%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE025+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 42.84s 5.82s
% Output : Proof 42.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 17
% Syntax : Number of formulae : 171 ( 149 unt; 0 def)
% Number of atoms : 231 ( 185 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 96 ( 36 ~; 29 |; 22 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 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 : 217 ( 6 sgn 83 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f4_nnf,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t131,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t594,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t131]) ).
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f7_nnf,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t160,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t343,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t160]) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& test(X2)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( multiplication(sk2,sk1) != multiplication(multiplication(sk2,sk1),sk3)
& multiplication(multiplication(sk2,sk1),c(sk3)) = zero
& test(sk3)
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f16_nnf]) ).
cnf(c24,plain,
multiplication(multiplication(sk2,sk1),c(sk3)) = zero,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t73,plain,
multiplication(multiplication(sk2,sk1),c(sk3)) = zero,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t535,plain,
multiplication(multiplication(sk2,sk1),c(sk3)) = zero,
inference(orient,[status(thm)],[t73]) ).
cnf(t52596,plain,
multiplication(sk2,multiplication(sk1,c(sk3))) = zero,
inference(step,[status(thm)],[t535,t594]) ).
cnf(t614,plain,
multiplication(sk2,multiplication(sk1,c(sk3))) = zero,
inference(rw,[status(thm)],[t52596]) ).
cnf(t937,plain,
multiplication(sk2,multiplication(sk1,c(sk3))) = zero,
inference(orient,[status(thm)],[t614]) ).
fof(f8,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f8_nnf,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t161,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t337,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t161]) ).
fof(f12,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
fof(f12_nnf,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| test(X0) )
& ( complement(sk0(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f12_nnf]) ).
cnf(c13,plain,
( complement(sk0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi13,axiom,
ifeq(test(X0),true,complement(sk0(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
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(h4,plain,
complement(sk0(sk3),sk3) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi23]) ).
fof(f13,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f13_nnf,plain,
! [X0,X1] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X1,X0] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c15,plain,
( multiplication(X0,X1) = zero
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi15,axiom,
ifeq(complement(X0,X1),true,multiplication(X1,X0),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t20,plain,
multiplication(sk3,sk0(sk3)) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h4]) ).
cnf(t510,plain,
multiplication(sk3,sk0(sk3)) = zero,
inference(orient,[status(thm)],[t20]) ).
cnf(t514,plain,
multiplication(addition(X1,sk3),sk0(sk3)) = addition(multiplication(X1,sk0(sk3)),zero),
inference(cp,[status(thm)],[t337,t510]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f2_nnf,plain,
! [A] : addition(A,zero) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : addition(A,zero) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(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(t52722,plain,
multiplication(addition(X1,sk3),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(step,[status(thm)],[t514,t259]) ).
cnf(t2563,plain,
multiplication(addition(X1,sk3),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(orient,[status(thm)],[t52722]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f0_nnf,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t21,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)],[t21]) ).
cnf(t2565,plain,
multiplication(X1,sk0(sk3)) = multiplication(addition(sk3,X1),sk0(sk3)),
inference(cp,[status(thm)],[t2563,t273]) ).
cnf(t2807,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(orient,[status(thm)],[t2565]) ).
fof(f14,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f14_nnf,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c19,plain,
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi19,axiom,
ifeq(test(X0),true,ifeq(c(X0),X1,complement(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(hi29,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h15,plain,
complement(sk3,or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi29]) ).
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(t54,plain,
addition(or(c(sk3),false),sk3) = one,
inference(hyper_resolution,[status(thm)],[hi17,h15]) ).
cnf(t52515,plain,
addition(sk3,or(c(sk3),false)) = one,
inference(step,[status(thm)],[t54,t273]) ).
cnf(t9,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t52516,plain,
addition(sk3,c(sk3)) = one,
inference(step,[status(thm)],[t52515,t256]) ).
cnf(t289,plain,
addition(sk3,c(sk3)) = one,
inference(orient,[status(thm)],[t52516]) ).
cnf(t2813,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(one,sk0(sk3)),
inference(cp,[status(thm)],[t2807,t289]) ).
cnf(t75,plain,
multiplication(or(c(sk3),false),sk3) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h15]) ).
cnf(t52581,plain,
multiplication(c(sk3),sk3) = zero,
inference(step,[status(thm)],[t75,t256]) ).
cnf(t468,plain,
multiplication(c(sk3),sk3) = zero,
inference(orient,[status(thm)],[t52581]) ).
cnf(t470,plain,
multiplication(c(sk3),addition(X1,sk3)) = addition(multiplication(c(sk3),X1),zero),
inference(cp,[status(thm)],[t343,t468]) ).
cnf(t52719,plain,
multiplication(c(sk3),addition(X1,sk3)) = multiplication(c(sk3),X1),
inference(step,[status(thm)],[t470,t259]) ).
cnf(t2521,plain,
multiplication(c(sk3),addition(X1,sk3)) = multiplication(c(sk3),X1),
inference(orient,[status(thm)],[t52719]) ).
cnf(t2523,plain,
multiplication(c(sk3),X1) = multiplication(c(sk3),addition(sk3,X1)),
inference(cp,[status(thm)],[t2521,t273]) ).
cnf(t2633,plain,
multiplication(c(sk3),addition(sk3,X1)) = multiplication(c(sk3),X1),
inference(orient,[status(thm)],[t2523]) ).
cnf(t14,plain,
addition(sk3,sk0(sk3)) = one,
inference(hyper_resolution,[status(thm)],[hi17,h4]) ).
cnf(t307,plain,
addition(sk3,sk0(sk3)) = one,
inference(orient,[status(thm)],[t14]) ).
cnf(t2640,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(c(sk3),one),
inference(cp,[status(thm)],[t2633,t307]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(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(t52728,plain,
multiplication(c(sk3),sk0(sk3)) = c(sk3),
inference(step,[status(thm)],[t2640,t260]) ).
cnf(t2664,plain,
multiplication(c(sk3),sk0(sk3)) = c(sk3),
inference(orient,[status(thm)],[t52728]) ).
cnf(t52736,plain,
c(sk3) = multiplication(one,sk0(sk3)),
inference(step,[status(thm)],[t2813,t2664]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f6_nnf,plain,
! [A] : multiplication(one,A) = A,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : multiplication(one,A) = A,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(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(t52737,plain,
c(sk3) = sk0(sk3),
inference(step,[status(thm)],[t52736,t261]) ).
cnf(t2828,plain,
c(sk3) = sk0(sk3),
inference(orient,[status(thm)],[t52737]) ).
cnf(t52754,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(step,[status(thm)],[t937,t2828]) ).
cnf(t2842,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(rw,[status(thm)],[t52754]) ).
cnf(t2919,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(orient,[status(thm)],[t2842]) ).
cnf(t2925,plain,
multiplication(sk2,addition(multiplication(sk1,sk0(sk3)),X1)) = addition(zero,multiplication(sk2,X1)),
inference(cp,[status(thm)],[t343,t2919]) ).
cnf(t274,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t273,t259]) ).
cnf(t641,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t274]) ).
cnf(t52972,plain,
multiplication(sk2,addition(multiplication(sk1,sk0(sk3)),X1)) = multiplication(sk2,X1),
inference(step,[status(thm)],[t2925,t641]) ).
cnf(t6345,plain,
multiplication(sk2,addition(multiplication(sk1,sk0(sk3)),X1)) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t52972]) ).
cnf(t6347,plain,
multiplication(sk2,multiplication(sk1,X1)) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),X1))),
inference(cp,[status(thm)],[t6345,t343]) ).
cnf(t52307,plain,
multiplication(sk2,multiplication(sk1,addition(sk0(sk3),X1))) = multiplication(sk2,multiplication(sk1,X1)),
inference(orient,[status(thm)],[t6347]) ).
cnf(t345,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t343,t260]) ).
cnf(t970,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t345]) ).
cnf(t2566,plain,
multiplication(addition(X1,sk3),addition(one,sk0(sk3))) = addition(addition(X1,sk3),multiplication(X1,sk0(sk3))),
inference(cp,[status(thm)],[t970,t2563]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t129,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)],[t129]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t125,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t379,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t125]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t123,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)],[t123]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f3_nnf,plain,
! [A] : addition(A,A) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : addition(A,A) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(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(t666,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t279]) ).
cnf(t678,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t379,t666]) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t24]) ).
cnf(t52626,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t678,t262]) ).
cnf(t694,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t52626]) ).
cnf(t700,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t694,t273]) ).
cnf(t707,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t700]) ).
cnf(t711,plain,
true = leq(sk0(sk3),one),
inference(cp,[status(thm)],[t707,t307]) ).
cnf(t720,plain,
leq(sk0(sk3),one) = true,
inference(orient,[status(thm)],[t711]) ).
cnf(t721,plain,
one = ifeq(true,true,addition(sk0(sk3),one),one),
inference(cp,[status(thm)],[t264,t720]) ).
cnf(t52629,plain,
one = addition(sk0(sk3),one),
inference(step,[status(thm)],[t721,t262]) ).
cnf(t52630,plain,
one = addition(one,sk0(sk3)),
inference(step,[status(thm)],[t52629,t273]) ).
cnf(t729,plain,
addition(one,sk0(sk3)) = one,
inference(orient,[status(thm)],[t52630]) ).
cnf(t52916,plain,
multiplication(addition(X1,sk3),one) = addition(addition(X1,sk3),multiplication(X1,sk0(sk3))),
inference(step,[status(thm)],[t2566,t729]) ).
cnf(t52917,plain,
addition(X1,sk3) = addition(addition(X1,sk3),multiplication(X1,sk0(sk3))),
inference(step,[status(thm)],[t52916,t260]) ).
cnf(t52918,plain,
addition(X1,sk3) = addition(X1,addition(sk3,multiplication(X1,sk0(sk3)))),
inference(step,[status(thm)],[t52917,t276]) ).
cnf(t5406,plain,
addition(X1,addition(sk3,multiplication(X1,sk0(sk3)))) = addition(X1,sk3),
inference(orient,[status(thm)],[t52918]) ).
cnf(t52316,plain,
multiplication(sk2,multiplication(sk1,addition(sk3,multiplication(sk0(sk3),sk0(sk3))))) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),sk3))),
inference(cp,[status(thm)],[t52307,t5406]) ).
cnf(t2814,plain,
multiplication(sk0(sk3),sk0(sk3)) = multiplication(one,sk0(sk3)),
inference(cp,[status(thm)],[t2807,t307]) ).
cnf(t52769,plain,
multiplication(sk0(sk3),sk0(sk3)) = sk0(sk3),
inference(step,[status(thm)],[t2814,t261]) ).
cnf(t2909,plain,
multiplication(sk0(sk3),sk0(sk3)) = sk0(sk3),
inference(orient,[status(thm)],[t52769]) ).
cnf(t53670,plain,
multiplication(sk2,multiplication(sk1,addition(sk3,sk0(sk3)))) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),sk3))),
inference(step,[status(thm)],[t52316,t2909]) ).
cnf(t53671,plain,
multiplication(sk2,multiplication(sk1,one)) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),sk3))),
inference(step,[status(thm)],[t53670,t307]) ).
cnf(t53672,plain,
multiplication(sk2,sk1) = multiplication(sk2,multiplication(sk1,addition(sk0(sk3),sk3))),
inference(step,[status(thm)],[t53671,t260]) ).
cnf(t53673,plain,
multiplication(sk2,sk1) = multiplication(sk2,multiplication(sk1,sk3)),
inference(step,[status(thm)],[t53672,t52307]) ).
cnf(t52417,plain,
multiplication(sk2,multiplication(sk1,sk3)) = multiplication(sk2,sk1),
inference(orient,[status(thm)],[t53673]) ).
cnf(c25,plain,
multiplication(sk2,sk1) != multiplication(multiplication(sk2,sk1),sk3),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(multiplication(sk2,sk1),sk3) != multiplication(sk2,sk1),
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(g0_0,plain,
multiplication(sk2,multiplication(sk1,sk3)) != multiplication(sk2,sk1),
inference(rw,[status(thm)],[goal_0,t594]) ).
cnf(g0_1,plain,
multiplication(sk2,sk1) != multiplication(sk2,sk1),
inference(rw,[status(thm)],[g0_0,t52417]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE025+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n014.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 18:40:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 42.84/5.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.84/5.82 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------