ifeq(true,true,addition(sk2,sk0(sk2)),one),
inference(cp,[status(thm)],[t368,t551]) ).
cnf(t40624,plain,
one = addition(sk2,sk0(sk2)),
inference(step,[status(thm)],[t554,t262]) ).
cnf(t595,plain,
addition(sk2,sk0(sk2)) = one,
inference(orient,[status(thm)],[t40624]) ).
cnf(t2946,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(c(sk2),one),
inference(cp,[status(thm)],[t2939,t595]) ).
cnf(t84,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t508,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(orient,[status(thm)],[t84]) ).
cnf(t553,plain,
zero = ifeq(true,true,multiplication(sk2,sk0(sk2)),zero),
inference(cp,[status(thm)],[t508,t551]) ).
cnf(t40623,plain,
zero = multiplication(sk2,sk0(sk2)),
inference(step,[status(thm)],[t553,t262]) ).
cnf(t586,plain,
multiplication(sk2,sk0(sk2)) = zero,
inference(orient,[status(thm)],[t40623]) ).
cnf(t588,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = addition(zero,multiplication(X1,sk0(sk2))),
inference(cp,[status(thm)],[t316,t586]) ).
cnf(t40767,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(step,[status(thm)],[t588,t532]) ).
cnf(t2775,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(orient,[status(thm)],[t40767]) ).
cnf(t26,plain,
addition(multiplication(c(sk2),one),sk2) = one,
inference(hyper_resolution,[status(thm)],[hi17,h9]) ).
cnf(t40559,plain,
addition(c(sk2),sk2) = one,
inference(step,[status(thm)],[t26,t256]) ).
cnf(t358,plain,
addition(c(sk2),sk2) = one,
inference(orient,[status(thm)],[t40559]) ).
cnf(t390,plain,
addition(c(sk2),sk2) = one,
inference(rw,[status(thm)],[t358]) ).
cnf(t40602,plain,
addition(sk2,c(sk2)) = one,
inference(step,[status(thm)],[t390,t384]) ).
cnf(t539,plain,
addition(sk2,c(sk2)) = one,
inference(orient,[status(thm)],[t40602]) ).
cnf(t2781,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(one,sk0(sk2)),
inference(cp,[status(thm)],[t2775,t539]) ).
cnf(t40768,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(step,[status(thm)],[t2781,t257]) ).
cnf(t2796,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(orient,[status(thm)],[t40768]) ).
cnf(t40805,plain,
sk0(sk2) = multiplication(c(sk2),one),
inference(step,[status(thm)],[t2946,t2796]) ).
cnf(t40806,plain,
sk0(sk2) = c(sk2),
inference(step,[status(thm)],[t40805,t256]) ).
cnf(t2958,plain,
c(sk2) = sk0(sk2),
inference(orient,[status(thm)],[t40806]) ).
cnf(t1965,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t1955,t384]) ).
cnf(t40745,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t1965,t395]) ).
cnf(t2487,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t40745]) ).
cnf(t680,plain,
true = leq(multiplication(X1,X2),multiplication(X1,addition(X3,X2))),
inference(cp,[status(thm)],[t674,t269]) ).
cnf(t11780,plain,
leq(multiplication(X1,X2),multiplication(X1,addition(X3,X2))) = true,
inference(orient,[status(thm)],[t680]) ).
cnf(t625,plain,
addition(sk2,c(sk2)) = addition(sk2,one),
inference(cp,[status(thm)],[t621,t539]) ).
cnf(t40629,plain,
one = addition(sk2,one),
inference(step,[status(thm)],[t625,t539]) ).
cnf(t641,plain,
addition(sk2,one) = one,
inference(orient,[status(thm)],[t40629]) ).
cnf(t644,plain,
addition(sk2,addition(one,X1)) = addition(one,X1),
inference(cp,[status(thm)],[t395,t641]) ).
cnf(t753,plain,
addition(sk2,addition(one,X1)) = addition(one,X1),
inference(orient,[status(thm)],[t644]) ).
cnf(t757,plain,
addition(addition(one,X1),sk2) = addition(addition(one,X1),addition(one,X1)),
inference(cp,[status(thm)],[t720,t753]) ).
cnf(t40649,plain,
addition(one,addition(X1,sk2)) = addition(addition(one,X1),addition(one,X1)),
inference(step,[status(thm)],[t757,t395]) ).
cnf(t40650,plain,
addition(one,addition(X1,sk2)) = addition(one,addition(X1,addition(one,X1))),
inference(step,[status(thm)],[t40649,t395]) ).
cnf(t40651,plain,
addition(one,addition(X1,sk2)) = addition(one,addition(X1,one)),
inference(step,[status(thm)],[t40650,t720]) ).
cnf(t40652,plain,
addition(one,addition(X1,sk2)) = addition(one,X1),
inference(step,[status(thm)],[t40651,t720]) ).
cnf(t803,plain,
addition(one,addition(X1,sk2)) = addition(one,X1),
inference(orient,[status(thm)],[t40652]) ).
cnf(t807,plain,
addition(one,X1) = addition(one,addition(sk2,X1)),
inference(cp,[status(thm)],[t803,t384]) ).
cnf(t823,plain,
addition(one,addition(sk2,X1)) = addition(one,X1),
inference(orient,[status(thm)],[t807]) ).
cnf(t901,plain,
addition(one,multiplication(X1,sk2)) = addition(one,multiplication(addition(one,X1),sk2)),
inference(cp,[status(thm)],[t823,t889]) ).
cnf(hi16,axiom,
ifeq(complement(X0,X1),true,multiplication(X0,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t43,plain,
multiplication(sk2,multiplication(c(sk2),one)) = zero,
inference(hyper_resolution,[status(thm)],[hi16,h9]) ).
cnf(t40547,plain,
multiplication(sk2,c(sk2)) = zero,
inference(step,[status(thm)],[t43,t256]) ).
cnf(t304,plain,
multiplication(sk2,c(sk2)) = zero,
inference(orient,[status(thm)],[t40547]) ).
cnf(t306,plain,
multiplication(sk2,addition(X1,c(sk2))) = addition(multiplication(sk2,X1),zero),
inference(cp,[status(thm)],[t269,t304]) ).
cnf(t40668,plain,
multiplication(sk2,addition(X1,c(sk2))) = multiplication(sk2,X1),
inference(step,[status(thm)],[t306,t261]) ).
cnf(t1088,plain,
multiplication(sk2,addition(X1,c(sk2))) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t40668]) ).
cnf(t1089,plain,
multiplication(sk2,sk2) = multiplication(sk2,one),
inference(cp,[status(thm)],[t1088,t539]) ).
cnf(t40669,plain,
multiplication(sk2,sk2) = sk2,
inference(step,[status(thm)],[t1089,t256]) ).
cnf(t1103,plain,
multiplication(sk2,sk2) = sk2,
inference(orient,[status(thm)],[t40669]) ).
cnf(t1108,plain,
multiplication(addition(sk2,X1),sk2) = addition(sk2,multiplication(X1,sk2)),
inference(cp,[status(thm)],[t316,t1103]) ).
cnf(t40670,plain,
multiplication(addition(sk2,X1),sk2) = multiplication(addition(one,X1),sk2),
inference(step,[status(thm)],[t1108,t889]) ).
cnf(t1126,plain,
multiplication(addition(one,X1),sk2) = multiplication(addition(sk2,X1),sk2),
inference(orient,[status(thm)],[t40670]) ).
cnf(t40918,plain,
addition(one,multiplication(X1,sk2)) = addition(one,multiplication(addition(sk2,X1),sk2)),
inference(step,[status(thm)],[t901,t1126]) ).
cnf(t5400,plain,
addition(one,multiplication(addition(sk2,X1),sk2)) = addition(one,multiplication(X1,sk2)),
inference(orient,[status(thm)],[t40918]) ).
cnf(t552,plain,
zero = ifeq(true,true,multiplication(sk0(sk2),sk2),zero),
inference(cp,[status(thm)],[t520,t551]) ).
cnf(t40622,plain,
zero = multiplication(sk0(sk2),sk2),
inference(step,[status(thm)],[t552,t262]) ).
cnf(t577,plain,
multiplication(sk0(sk2),sk2) = zero,
inference(orient,[status(thm)],[t40622]) ).
cnf(t579,plain,
multiplication(addition(sk0(sk2),X1),sk2) = addition(zero,multiplication(X1,sk2)),
inference(cp,[status(thm)],[t316,t577]) ).
cnf(t40679,plain,
multiplication(addition(sk0(sk2),X1),sk2) = multiplication(X1,sk2),
inference(step,[status(thm)],[t579,t532]) ).
cnf(t1273,plain,
multiplication(addition(sk0(sk2),X1),sk2) = multiplication(X1,sk2),
inference(orient,[status(thm)],[t40679]) ).
cnf(t598,plain,
addition(sk2,addition(sk0(sk2),X1)) = addition(one,X1),
inference(cp,[status(thm)],[t395,t595]) ).
cnf(t1327,plain,
addition(sk2,addition(sk0(sk2),X1)) = addition(one,X1),
inference(orient,[status(thm)],[t598]) ).
cnf(t1336,plain,
addition(addition(sk0(sk2),X1),sk2) = addition(addition(sk0(sk2),X1),addition(one,X1)),
inference(cp,[status(thm)],[t720,t1327]) ).
cnf(t40863,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(addition(sk0(sk2),X1),addition(one,X1)),
inference(step,[status(thm)],[t1336,t395]) ).
cnf(t40864,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(sk0(sk2),addition(X1,addition(one,X1))),
inference(step,[status(thm)],[t40863,t395]) ).
cnf(t40865,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(sk0(sk2),addition(X1,one)),
inference(step,[status(thm)],[t40864,t720]) ).
cnf(t676,plain,
true = leq(sk0(sk2),one),
inference(cp,[status(thm)],[t674,t595]) ).
cnf(t687,plain,
leq(sk0(sk2),one) = true,
inference(orient,[status(thm)],[t676]) ).
cnf(t688,plain,
one = ifeq(true,true,addition(sk0(sk2),one),one),
inference(cp,[status(thm)],[t264,t687]) ).
cnf(t40639,plain,
one = addition(sk0(sk2),one),
inference(step,[status(thm)],[t688,t262]) ).
cnf(t40640,plain,
one = addition(one,sk0(sk2)),
inference(step,[status(thm)],[t40639,t384]) ).
cnf(t696,plain,
addition(one,sk0(sk2)) = one,
inference(orient,[status(thm)],[t40640]) ).
cnf(t1984,plain,
true = leq(sk0(sk2),addition(X1,one)),
inference(cp,[status(thm)],[t1955,t696]) ).
cnf(t2089,plain,
leq(sk0(sk2),addition(X1,one)) = true,
inference(orient,[status(thm)],[t1984]) ).
cnf(t2091,plain,
addition(X1,one) = ifeq(true,true,addition(sk0(sk2),addition(X1,one)),addition(X1,one)),
inference(cp,[status(thm)],[t264,t2089]) ).
cnf(t40723,plain,
addition(X1,one) = addition(sk0(sk2),addition(X1,one)),
inference(step,[status(thm)],[t2091,t262]) ).
cnf(t2168,plain,
addition(sk0(sk2),addition(X1,one)) = addition(X1,one),
inference(orient,[status(thm)],[t40723]) ).
cnf(t40866,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(X1,one),
inference(step,[status(thm)],[t40865,t2168]) ).
cnf(t3908,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(X1,one),
inference(orient,[status(thm)],[t40866]) ).
cnf(t3922,plain,
multiplication(addition(X1,sk2),sk2) = multiplication(addition(X1,one),sk2),
inference(cp,[status(thm)],[t1273,t3908]) ).
cnf(t3961,plain,
multiplication(addition(X1,one),sk2) = multiplication(addition(X1,sk2),sk2),
inference(orient,[status(thm)],[t3922]) ).
cnf(t623,plain,
addition(sk1,c(sk1)) = addition(sk1,one),
inference(cp,[status(thm)],[t621,t545]) ).
cnf(t40628,plain,
one = addition(sk1,one),
inference(step,[status(thm)],[t623,t545]) ).
cnf(t635,plain,
addition(sk1,one) = one,
inference(orient,[status(thm)],[t40628]) ).
cnf(t3962,plain,
multiplication(addition(sk1,sk2),sk2) = multiplication(one,sk2),
inference(cp,[status(thm)],[t3961,t635]) ).
cnf(t40869,plain,
multiplication(addition(sk2,sk1),sk2) = multiplication(one,sk2),
inference(step,[status(thm)],[t3962,t384]) ).
cnf(t40870,plain,
multiplication(addition(sk2,sk1),sk2) = sk2,
inference(step,[status(thm)],[t40869,t257]) ).
cnf(t3980,plain,
multiplication(addition(sk2,sk1),sk2) = sk2,
inference(orient,[status(thm)],[t40870]) ).
cnf(t5402,plain,
addition(one,multiplication(sk1,sk2)) = addition(one,sk2),
inference(cp,[status(thm)],[t5400,t3980]) ).
cnf(t40919,plain,
addition(one,multiplication(sk1,sk2)) = addition(sk2,one),
inference(step,[status(thm)],[t5402,t384]) ).
cnf(t40920,plain,
addition(one,multiplication(sk1,sk2)) = one,
inference(step,[status(thm)],[t40919,t641]) ).
cnf(t5442,plain,
addition(one,multiplication(sk1,sk2)) = one,
inference(orient,[status(thm)],[t40920]) ).
cnf(t11922,plain,
true = leq(multiplication(X1,multiplication(sk1,sk2)),multiplication(X1,one)),
inference(cp,[status(thm)],[t11780,t5442]) ).
cnf(t41094,plain,
true = leq(multiplication(X1,multiplication(sk1,sk2)),X1),
inference(step,[status(thm)],[t11922,t256]) ).
cnf(t11996,plain,
leq(multiplication(X1,multiplication(sk1,sk2)),X1) = true,
inference(orient,[status(thm)],[t41094]) ).
cnf(t337,plain,
multiplication(addition(X1,c(sk1)),sk1) = addition(multiplication(X1,sk1),zero),
inference(cp,[status(thm)],[t316,t276]) ).
cnf(t40678,plain,
multiplication(addition(X1,c(sk1)),sk1) = multiplication(X1,sk1),
inference(step,[status(thm)],[t337,t261]) ).
cnf(t1231,plain,
multiplication(addition(X1,c(sk1)),sk1) = multiplication(X1,sk1),
inference(orient,[status(thm)],[t40678]) ).
cnf(t1233,plain,
multiplication(X1,sk1) = multiplication(addition(c(sk1),X1),sk1),
inference(cp,[status(thm)],[t1231,t384]) ).
cnf(t1752,plain,
multiplication(addition(c(sk1),X1),sk1) = multiplication(X1,sk1),
inference(orient,[status(thm)],[t1233]) ).
cnf(t1753,plain,
multiplication(sk0(c(sk1)),sk1) = multiplication(one,sk1),
inference(cp,[status(thm)],[t1752,t362]) ).
cnf(t40690,plain,
multiplication(sk0(c(sk1)),sk1) = sk1,
inference(step,[status(thm)],[t1753,t257]) ).
cnf(t1767,plain,
multiplication(sk0(c(sk1)),sk1) = sk1,
inference(orient,[status(thm)],[t40690]) ).
cnf(t40786,plain,
multiplication(sk0(sk0(sk1)),sk1) = sk1,
inference(step,[status(thm)],[t1767,t2873]) ).
cnf(t2883,plain,
multiplication(sk0(sk0(sk1)),sk1) = sk1,
inference(rw,[status(thm)],[t40786]) ).
cnf(t2909,plain,
multiplication(sk0(sk0(sk1)),sk1) = sk1,
inference(orient,[status(thm)],[t2883]) ).
cnf(t2918,plain,
multiplication(sk0(sk0(sk1)),multiplication(sk1,X1)) = multiplication(sk1,X1),
inference(cp,[status(thm)],[t268,t2909]) ).
cnf(t3332,plain,
multiplication(sk0(sk0(sk1)),multiplication(sk1,X1)) = multiplication(sk1,X1),
inference(orient,[status(thm)],[t2918]) ).
cnf(t11998,plain,
true = leq(multiplication(sk1,sk2),sk0(sk0(sk1))),
inference(cp,[status(thm)],[t11996,t3332]) ).
cnf(t12017,plain,
leq(multiplication(sk1,sk2),sk0(sk0(sk1))) = true,
inference(orient,[status(thm)],[t11998]) ).
cnf(t12018,plain,
sk0(sk0(sk1)) = ifeq(true,true,addition(multiplication(sk1,sk2),sk0(sk0(sk1))),sk0(sk0(sk1))),
inference(cp,[status(thm)],[t264,t12017]) ).
cnf(t41096,plain,
sk0(sk0(sk1)) = addition(multiplication(sk1,sk2),sk0(sk0(sk1))),
inference(step,[status(thm)],[t12018,t262]) ).
cnf(t12032,plain,
addition(multiplication(sk1,sk2),sk0(sk0(sk1))) = sk0(sk0(sk1)),
inference(orient,[status(thm)],[t41096]) ).
cnf(t12048,plain,
true = leq(multiplication(sk1,sk2),addition(X1,sk0(sk0(sk1)))),
inference(cp,[status(thm)],[t2487,t12032]) ).
cnf(t19685,plain,
leq(multiplication(sk1,sk2),addition(X1,sk0(sk0(sk1)))) = true,
inference(orient,[status(thm)],[t12048]) ).
cnf(t19687,plain,
true = leq(multiplication(sk1,sk2),addition(sk0(sk0(sk1)),X1)),
inference(cp,[status(thm)],[t19685,t384]) ).
cnf(t25989,plain,
leq(multiplication(sk1,sk2),addition(sk0(sk0(sk1)),X1)) = true,
inference(orient,[status(thm)],[t19687]) ).
cnf(t2916,plain,
multiplication(sk0(sk0(sk1)),addition(sk1,X1)) = addition(sk1,multiplication(sk0(sk0(sk1)),X1)),
inference(cp,[status(thm)],[t269,t2909]) ).
cnf(t40059,plain,
addition(sk1,multiplication(sk0(sk0(sk1)),X1)) = multiplication(sk0(sk0(sk1)),addition(sk1,X1)),
inference(orient,[status(thm)],[t2916]) ).
cnf(h52,plain,
test(multiplication(c(sk1),one)) = true,
inference(hyper_resolution,[status(thm)],[hi14,h8]) ).
cnf(h134,plain,
complement(sk0(multiplication(c(sk1),one)),multiplication(c(sk1),one)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h52]) ).
cnf(t106,plain,
multiplication(sk0(multiplication(c(sk1),one)),multiplication(c(sk1),one)) = zero,
inference(hyper_resolution,[status(thm)],[hi16,h134]) ).
cnf(t40554,plain,
multiplication(sk0(c(sk1)),multiplication(c(sk1),one)) = zero,
inference(step,[status(thm)],[t106,t256]) ).
cnf(t40555,plain,
multiplication(sk0(c(sk1)),c(sk1)) = zero,
inference(step,[status(thm)],[t40554,t256]) ).
cnf(t344,plain,
multiplication(sk0(c(sk1)),c(sk1)) = zero,
inference(orient,[status(thm)],[t40555]) ).
cnf(t40794,plain,
multiplication(sk0(sk0(sk1)),c(sk1)) = zero,
inference(step,[status(thm)],[t344,t2873]) ).
cnf(t40795,plain,
multiplication(sk0(sk0(sk1)),sk0(sk1)) = zero,
inference(step,[status(thm)],[t40794,t2873]) ).
cnf(t2889,plain,
multiplication(sk0(sk0(sk1)),sk0(sk1)) = zero,
inference(rw,[status(thm)],[t40795]) ).
cnf(t3086,plain,
multiplication(sk0(sk0(sk1)),sk0(sk1)) = zero,
inference(orient,[status(thm)],[t2889]) ).
cnf(t40061,plain,
multiplication(sk0(sk0(sk1)),addition(sk1,sk0(sk1))) = addition(sk1,zero),
inference(cp,[status(thm)],[t40059,t3086]) ).
cnf(t41467,plain,
multiplication(sk0(sk0(sk1)),one) = addition(sk1,zero),
inference(step,[status(thm)],[t40061,t617]) ).
cnf(t41468,plain,
sk0(sk0(sk1)) = addition(sk1,zero),
inference(step,[status(thm)],[t41467,t256]) ).
cnf(t41469,plain,
sk0(sk0(sk1)) = sk1,
inference(step,[status(thm)],[t41468,t261]) ).
cnf(t40187,plain,
sk0(sk0(sk1)) = sk1,
inference(orient,[status(thm)],[t41469]) ).
cnf(t41476,plain,
leq(multiplication(sk1,sk2),addition(sk1,X1)) = true,
inference(step,[status(thm)],[t25989,t40187]) ).
cnf(t40192,plain,
leq(multiplication(sk1,sk2),addition(sk1,X1)) = true,
inference(rw,[status(thm)],[t41476]) ).
cnf(t40206,plain,
leq(multiplication(sk1,sk2),addition(sk1,X1)) = true,
inference(orient,[status(thm)],[t40192]) ).
cnf(t40214,plain,
addition(sk1,X1) = ifeq(true,true,addition(multiplication(sk1,sk2),addition(sk1,X1)),addition(sk1,X1)),
inference(cp,[status(thm)],[t264,t40206]) ).
cnf(t41500,plain,
addition(sk1,X1) = addition(multiplication(sk1,sk2),addition(sk1,X1)),
inference(step,[status(thm)],[t40214,t262]) ).
cnf(t2514,plain,
addition(X1,addition(X2,X3)) = ifeq(true,true,addition(X2,addition(X1,addition(X2,X3))),addition(X1,addition(X2,X3))),
inference(cp,[status(thm)],[t264,t2487]) ).
cnf(t40951,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,addition(X2,X3))),
inference(step,[status(thm)],[t2514,t262]) ).
cnf(t734,plain,
addition(X1,addition(addition(X2,X1),X3)) = addition(addition(X1,X2),X3),
inference(cp,[status(thm)],[t395,t720]) ).
cnf(t40889,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(addition(X1,X2),X3),
inference(step,[status(thm)],[t734,t395]) ).
cnf(t40890,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X1,addition(X2,X3)),
inference(step,[status(thm)],[t40889,t395]) ).
cnf(t4643,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t40890]) ).
cnf(t40952,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(step,[status(thm)],[t40951,t4643]) ).
cnf(t6989,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(orient,[status(thm)],[t40952]) ).
cnf(t41501,plain,
addition(sk1,X1) = addition(sk1,addition(multiplication(sk1,sk2),X1)),
inference(step,[status(thm)],[t41500,t6989]) ).
cnf(t40224,plain,
addition(sk1,addition(multiplication(sk1,sk2),X1)) = addition(sk1,X1),
inference(orient,[status(thm)],[t41501]) ).
cnf(t40231,plain,
addition(sk1,multiplication(X1,sk2)) = addition(sk1,multiplication(addition(sk1,X1),sk2)),
inference(cp,[status(thm)],[t40224,t316]) ).
cnf(t40410,plain,
addition(sk1,multiplication(addition(sk1,X1),sk2)) = addition(sk1,multiplication(X1,sk2)),
inference(orient,[status(thm)],[t40231]) ).
cnf(c24,plain,
one != addition(addition(multiplication(addition(sk2,c(sk2)),sk1),multiplication(addition(sk1,c(sk1)),sk2)),multiplication(c(sk1),c(sk2))),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
addition(addition(multiplication(addition(sk2,c(sk2)),sk1),multiplication(addition(sk1,c(sk1)),sk2)),multiplication(c(sk1),c(sk2))) != one,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(g0_0,plain,
addition(multiplication(addition(sk2,c(sk2)),sk1),addition(multiplication(addition(sk1,c(sk1)),sk2),multiplication(c(sk1),c(sk2)))) != one,
inference(rw,[status(thm)],[goal_0,t395]) ).
cnf(g0_1,plain,
addition(multiplication(c(sk1),c(sk2)),addition(multiplication(addition(sk2,c(sk2)),sk1),multiplication(addition(sk1,c(sk1)),sk2))) != one,
inference(rw,[status(thm)],[g0_0,t6605]) ).
cnf(g0_2,plain,
addition(multiplication(sk0(sk1),c(sk2)),addition(multiplication(addition(sk2,c(sk2)),sk1),multiplication(addition(sk1,c(sk1)),sk2))) != one,
inference(rw,[status(thm)],[g0_1,t2873]) ).
cnf(g0_3,plain,
addition(multiplication(sk0(sk1),sk0(sk2)),addition(multiplication(addition(sk2,c(sk2)),sk1),multiplication(addition(sk1,c(sk1)),sk2))) != one,
inference(rw,[status(thm)],[g0_2,t2958]) ).
cnf(g0_4,plain,
addition(multiplication(sk0(sk1),sk0(sk2)),addition(multiplication(addition(sk2,sk0(sk2)),sk1),multiplication(addition(sk1,c(sk1)),sk2))) != one,
inference(rw,[status(thm)],[g0_3,t2958]) ).
cnf(g0_5,plain,
addition(multiplication(sk0(sk1),sk0(sk2)),addition(multiplication(one,sk1),multiplication(addition(sk1,c(sk1)),sk2))) != one,
inference(rw,[status(thm)],[g0_4,t595]) ).
cnf(g0_6,plain,
addition(multiplication(sk0(sk1),sk0(sk2)),addition(sk1,multiplication(addition(sk1,c(sk1)),sk2))) != one,
inference(rw,[status(thm)],[g0_5,t257]) ).
cnf(g0_7,plain,
addition(multiplication(sk0(sk1),sk0(sk2)),addition(sk1,multiplication(c(sk1),sk2))) != one,
inference(rw,[status(thm)],[g0_6,t40410]) ).
cnf(g0_8,plain,
addition(sk1,addition(multiplication(sk0(sk1),sk0(sk2)),multiplication(c(sk1),sk2))) != one,
inference(rw,[status(thm)],[g0_7,t6989]) ).
cnf(g0_9,plain,
addition(sk1,addition(multiplication(c(sk1),sk2),multiplication(sk0(sk1),sk0(sk2)))) != one,
inference(rw,[status(thm)],[g0_8,t384]) ).
cnf(g0_10,plain,
addition(sk1,addition(multiplication(sk0(sk1),sk2),multiplication(sk0(sk1),sk0(sk2)))) != one,
inference(rw,[status(thm)],[g0_9,t2873]) ).
cnf(g0_11,plain,
addition(sk1,multiplication(sk0(sk1),addition(sk2,sk0(sk2)))) != one,
inference(rw,[status(thm)],[g0_10,t269]) ).
cnf(g0_12,plain,
addition(sk1,multiplication(sk0(sk1),one)) != one,
inference(rw,[status(thm)],[g0_11,t595]) ).
cnf(g0_13,plain,
addition(sk1,sk0(sk1)) != one,
inference(rw,[status(thm)],[g0_12,t256]) ).
cnf(g0_14,plain,
one != one,
inference(rw,[status(thm)],[g0_13,t617]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE011+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n006.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
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 18:34:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 86.07/11.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 86.07/11.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------