%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE023+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 75.13s 10.81s
% Output : Proof 75.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 18
% Syntax : Number of formulae : 256 ( 232 unt; 0 def)
% Number of atoms : 318 ( 268 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 102 ( 40 ~; 31 |; 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 : 266 ( 11 sgn 86 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(t151,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t384,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t151]) ).
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(f18,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(f18_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)],[f18]) ).
fof(f18_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)],[f18_neg]) ).
fof(f18_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])],[f18_nnf]) ).
cnf(c25,plain,
test(sk3),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi25,negated_conjecture,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(hi31,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h24,plain,
complement(sk3,or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi25,hi31]) ).
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(hi16,axiom,
ifeq(complement(X0,X1),true,multiplication(X0,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t73,plain,
multiplication(sk3,or(c(sk3),false)) = zero,
inference(hyper_resolution,[status(thm)],[hi16,h24]) ).
cnf(t11,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t112305,plain,
multiplication(sk3,c(sk3)) = zero,
inference(step,[status(thm)],[t73,t256]) ).
cnf(t476,plain,
multiplication(sk3,c(sk3)) = zero,
inference(orient,[status(thm)],[t112305]) ).
cnf(t481,plain,
multiplication(addition(X1,sk3),c(sk3)) = addition(multiplication(X1,c(sk3)),zero),
inference(cp,[status(thm)],[t384,t476]) ).
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(t112532,plain,
multiplication(addition(X1,sk3),c(sk3)) = multiplication(X1,c(sk3)),
inference(step,[status(thm)],[t481,t259]) ).
cnf(t3369,plain,
multiplication(addition(X1,sk3),c(sk3)) = multiplication(X1,c(sk3)),
inference(orient,[status(thm)],[t112532]) ).
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(t15,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t291,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t15]) ).
cnf(t3371,plain,
multiplication(X1,c(sk3)) = multiplication(addition(sk3,X1),c(sk3)),
inference(cp,[status(thm)],[t3369,t291]) ).
cnf(t3801,plain,
multiplication(addition(sk3,X1),c(sk3)) = multiplication(X1,c(sk3)),
inference(orient,[status(thm)],[t3371]) ).
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(t775,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/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(t124,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t716,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t124]) ).
cnf(t1,plain,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t571,plain,
test(sk3) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t719,plain,
true = ifeq(true,true,complement(sk0(sk3),sk3),true),
inference(cp,[status(thm)],[t716,t571]) ).
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(t112379,plain,
true = complement(sk0(sk3),sk3),
inference(step,[status(thm)],[t719,t262]) ).
cnf(t858,plain,
complement(sk0(sk3),sk3) = true,
inference(orient,[status(thm)],[t112379]) ).
cnf(t859,plain,
one = ifeq(true,true,addition(sk3,sk0(sk3)),one),
inference(cp,[status(thm)],[t775,t858]) ).
cnf(t112381,plain,
one = addition(sk3,sk0(sk3)),
inference(step,[status(thm)],[t859,t262]) ).
cnf(t872,plain,
addition(sk3,sk0(sk3)) = one,
inference(orient,[status(thm)],[t112381]) ).
cnf(t3809,plain,
multiplication(sk0(sk3),c(sk3)) = multiplication(one,c(sk3)),
inference(cp,[status(thm)],[t3801,t872]) ).
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(t150,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t402,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t150]) ).
cnf(t121,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t757,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t121]) ).
cnf(t860,plain,
zero = ifeq(true,true,multiplication(sk0(sk3),sk3),zero),
inference(cp,[status(thm)],[t757,t858]) ).
cnf(t112382,plain,
zero = multiplication(sk0(sk3),sk3),
inference(step,[status(thm)],[t860,t262]) ).
cnf(t878,plain,
multiplication(sk0(sk3),sk3) = zero,
inference(orient,[status(thm)],[t112382]) ).
cnf(t881,plain,
multiplication(sk0(sk3),addition(sk3,X1)) = addition(zero,multiplication(sk0(sk3),X1)),
inference(cp,[status(thm)],[t402,t878]) ).
cnf(t298,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t291,t259]) ).
cnf(t804,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t298]) ).
cnf(t112536,plain,
multiplication(sk0(sk3),addition(sk3,X1)) = multiplication(sk0(sk3),X1),
inference(step,[status(thm)],[t881,t804]) ).
cnf(t3429,plain,
multiplication(sk0(sk3),addition(sk3,X1)) = multiplication(sk0(sk3),X1),
inference(orient,[status(thm)],[t112536]) ).
cnf(hi17,axiom,
ifeq(complement(X0,X1),true,addition(X1,X0),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t37,plain,
addition(or(c(sk3),false),sk3) = one,
inference(hyper_resolution,[status(thm)],[hi17,h24]) ).
cnf(t112261,plain,
addition(sk3,or(c(sk3),false)) = one,
inference(step,[status(thm)],[t37,t291]) ).
cnf(t112262,plain,
addition(sk3,c(sk3)) = one,
inference(step,[status(thm)],[t112261,t256]) ).
cnf(t332,plain,
addition(sk3,c(sk3)) = one,
inference(orient,[status(thm)],[t112262]) ).
cnf(t3435,plain,
multiplication(sk0(sk3),c(sk3)) = multiplication(sk0(sk3),one),
inference(cp,[status(thm)],[t3429,t332]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t7,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t260,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t112537,plain,
multiplication(sk0(sk3),c(sk3)) = sk0(sk3),
inference(step,[status(thm)],[t3435,t260]) ).
cnf(t3453,plain,
multiplication(sk0(sk3),c(sk3)) = sk0(sk3),
inference(orient,[status(thm)],[t112537]) ).
cnf(t112558,plain,
sk0(sk3) = multiplication(one,c(sk3)),
inference(step,[status(thm)],[t3809,t3453]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f6_nnf,plain,
! [A] : multiplication(one,A) = A,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : multiplication(one,A) = A,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t9,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t261,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t112559,plain,
sk0(sk3) = c(sk3),
inference(step,[status(thm)],[t112558,t261]) ).
cnf(t3823,plain,
c(sk3) = sk0(sk3),
inference(orient,[status(thm)],[t112559]) ).
cnf(c24,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi24,negated_conjecture,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h25,plain,
complement(sk2,or(c(sk2),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi24,hi31]) ).
cnf(t68,plain,
multiplication(sk2,or(c(sk2),false)) = zero,
inference(hyper_resolution,[status(thm)],[hi16,h25]) ).
cnf(t112306,plain,
multiplication(sk2,c(sk2)) = zero,
inference(step,[status(thm)],[t68,t256]) ).
cnf(t483,plain,
multiplication(sk2,c(sk2)) = zero,
inference(orient,[status(thm)],[t112306]) ).
cnf(t488,plain,
multiplication(addition(X1,sk2),c(sk2)) = addition(multiplication(X1,c(sk2)),zero),
inference(cp,[status(thm)],[t384,t483]) ).
cnf(t112533,plain,
multiplication(addition(X1,sk2),c(sk2)) = multiplication(X1,c(sk2)),
inference(step,[status(thm)],[t488,t259]) ).
cnf(t3384,plain,
multiplication(addition(X1,sk2),c(sk2)) = multiplication(X1,c(sk2)),
inference(orient,[status(thm)],[t112533]) ).
cnf(t3386,plain,
multiplication(X1,c(sk2)) = multiplication(addition(sk2,X1),c(sk2)),
inference(cp,[status(thm)],[t3384,t291]) ).
cnf(t4167,plain,
multiplication(addition(sk2,X1),c(sk2)) = multiplication(X1,c(sk2)),
inference(orient,[status(thm)],[t3386]) ).
cnf(t0,plain,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t577,plain,
test(sk2) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t720,plain,
true = ifeq(true,true,complement(sk0(sk2),sk2),true),
inference(cp,[status(thm)],[t716,t577]) ).
cnf(t112380,plain,
true = complement(sk0(sk2),sk2),
inference(step,[status(thm)],[t720,t262]) ).
cnf(t865,plain,
complement(sk0(sk2),sk2) = true,
inference(orient,[status(thm)],[t112380]) ).
cnf(t866,plain,
one = ifeq(true,true,addition(sk2,sk0(sk2)),one),
inference(cp,[status(thm)],[t775,t865]) ).
cnf(t112384,plain,
one = addition(sk2,sk0(sk2)),
inference(step,[status(thm)],[t866,t262]) ).
cnf(t897,plain,
addition(sk2,sk0(sk2)) = one,
inference(orient,[status(thm)],[t112384]) ).
cnf(t4175,plain,
multiplication(sk0(sk2),c(sk2)) = multiplication(one,c(sk2)),
inference(cp,[status(thm)],[t4167,t897]) ).
cnf(t867,plain,
zero = ifeq(true,true,multiplication(sk0(sk2),sk2),zero),
inference(cp,[status(thm)],[t757,t865]) ).
cnf(t112385,plain,
zero = multiplication(sk0(sk2),sk2),
inference(step,[status(thm)],[t867,t262]) ).
cnf(t903,plain,
multiplication(sk0(sk2),sk2) = zero,
inference(orient,[status(thm)],[t112385]) ).
cnf(t906,plain,
multiplication(sk0(sk2),addition(sk2,X1)) = addition(zero,multiplication(sk0(sk2),X1)),
inference(cp,[status(thm)],[t402,t903]) ).
cnf(t112546,plain,
multiplication(sk0(sk2),addition(sk2,X1)) = multiplication(sk0(sk2),X1),
inference(step,[status(thm)],[t906,t804]) ).
cnf(t3574,plain,
multiplication(sk0(sk2),addition(sk2,X1)) = multiplication(sk0(sk2),X1),
inference(orient,[status(thm)],[t112546]) ).
cnf(t36,plain,
addition(or(c(sk2),false),sk2) = one,
inference(hyper_resolution,[status(thm)],[hi17,h25]) ).
cnf(t112265,plain,
addition(sk2,or(c(sk2),false)) = one,
inference(step,[status(thm)],[t36,t291]) ).
cnf(t112266,plain,
addition(sk2,c(sk2)) = one,
inference(step,[status(thm)],[t112265,t256]) ).
cnf(t338,plain,
addition(sk2,c(sk2)) = one,
inference(orient,[status(thm)],[t112266]) ).
cnf(t3580,plain,
multiplication(sk0(sk2),c(sk2)) = multiplication(sk0(sk2),one),
inference(cp,[status(thm)],[t3574,t338]) ).
cnf(t112547,plain,
multiplication(sk0(sk2),c(sk2)) = sk0(sk2),
inference(step,[status(thm)],[t3580,t260]) ).
cnf(t3598,plain,
multiplication(sk0(sk2),c(sk2)) = sk0(sk2),
inference(orient,[status(thm)],[t112547]) ).
cnf(t112617,plain,
sk0(sk2) = multiplication(one,c(sk2)),
inference(step,[status(thm)],[t4175,t3598]) ).
cnf(t112618,plain,
sk0(sk2) = c(sk2),
inference(step,[status(thm)],[t112617,t261]) ).
cnf(t4189,plain,
c(sk2) = sk0(sk2),
inference(orient,[status(thm)],[t112618]) ).
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(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(t619,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/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(t117,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t303,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t117]) ).
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(t306,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t303,t258]) ).
cnf(t923,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t306]) ).
cnf(t936,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t619,t923]) ).
cnf(t112391,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t936,t262]) ).
cnf(t955,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t112391]) ).
cnf(t957,plain,
true = leq(multiplication(X1,X2),multiplication(X1,addition(X2,X3))),
inference(cp,[status(thm)],[t955,t402]) ).
cnf(t9791,plain,
leq(multiplication(X1,X2),multiplication(X1,addition(X2,X3))) = true,
inference(orient,[status(thm)],[t957]) ).
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(h108,plain,
test(or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi14,h24]) ).
cnf(hi13,axiom,
ifeq(test(X0),true,complement(sk0(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h599,plain,
complement(sk0(or(c(sk3),false)),or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h108]) ).
cnf(t133,plain,
addition(or(c(sk3),false),sk0(or(c(sk3),false))) = one,
inference(hyper_resolution,[status(thm)],[hi17,h599]) ).
cnf(t112263,plain,
addition(c(sk3),sk0(or(c(sk3),false))) = one,
inference(step,[status(thm)],[t133,t256]) ).
cnf(t112264,plain,
addition(c(sk3),sk0(c(sk3))) = one,
inference(step,[status(thm)],[t112263,t256]) ).
cnf(t335,plain,
addition(c(sk3),sk0(c(sk3))) = one,
inference(orient,[status(thm)],[t112264]) ).
cnf(t112594,plain,
addition(sk0(sk3),sk0(c(sk3))) = one,
inference(step,[status(thm)],[t335,t3823]) ).
cnf(t112595,plain,
addition(sk0(sk3),sk0(sk0(sk3))) = one,
inference(step,[status(thm)],[t112594,t3823]) ).
cnf(t3864,plain,
addition(sk0(sk3),sk0(sk0(sk3))) = one,
inference(rw,[status(thm)],[t112595]) ).
cnf(t4001,plain,
addition(sk0(sk3),sk0(sk0(sk3))) = one,
inference(orient,[status(thm)],[t3864]) ).
cnf(t9903,plain,
true = leq(multiplication(X1,sk0(sk3)),multiplication(X1,one)),
inference(cp,[status(thm)],[t9791,t4001]) ).
cnf(t112918,plain,
true = leq(multiplication(X1,sk0(sk3)),X1),
inference(step,[status(thm)],[t9903,t260]) ).
cnf(t10209,plain,
leq(multiplication(X1,sk0(sk3)),X1) = true,
inference(orient,[status(thm)],[t112918]) ).
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(t125,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t423,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t125]) ).
cnf(t10210,plain,
true = leq(multiplication(X1,multiplication(X2,sk0(sk3))),multiplication(X1,X2)),
inference(cp,[status(thm)],[t10209,t423]) ).
cnf(t72722,plain,
leq(multiplication(X1,multiplication(X2,sk0(sk3))),multiplication(X1,X2)) = true,
inference(orient,[status(thm)],[t10210]) ).
cnf(t486,plain,
multiplication(sk2,addition(X1,c(sk2))) = addition(multiplication(sk2,X1),zero),
inference(cp,[status(thm)],[t402,t483]) ).
cnf(t112444,plain,
multiplication(sk2,addition(X1,c(sk2))) = multiplication(sk2,X1),
inference(step,[status(thm)],[t486,t259]) ).
cnf(t1684,plain,
multiplication(sk2,addition(X1,c(sk2))) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t112444]) ).
cnf(t1685,plain,
multiplication(sk2,sk2) = multiplication(sk2,one),
inference(cp,[status(thm)],[t1684,t338]) ).
cnf(t112445,plain,
multiplication(sk2,sk2) = sk2,
inference(step,[status(thm)],[t1685,t260]) ).
cnf(t1701,plain,
multiplication(sk2,sk2) = sk2,
inference(orient,[status(thm)],[t112445]) ).
cnf(t1706,plain,
multiplication(sk2,multiplication(sk2,X1)) = multiplication(sk2,X1),
inference(cp,[status(thm)],[t423,t1701]) ).
cnf(t1713,plain,
multiplication(sk2,multiplication(sk2,X1)) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t1706]) ).
cnf(t1718,plain,
multiplication(sk2,addition(multiplication(sk2,X1),X2)) = addition(multiplication(sk2,X1),multiplication(sk2,X2)),
inference(cp,[status(thm)],[t402,t1713]) ).
cnf(t112753,plain,
multiplication(sk2,addition(multiplication(sk2,X1),X2)) = multiplication(sk2,addition(X1,X2)),
inference(step,[status(thm)],[t1718,t402]) ).
cnf(t6208,plain,
multiplication(sk2,addition(multiplication(sk2,X1),X2)) = multiplication(sk2,addition(X1,X2)),
inference(orient,[status(thm)],[t112753]) ).
cnf(c26,plain,
addition(multiplication(sk2,sk1),multiplication(sk1,sk3)) = multiplication(sk1,sk3),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t118,plain,
addition(multiplication(sk2,sk1),multiplication(sk1,sk3)) = multiplication(sk1,sk3),
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t420,plain,
addition(multiplication(sk2,sk1),multiplication(sk1,sk3)) = multiplication(sk1,sk3),
inference(orient,[status(thm)],[t118]) ).
cnf(t6209,plain,
multiplication(sk2,addition(sk1,multiplication(sk1,sk3))) = multiplication(sk2,multiplication(sk1,sk3)),
inference(cp,[status(thm)],[t6208,t420]) ).
cnf(t404,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t402,t260]) ).
cnf(t1313,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t404]) ).
cnf(t112800,plain,
multiplication(sk2,multiplication(sk1,addition(one,sk3))) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t6209,t1313]) ).
cnf(t112801,plain,
multiplication(sk2,multiplication(sk1,addition(sk3,one))) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t112800,t291]) ).
cnf(t927,plain,
addition(sk3,c(sk3)) = addition(sk3,one),
inference(cp,[status(thm)],[t923,t332]) ).
cnf(t112388,plain,
one = addition(sk3,one),
inference(step,[status(thm)],[t927,t332]) ).
cnf(t946,plain,
addition(sk3,one) = one,
inference(orient,[status(thm)],[t112388]) ).
cnf(t112802,plain,
multiplication(sk2,multiplication(sk1,one)) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t112801,t946]) ).
cnf(t112803,plain,
multiplication(sk2,sk1) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t112802,t260]) ).
cnf(t6923,plain,
multiplication(sk2,multiplication(sk1,sk3)) = multiplication(sk2,sk1),
inference(orient,[status(thm)],[t112803]) ).
cnf(t6929,plain,
multiplication(sk2,multiplication(multiplication(sk1,sk3),X1)) = multiplication(multiplication(sk2,sk1),X1),
inference(cp,[status(thm)],[t423,t6923]) ).
cnf(t112814,plain,
multiplication(sk2,multiplication(sk1,multiplication(sk3,X1))) = multiplication(multiplication(sk2,sk1),X1),
inference(step,[status(thm)],[t6929,t423]) ).
cnf(t112815,plain,
multiplication(sk2,multiplication(sk1,multiplication(sk3,X1))) = multiplication(sk2,multiplication(sk1,X1)),
inference(step,[status(thm)],[t112814,t423]) ).
cnf(t7123,plain,
multiplication(sk2,multiplication(sk1,multiplication(sk3,X1))) = multiplication(sk2,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t112815]) ).
cnf(c15,plain,
( multiplication(X0,X1) = zero
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t122,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t739,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(orient,[status(thm)],[t122]) ).
cnf(t861,plain,
zero = ifeq(true,true,multiplication(sk3,sk0(sk3)),zero),
inference(cp,[status(thm)],[t739,t858]) ).
cnf(t112383,plain,
zero = multiplication(sk3,sk0(sk3)),
inference(step,[status(thm)],[t861,t262]) ).
cnf(t888,plain,
multiplication(sk3,sk0(sk3)) = zero,
inference(orient,[status(thm)],[t112383]) ).
cnf(t7149,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = multiplication(sk2,multiplication(sk1,zero)),
inference(cp,[status(thm)],[t7123,t888]) ).
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(t8,plain,
multiplication(X1,zero) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t433,plain,
multiplication(X1,zero) = zero,
inference(orient,[status(thm)],[t8]) ).
cnf(t112816,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = multiplication(sk2,zero),
inference(step,[status(thm)],[t7149,t433]) ).
cnf(t112817,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(step,[status(thm)],[t112816,t433]) ).
cnf(t7165,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(orient,[status(thm)],[t112817]) ).
cnf(t7174,plain,
multiplication(addition(sk2,X1),multiplication(sk1,sk0(sk3))) = addition(zero,multiplication(X1,multiplication(sk1,sk0(sk3)))),
inference(cp,[status(thm)],[t384,t7165]) ).
cnf(t114100,plain,
multiplication(addition(sk2,X1),multiplication(sk1,sk0(sk3))) = multiplication(X1,multiplication(sk1,sk0(sk3))),
inference(step,[status(thm)],[t7174,t804]) ).
cnf(t103862,plain,
multiplication(addition(sk2,X1),multiplication(sk1,sk0(sk3))) = multiplication(X1,multiplication(sk1,sk0(sk3))),
inference(orient,[status(thm)],[t114100]) ).
cnf(t103890,plain,
multiplication(sk0(sk2),multiplication(sk1,sk0(sk3))) = multiplication(one,multiplication(sk1,sk0(sk3))),
inference(cp,[status(thm)],[t103862,t897]) ).
cnf(t114101,plain,
multiplication(sk0(sk2),multiplication(sk1,sk0(sk3))) = multiplication(sk1,sk0(sk3)),
inference(step,[status(thm)],[t103890,t261]) ).
cnf(t103979,plain,
multiplication(sk0(sk2),multiplication(sk1,sk0(sk3))) = multiplication(sk1,sk0(sk3)),
inference(orient,[status(thm)],[t114101]) ).
cnf(t104024,plain,
true = leq(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)),
inference(cp,[status(thm)],[t72722,t103979]) ).
cnf(t104053,plain,
leq(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = true,
inference(orient,[status(thm)],[t104024]) ).
cnf(t104054,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,t104053]) ).
cnf(t114148,plain,
multiplication(sk0(sk2),sk1) = addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)),
inference(step,[status(thm)],[t104054,t262]) ).
cnf(t112173,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = multiplication(sk0(sk2),sk1),
inference(orient,[status(thm)],[t114148]) ).
cnf(c27,plain,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) != multiplication(c(sk2),sk1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) != multiplication(c(sk2),sk1),
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(c(sk2),sk1)) != multiplication(c(sk2),sk1),
inference(rw,[status(thm)],[goal_0,t3823]) ).
cnf(g0_1,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) != multiplication(c(sk2),sk1),
inference(rw,[status(thm)],[g0_0,t4189]) ).
cnf(g0_2,plain,
multiplication(sk0(sk2),sk1) != multiplication(c(sk2),sk1),
inference(rw,[status(thm)],[g0_1,t112173]) ).
cnf(g0_3,plain,
multiplication(sk0(sk2),sk1) != multiplication(sk0(sk2),sk1),
inference(rw,[status(thm)],[g0_2,t4189]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE023+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 18:38:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 75.13/10.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 75.13/10.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------