%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE023+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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:51:24 PM UTC 2026
% Result : Theorem 77.77s 10.23s
% Output : Proof 77.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 18
% Syntax : Number of formulae : 250 ( 227 unt; 0 def)
% Number of atoms : 311 ( 262 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 100 ( 39 ~; 30 |; 22 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 260 ( 11 sgn 86 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(t152,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)],[t152]) ).
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]) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] :
( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) != multiplication(c(X1),X0)
& addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
& test(X2)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) != multiplication(c(sk2),sk1)
& addition(multiplication(sk2,sk1),multiplication(sk1,sk3)) = multiplication(sk1,sk3)
& test(sk3)
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f16_nnf]) ).
cnf(c23,plain,
test(sk3),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi23,negated_conjecture,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(hi29,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h16,plain,
complement(sk3,or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi29]) ).
fof(f13,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f13_nnf,plain,
! [X0,X1] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X1,X0] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c15,plain,
( multiplication(X0,X1) = zero
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi15,axiom,
ifeq(complement(X0,X1),true,multiplication(X1,X0),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t66,plain,
multiplication(or(c(sk3),false),sk3) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h16]) ).
cnf(t9,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t107825,plain,
multiplication(c(sk3),sk3) = zero,
inference(step,[status(thm)],[t66,t256]) ).
cnf(t353,plain,
multiplication(c(sk3),sk3) = zero,
inference(orient,[status(thm)],[t107825]) ).
cnf(t355,plain,
multiplication(c(sk3),addition(X1,sk3)) = addition(multiplication(c(sk3),X1),zero),
inference(cp,[status(thm)],[t337,t353]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f2_nnf,plain,
! [A] : addition(A,zero) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : addition(A,zero) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t259,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t108023,plain,
multiplication(c(sk3),addition(X1,sk3)) = multiplication(c(sk3),X1),
inference(step,[status(thm)],[t355,t259]) ).
cnf(t2685,plain,
multiplication(c(sk3),addition(X1,sk3)) = multiplication(c(sk3),X1),
inference(orient,[status(thm)],[t108023]) ).
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(t273,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t2687,plain,
multiplication(c(sk3),X1) = multiplication(c(sk3),addition(sk3,X1)),
inference(cp,[status(thm)],[t2685,t273]) ).
cnf(t3133,plain,
multiplication(c(sk3),addition(sk3,X1)) = multiplication(c(sk3),X1),
inference(orient,[status(thm)],[t2687]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t118,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t581,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t118]) ).
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(t122,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t540,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t122]) ).
cnf(t1,plain,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t445,plain,
test(sk3) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t542,plain,
true = ifeq(true,true,complement(sk0(sk3),sk3),true),
inference(cp,[status(thm)],[t540,t445]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t107898,plain,
true = complement(sk0(sk3),sk3),
inference(step,[status(thm)],[t542,t262]) ).
cnf(t639,plain,
complement(sk0(sk3),sk3) = true,
inference(orient,[status(thm)],[t107898]) ).
cnf(t640,plain,
one = ifeq(true,true,addition(sk3,sk0(sk3)),one),
inference(cp,[status(thm)],[t581,t639]) ).
cnf(t107902,plain,
one = addition(sk3,sk0(sk3)),
inference(step,[status(thm)],[t640,t262]) ).
cnf(t668,plain,
addition(sk3,sk0(sk3)) = one,
inference(orient,[status(thm)],[t107902]) ).
cnf(t3140,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(c(sk3),one),
inference(cp,[status(thm)],[t3133,t668]) ).
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(t153,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)],[t153]) ).
cnf(t120,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t405,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(orient,[status(thm)],[t120]) ).
cnf(t642,plain,
zero = ifeq(true,true,multiplication(sk3,sk0(sk3)),zero),
inference(cp,[status(thm)],[t405,t639]) ).
cnf(t107904,plain,
zero = multiplication(sk3,sk0(sk3)),
inference(step,[status(thm)],[t642,t262]) ).
cnf(t682,plain,
multiplication(sk3,sk0(sk3)) = zero,
inference(orient,[status(thm)],[t107904]) ).
cnf(t687,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = addition(zero,multiplication(X1,sk0(sk3))),
inference(cp,[status(thm)],[t331,t682]) ).
cnf(t274,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t273,t259]) ).
cnf(t607,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t274]) ).
cnf(t108045,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(step,[status(thm)],[t687,t607]) ).
cnf(t3087,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(orient,[status(thm)],[t108045]) ).
cnf(hi17,axiom,
ifeq(complement(X0,X1),true,addition(X1,X0),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t46,plain,
addition(or(c(sk3),false),sk3) = one,
inference(hyper_resolution,[status(thm)],[hi17,h16]) ).
cnf(t107786,plain,
addition(sk3,or(c(sk3),false)) = one,
inference(step,[status(thm)],[t46,t273]) ).
cnf(t107787,plain,
addition(sk3,c(sk3)) = one,
inference(step,[status(thm)],[t107786,t256]) ).
cnf(t289,plain,
addition(sk3,c(sk3)) = one,
inference(orient,[status(thm)],[t107787]) ).
cnf(t3093,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(one,sk0(sk3)),
inference(cp,[status(thm)],[t3087,t289]) ).
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(t261,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t108046,plain,
multiplication(c(sk3),sk0(sk3)) = sk0(sk3),
inference(step,[status(thm)],[t3093,t261]) ).
cnf(t3109,plain,
multiplication(c(sk3),sk0(sk3)) = sk0(sk3),
inference(orient,[status(thm)],[t108046]) ).
cnf(t108048,plain,
sk0(sk3) = multiplication(c(sk3),one),
inference(step,[status(thm)],[t3140,t3109]) ).
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(t5,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t260,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t108049,plain,
sk0(sk3) = c(sk3),
inference(step,[status(thm)],[t108048,t260]) ).
cnf(t3154,plain,
c(sk3) = sk0(sk3),
inference(orient,[status(thm)],[t108049]) ).
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(h17,plain,
complement(sk2,or(c(sk2),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi22,hi29]) ).
cnf(t65,plain,
multiplication(or(c(sk2),false),sk2) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h17]) ).
cnf(t107828,plain,
multiplication(c(sk2),sk2) = zero,
inference(step,[status(thm)],[t65,t256]) ).
cnf(t363,plain,
multiplication(c(sk2),sk2) = zero,
inference(orient,[status(thm)],[t107828]) ).
cnf(t365,plain,
multiplication(c(sk2),addition(X1,sk2)) = addition(multiplication(c(sk2),X1),zero),
inference(cp,[status(thm)],[t337,t363]) ).
cnf(t108024,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(step,[status(thm)],[t365,t259]) ).
cnf(t2699,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t108024]) ).
cnf(t2701,plain,
multiplication(c(sk2),X1) = multiplication(c(sk2),addition(sk2,X1)),
inference(cp,[status(thm)],[t2699,t273]) ).
cnf(t3336,plain,
multiplication(c(sk2),addition(sk2,X1)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t2701]) ).
cnf(t0,plain,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t447,plain,
test(sk2) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t541,plain,
true = ifeq(true,true,complement(sk0(sk2),sk2),true),
inference(cp,[status(thm)],[t540,t447]) ).
cnf(t107897,plain,
true = complement(sk0(sk2),sk2),
inference(step,[status(thm)],[t541,t262]) ).
cnf(t632,plain,
complement(sk0(sk2),sk2) = true,
inference(orient,[status(thm)],[t107897]) ).
cnf(t633,plain,
one = ifeq(true,true,addition(sk2,sk0(sk2)),one),
inference(cp,[status(thm)],[t581,t632]) ).
cnf(t107899,plain,
one = addition(sk2,sk0(sk2)),
inference(step,[status(thm)],[t633,t262]) ).
cnf(t646,plain,
addition(sk2,sk0(sk2)) = one,
inference(orient,[status(thm)],[t107899]) ).
cnf(t3343,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(c(sk2),one),
inference(cp,[status(thm)],[t3336,t646]) ).
cnf(t635,plain,
zero = ifeq(true,true,multiplication(sk2,sk0(sk2)),zero),
inference(cp,[status(thm)],[t405,t632]) ).
cnf(t107901,plain,
zero = multiplication(sk2,sk0(sk2)),
inference(step,[status(thm)],[t635,t262]) ).
cnf(t660,plain,
multiplication(sk2,sk0(sk2)) = zero,
inference(orient,[status(thm)],[t107901]) ).
cnf(t665,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = addition(zero,multiplication(X1,sk0(sk2))),
inference(cp,[status(thm)],[t331,t660]) ).
cnf(t108034,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(step,[status(thm)],[t665,t607]) ).
cnf(t2826,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(orient,[status(thm)],[t108034]) ).
cnf(t45,plain,
addition(or(c(sk2),false),sk2) = one,
inference(hyper_resolution,[status(thm)],[hi17,h17]) ).
cnf(t107790,plain,
addition(sk2,or(c(sk2),false)) = one,
inference(step,[status(thm)],[t45,t273]) ).
cnf(t107791,plain,
addition(sk2,c(sk2)) = one,
inference(step,[status(thm)],[t107790,t256]) ).
cnf(t295,plain,
addition(sk2,c(sk2)) = one,
inference(orient,[status(thm)],[t107791]) ).
cnf(t2832,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(one,sk0(sk2)),
inference(cp,[status(thm)],[t2826,t295]) ).
cnf(t108035,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(step,[status(thm)],[t2832,t261]) ).
cnf(t2847,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(orient,[status(thm)],[t108035]) ).
cnf(t108075,plain,
sk0(sk2) = multiplication(c(sk2),one),
inference(step,[status(thm)],[t3343,t2847]) ).
cnf(t108076,plain,
sk0(sk2) = c(sk2),
inference(step,[status(thm)],[t108075,t260]) ).
cnf(t3357,plain,
c(sk2) = sk0(sk2),
inference(orient,[status(thm)],[t108076]) ).
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(t121,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)],[t121]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t117,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t465,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t117]) ).
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(t115,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)],[t115]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f3_nnf,plain,
! [A] : addition(A,A) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : addition(A,A) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t2,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t258,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t279,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t276,t258]) ).
cnf(t690,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t279]) ).
cnf(t702,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t465,t690]) ).
cnf(t107909,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t702,t262]) ).
cnf(t718,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t107909]) ).
cnf(t720,plain,
true = leq(multiplication(X1,X2),multiplication(X1,addition(X2,X3))),
inference(cp,[status(thm)],[t718,t337]) ).
cnf(t8452,plain,
leq(multiplication(X1,X2),multiplication(X1,addition(X2,X3))) = true,
inference(orient,[status(thm)],[t720]) ).
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(h90,plain,
test(or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi14,h16]) ).
cnf(hi13,axiom,
ifeq(test(X0),true,complement(sk0(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h207,plain,
complement(sk0(or(c(sk3),false)),or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h90]) ).
cnf(t131,plain,
addition(or(c(sk3),false),sk0(or(c(sk3),false))) = one,
inference(hyper_resolution,[status(thm)],[hi17,h207]) ).
cnf(t107788,plain,
addition(c(sk3),sk0(or(c(sk3),false))) = one,
inference(step,[status(thm)],[t131,t256]) ).
cnf(t107789,plain,
addition(c(sk3),sk0(c(sk3))) = one,
inference(step,[status(thm)],[t107788,t256]) ).
cnf(t292,plain,
addition(c(sk3),sk0(c(sk3))) = one,
inference(orient,[status(thm)],[t107789]) ).
cnf(t108065,plain,
addition(sk0(sk3),sk0(c(sk3))) = one,
inference(step,[status(thm)],[t292,t3154]) ).
cnf(t108066,plain,
addition(sk0(sk3),sk0(sk0(sk3))) = one,
inference(step,[status(thm)],[t108065,t3154]) ).
cnf(t3169,plain,
addition(sk0(sk3),sk0(sk0(sk3))) = one,
inference(rw,[status(thm)],[t108066]) ).
cnf(t3263,plain,
addition(sk0(sk3),sk0(sk0(sk3))) = one,
inference(orient,[status(thm)],[t3169]) ).
cnf(t8541,plain,
true = leq(multiplication(X1,sk0(sk3)),multiplication(X1,one)),
inference(cp,[status(thm)],[t8452,t3263]) ).
cnf(t108298,plain,
true = leq(multiplication(X1,sk0(sk3)),X1),
inference(step,[status(thm)],[t8541,t260]) ).
cnf(t8615,plain,
leq(multiplication(X1,sk0(sk3)),X1) = true,
inference(orient,[status(thm)],[t108298]) ).
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(t123,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t563,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t123]) ).
cnf(t8616,plain,
true = leq(multiplication(X1,multiplication(X2,sk0(sk3))),multiplication(X1,X2)),
inference(cp,[status(thm)],[t8615,t563]) ).
cnf(t74530,plain,
leq(multiplication(X1,multiplication(X2,sk0(sk3))),multiplication(X1,X2)) = true,
inference(orient,[status(thm)],[t8616]) ).
cnf(t367,plain,
multiplication(addition(X1,c(sk2)),sk2) = addition(multiplication(X1,sk2),zero),
inference(cp,[status(thm)],[t331,t363]) ).
cnf(t107942,plain,
multiplication(addition(X1,c(sk2)),sk2) = multiplication(X1,sk2),
inference(step,[status(thm)],[t367,t259]) ).
cnf(t1211,plain,
multiplication(addition(X1,c(sk2)),sk2) = multiplication(X1,sk2),
inference(orient,[status(thm)],[t107942]) ).
cnf(t1212,plain,
multiplication(sk2,sk2) = multiplication(one,sk2),
inference(cp,[status(thm)],[t1211,t295]) ).
cnf(t107943,plain,
multiplication(sk2,sk2) = sk2,
inference(step,[status(thm)],[t1212,t261]) ).
cnf(t1226,plain,
multiplication(sk2,sk2) = sk2,
inference(orient,[status(thm)],[t107943]) ).
cnf(t1229,plain,
multiplication(sk2,multiplication(sk2,X1)) = multiplication(sk2,X1),
inference(cp,[status(thm)],[t563,t1226]) ).
cnf(t1238,plain,
multiplication(sk2,multiplication(sk2,X1)) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t1229]) ).
cnf(t1243,plain,
multiplication(sk2,addition(multiplication(sk2,X1),X2)) = addition(multiplication(sk2,X1),multiplication(sk2,X2)),
inference(cp,[status(thm)],[t337,t1238]) ).
cnf(t108142,plain,
multiplication(sk2,addition(multiplication(sk2,X1),X2)) = multiplication(sk2,addition(X1,X2)),
inference(step,[status(thm)],[t1243,t337]) ).
cnf(t4904,plain,
multiplication(sk2,addition(multiplication(sk2,X1),X2)) = multiplication(sk2,addition(X1,X2)),
inference(orient,[status(thm)],[t108142]) ).
cnf(c24,plain,
addition(multiplication(sk2,sk1),multiplication(sk1,sk3)) = multiplication(sk1,sk3),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t116,plain,
addition(multiplication(sk2,sk1),multiplication(sk1,sk3)) = multiplication(sk1,sk3),
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t343,plain,
addition(multiplication(sk2,sk1),multiplication(sk1,sk3)) = multiplication(sk1,sk3),
inference(orient,[status(thm)],[t116]) ).
cnf(t4905,plain,
multiplication(sk2,addition(sk1,multiplication(sk1,sk3))) = multiplication(sk2,multiplication(sk1,sk3)),
inference(cp,[status(thm)],[t4904,t343]) ).
cnf(t339,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t337,t260]) ).
cnf(t984,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t339]) ).
cnf(t108194,plain,
multiplication(sk2,multiplication(sk1,addition(one,sk3))) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t4905,t984]) ).
cnf(t108195,plain,
multiplication(sk2,multiplication(sk1,addition(sk3,one))) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t108194,t273]) ).
cnf(t694,plain,
addition(sk3,c(sk3)) = addition(sk3,one),
inference(cp,[status(thm)],[t690,t289]) ).
cnf(t107906,plain,
one = addition(sk3,one),
inference(step,[status(thm)],[t694,t289]) ).
cnf(t710,plain,
addition(sk3,one) = one,
inference(orient,[status(thm)],[t107906]) ).
cnf(t108196,plain,
multiplication(sk2,multiplication(sk1,one)) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t108195,t710]) ).
cnf(t108197,plain,
multiplication(sk2,sk1) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t108196,t260]) ).
cnf(t5672,plain,
multiplication(sk2,multiplication(sk1,sk3)) = multiplication(sk2,sk1),
inference(orient,[status(thm)],[t108197]) ).
cnf(t5675,plain,
multiplication(sk2,multiplication(multiplication(sk1,sk3),X1)) = multiplication(multiplication(sk2,sk1),X1),
inference(cp,[status(thm)],[t563,t5672]) ).
cnf(t108208,plain,
multiplication(sk2,multiplication(sk1,multiplication(sk3,X1))) = multiplication(multiplication(sk2,sk1),X1),
inference(step,[status(thm)],[t5675,t563]) ).
cnf(t108209,plain,
multiplication(sk2,multiplication(sk1,multiplication(sk3,X1))) = multiplication(sk2,multiplication(sk1,X1)),
inference(step,[status(thm)],[t108208,t563]) ).
cnf(t6097,plain,
multiplication(sk2,multiplication(sk1,multiplication(sk3,X1))) = multiplication(sk2,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t108209]) ).
cnf(t6119,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = multiplication(sk2,multiplication(sk1,zero)),
inference(cp,[status(thm)],[t6097,t682]) ).
fof(f9,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/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(t6,plain,
multiplication(X1,zero) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t346,plain,
multiplication(X1,zero) = zero,
inference(orient,[status(thm)],[t6]) ).
cnf(t108210,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = multiplication(sk2,zero),
inference(step,[status(thm)],[t6119,t346]) ).
cnf(t108211,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(step,[status(thm)],[t108210,t346]) ).
cnf(t6138,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(orient,[status(thm)],[t108211]) ).
cnf(t6146,plain,
multiplication(addition(sk2,X1),multiplication(sk1,sk0(sk3))) = addition(zero,multiplication(X1,multiplication(sk1,sk0(sk3)))),
inference(cp,[status(thm)],[t331,t6138]) ).
cnf(t109430,plain,
multiplication(addition(sk2,X1),multiplication(sk1,sk0(sk3))) = multiplication(X1,multiplication(sk1,sk0(sk3))),
inference(step,[status(thm)],[t6146,t607]) ).
cnf(t99622,plain,
multiplication(addition(sk2,X1),multiplication(sk1,sk0(sk3))) = multiplication(X1,multiplication(sk1,sk0(sk3))),
inference(orient,[status(thm)],[t109430]) ).
cnf(t99647,plain,
multiplication(sk0(sk2),multiplication(sk1,sk0(sk3))) = multiplication(one,multiplication(sk1,sk0(sk3))),
inference(cp,[status(thm)],[t99622,t646]) ).
cnf(t109431,plain,
multiplication(sk0(sk2),multiplication(sk1,sk0(sk3))) = multiplication(sk1,sk0(sk3)),
inference(step,[status(thm)],[t99647,t261]) ).
cnf(t99748,plain,
multiplication(sk0(sk2),multiplication(sk1,sk0(sk3))) = multiplication(sk1,sk0(sk3)),
inference(orient,[status(thm)],[t109431]) ).
cnf(t99803,plain,
true = leq(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)),
inference(cp,[status(thm)],[t74530,t99748]) ).
cnf(t99830,plain,
leq(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = true,
inference(orient,[status(thm)],[t99803]) ).
cnf(t99831,plain,
multiplication(sk0(sk2),sk1) = ifeq(true,true,addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)),multiplication(sk0(sk2),sk1)),
inference(cp,[status(thm)],[t264,t99830]) ).
cnf(t109479,plain,
multiplication(sk0(sk2),sk1) = addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)),
inference(step,[status(thm)],[t99831,t262]) ).
cnf(t107701,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = multiplication(sk0(sk2),sk1),
inference(orient,[status(thm)],[t109479]) ).
cnf(c25,plain,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) != multiplication(c(sk2),sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) != multiplication(c(sk2),sk1),
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(g0_0,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(c(sk2),sk1)) != multiplication(c(sk2),sk1),
inference(rw,[status(thm)],[goal_0,t3154]) ).
cnf(g0_1,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) != multiplication(c(sk2),sk1),
inference(rw,[status(thm)],[g0_0,t3357]) ).
cnf(g0_2,plain,
multiplication(sk0(sk2),sk1) != multiplication(c(sk2),sk1),
inference(rw,[status(thm)],[g0_1,t107701]) ).
cnf(g0_3,plain,
multiplication(sk0(sk2),sk1) != multiplication(sk0(sk2),sk1),
inference(rw,[status(thm)],[g0_2,t3357]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE023+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 18:39:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 77.77/10.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 77.77/10.23 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------