%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE020+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 : n017.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 01:51:22 PM UTC 2026
% Result : Theorem 199.70s 28.63s
% Output : Proof 199.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 17
% Syntax : Number of formulae : 274 ( 252 unt; 0 def)
% Number of atoms : 334 ( 282 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 97 ( 37 ~; 29 |; 24 &)
% ( 4 <=>; 3 =>; 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 : 301 ( 22 sgn 83 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(t26,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t372,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t26]) ).
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(t184,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t477,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t184]) ).
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(t183,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t485,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t183]) ).
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(hi13,axiom,
ifeq(test(X0),true,complement(sk0(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> addition(X0,multiplication(X1,X2)) = multiplication(addition(X0,X1),addition(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> addition(X0,multiplication(X1,X2)) = multiplication(addition(X0,X1),addition(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] :
( addition(X0,multiplication(X1,X2)) != multiplication(addition(X0,X1),addition(X0,X2))
& test(X2)
& test(X1)
& test(X0) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( addition(sk1,multiplication(sk2,sk3)) != multiplication(addition(sk1,sk2),addition(sk1,sk3))
& test(sk3)
& test(sk2)
& test(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f16_nnf]) ).
cnf(c22,plain,
test(sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi22,negated_conjecture,
test(sk1) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h0,plain,
complement(sk0(sk1),sk1) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi22]) ).
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(t23,plain,
multiplication(sk1,sk0(sk1)) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h0]) ).
cnf(t567,plain,
multiplication(sk1,sk0(sk1)) = zero,
inference(orient,[status(thm)],[t23]) ).
cnf(t570,plain,
multiplication(sk1,addition(X1,sk0(sk1))) = addition(multiplication(sk1,X1),zero),
inference(cp,[status(thm)],[t485,t567]) ).
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(t4,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t259,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t121735,plain,
multiplication(sk1,addition(X1,sk0(sk1))) = multiplication(sk1,X1),
inference(step,[status(thm)],[t570,t259]) ).
cnf(t1953,plain,
multiplication(sk1,addition(X1,sk0(sk1))) = multiplication(sk1,X1),
inference(orient,[status(thm)],[t121735]) ).
cnf(t1955,plain,
multiplication(sk1,X1) = multiplication(sk1,addition(sk0(sk1),X1)),
inference(cp,[status(thm)],[t1953,t372]) ).
cnf(t2415,plain,
multiplication(sk1,addition(sk0(sk1),X1)) = multiplication(sk1,X1),
inference(orient,[status(thm)],[t1955]) ).
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(t157,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t378,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t157]) ).
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(t3,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t258,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t381,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t378,t258]) ).
cnf(t692,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t381]) ).
cnf(t704,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t692,t372]) ).
cnf(t814,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t704]) ).
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(t14,plain,
addition(sk1,sk0(sk1)) = one,
inference(hyper_resolution,[status(thm)],[hi17,h0]) ).
cnf(t442,plain,
addition(sk1,sk0(sk1)) = one,
inference(orient,[status(thm)],[t14]) ).
cnf(t444,plain,
addition(sk1,addition(sk0(sk1),X1)) = addition(one,X1),
inference(cp,[status(thm)],[t378,t442]) ).
cnf(t1208,plain,
addition(sk1,addition(sk0(sk1),X1)) = addition(one,X1),
inference(orient,[status(thm)],[t444]) ).
cnf(t1217,plain,
addition(addition(sk0(sk1),X1),sk1) = addition(addition(sk0(sk1),X1),addition(one,X1)),
inference(cp,[status(thm)],[t814,t1208]) ).
cnf(t122077,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(addition(sk0(sk1),X1),addition(one,X1)),
inference(step,[status(thm)],[t1217,t378]) ).
cnf(t122078,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(sk0(sk1),addition(X1,addition(one,X1))),
inference(step,[status(thm)],[t122077,t378]) ).
cnf(t122079,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(sk0(sk1),addition(X1,one)),
inference(step,[status(thm)],[t122078,t814]) ).
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(t162,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)],[t162]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t158,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t318,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t158]) ).
cnf(t707,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t318,t692]) ).
cnf(t30,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t30]) ).
cnf(t121647,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t707,t262]) ).
cnf(t731,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t121647]) ).
cnf(t738,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t731,t372]) ).
cnf(t748,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t738]) ).
cnf(t757,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t748,t378]) ).
cnf(t2515,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t757]) ).
cnf(t751,plain,
true = leq(sk0(sk1),one),
inference(cp,[status(thm)],[t748,t442]) ).
cnf(t760,plain,
leq(sk0(sk1),one) = true,
inference(orient,[status(thm)],[t751]) ).
cnf(t761,plain,
one = ifeq(true,true,addition(sk0(sk1),one),one),
inference(cp,[status(thm)],[t264,t760]) ).
cnf(t121648,plain,
one = addition(sk0(sk1),one),
inference(step,[status(thm)],[t761,t262]) ).
cnf(t121649,plain,
one = addition(one,sk0(sk1)),
inference(step,[status(thm)],[t121648,t372]) ).
cnf(t769,plain,
addition(one,sk0(sk1)) = one,
inference(orient,[status(thm)],[t121649]) ).
cnf(t2557,plain,
true = leq(sk0(sk1),addition(X1,one)),
inference(cp,[status(thm)],[t2515,t769]) ).
cnf(t2618,plain,
leq(sk0(sk1),addition(X1,one)) = true,
inference(orient,[status(thm)],[t2557]) ).
cnf(t2620,plain,
addition(X1,one) = ifeq(true,true,addition(sk0(sk1),addition(X1,one)),addition(X1,one)),
inference(cp,[status(thm)],[t264,t2618]) ).
cnf(t121778,plain,
addition(X1,one) = addition(sk0(sk1),addition(X1,one)),
inference(step,[status(thm)],[t2620,t262]) ).
cnf(t2745,plain,
addition(sk0(sk1),addition(X1,one)) = addition(X1,one),
inference(orient,[status(thm)],[t121778]) ).
cnf(t122080,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(X1,one),
inference(step,[status(thm)],[t122079,t2745]) ).
cnf(t5832,plain,
addition(sk0(sk1),addition(X1,sk1)) = addition(X1,one),
inference(orient,[status(thm)],[t122080]) ).
cnf(t5845,plain,
multiplication(sk1,addition(X1,sk1)) = multiplication(sk1,addition(X1,one)),
inference(cp,[status(thm)],[t2415,t5832]) ).
cnf(t5886,plain,
multiplication(sk1,addition(X1,one)) = multiplication(sk1,addition(X1,sk1)),
inference(orient,[status(thm)],[t5845]) ).
fof(f14,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f14_nnf,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c19,plain,
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi19,axiom,
ifeq(test(X0),true,ifeq(c(X0),X1,complement(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(c24,plain,
test(sk3),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi24,negated_conjecture,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(hi29,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h21,plain,
complement(sk3,or(c(sk3),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi24,hi29]) ).
cnf(t75,plain,
addition(or(c(sk3),false),sk3) = one,
inference(hyper_resolution,[status(thm)],[hi17,h21]) ).
cnf(t121580,plain,
addition(sk3,or(c(sk3),false)) = one,
inference(step,[status(thm)],[t75,t372]) ).
cnf(t10,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t121581,plain,
addition(sk3,c(sk3)) = one,
inference(step,[status(thm)],[t121580,t256]) ).
cnf(t412,plain,
addition(sk3,c(sk3)) = one,
inference(orient,[status(thm)],[t121581]) ).
cnf(t696,plain,
addition(sk3,c(sk3)) = addition(sk3,one),
inference(cp,[status(thm)],[t692,t412]) ).
cnf(t121642,plain,
one = addition(sk3,one),
inference(step,[status(thm)],[t696,t412]) ).
cnf(t715,plain,
addition(sk3,one) = one,
inference(orient,[status(thm)],[t121642]) ).
cnf(t5887,plain,
multiplication(sk1,addition(sk3,sk1)) = multiplication(sk1,one),
inference(cp,[status(thm)],[t5886,t715]) ).
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(t6,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t260,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t122083,plain,
multiplication(sk1,addition(sk3,sk1)) = sk1,
inference(step,[status(thm)],[t5887,t260]) ).
cnf(t5901,plain,
multiplication(sk1,addition(sk3,sk1)) = sk1,
inference(orient,[status(thm)],[t122083]) ).
cnf(t5909,plain,
multiplication(addition(sk1,X1),addition(sk3,sk1)) = addition(sk1,multiplication(X1,addition(sk3,sk1))),
inference(cp,[status(thm)],[t477,t5901]) ).
cnf(t120807,plain,
addition(sk1,multiplication(X1,addition(sk3,sk1))) = multiplication(addition(sk1,X1),addition(sk3,sk1)),
inference(orient,[status(thm)],[t5909]) ).
cnf(t374,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t264,t372]) ).
cnf(t7445,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t374]) ).
cnf(t749,plain,
true = leq(multiplication(X1,X2),multiplication(addition(X3,X1),X2)),
inference(cp,[status(thm)],[t748,t477]) ).
cnf(t20897,plain,
leq(multiplication(X1,X2),multiplication(addition(X3,X1),X2)) = true,
inference(orient,[status(thm)],[t749]) ).
cnf(c23,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi23,negated_conjecture,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h22,plain,
complement(sk2,or(c(sk2),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi29]) ).
cnf(t74,plain,
addition(or(c(sk2),false),sk2) = one,
inference(hyper_resolution,[status(thm)],[hi17,h22]) ).
cnf(t121576,plain,
addition(sk2,or(c(sk2),false)) = one,
inference(step,[status(thm)],[t74,t372]) ).
cnf(t121577,plain,
addition(sk2,c(sk2)) = one,
inference(step,[status(thm)],[t121576,t256]) ).
cnf(t402,plain,
addition(sk2,c(sk2)) = one,
inference(orient,[status(thm)],[t121577]) ).
cnf(t698,plain,
addition(sk2,c(sk2)) = addition(sk2,one),
inference(cp,[status(thm)],[t692,t402]) ).
cnf(t121643,plain,
one = addition(sk2,one),
inference(step,[status(thm)],[t698,t402]) ).
cnf(t722,plain,
addition(sk2,one) = one,
inference(orient,[status(thm)],[t121643]) ).
cnf(t725,plain,
addition(sk2,addition(one,X1)) = addition(one,X1),
inference(cp,[status(thm)],[t378,t722]) ).
cnf(t865,plain,
addition(sk2,addition(one,X1)) = addition(one,X1),
inference(orient,[status(thm)],[t725]) ).
cnf(t869,plain,
addition(addition(one,X1),sk2) = addition(addition(one,X1),addition(one,X1)),
inference(cp,[status(thm)],[t814,t865]) ).
cnf(t121668,plain,
addition(one,addition(X1,sk2)) = addition(addition(one,X1),addition(one,X1)),
inference(step,[status(thm)],[t869,t378]) ).
cnf(t121669,plain,
addition(one,addition(X1,sk2)) = addition(one,addition(X1,addition(one,X1))),
inference(step,[status(thm)],[t121668,t378]) ).
cnf(t121670,plain,
addition(one,addition(X1,sk2)) = addition(one,addition(X1,one)),
inference(step,[status(thm)],[t121669,t814]) ).
cnf(t121671,plain,
addition(one,addition(X1,sk2)) = addition(one,X1),
inference(step,[status(thm)],[t121670,t814]) ).
cnf(t941,plain,
addition(one,addition(X1,sk2)) = addition(one,X1),
inference(orient,[status(thm)],[t121671]) ).
cnf(t945,plain,
addition(one,X1) = addition(one,addition(sk2,X1)),
inference(cp,[status(thm)],[t941,t372]) ).
cnf(t972,plain,
addition(one,addition(sk2,X1)) = addition(one,X1),
inference(orient,[status(thm)],[t945]) ).
cnf(t487,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t485,t260]) ).
cnf(t1082,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t487]) ).
cnf(t1096,plain,
addition(one,multiplication(sk2,X1)) = addition(one,multiplication(sk2,addition(one,X1))),
inference(cp,[status(thm)],[t972,t1082]) ).
cnf(t101,plain,
multiplication(or(c(sk2),false),sk2) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h22]) ).
cnf(t121603,plain,
multiplication(c(sk2),sk2) = zero,
inference(step,[status(thm)],[t101,t256]) ).
cnf(t503,plain,
multiplication(c(sk2),sk2) = zero,
inference(orient,[status(thm)],[t121603]) ).
cnf(t508,plain,
multiplication(addition(X1,c(sk2)),sk2) = addition(multiplication(X1,sk2),zero),
inference(cp,[status(thm)],[t477,t503]) ).
cnf(t121684,plain,
multiplication(addition(X1,c(sk2)),sk2) = multiplication(X1,sk2),
inference(step,[status(thm)],[t508,t259]) ).
cnf(t1274,plain,
multiplication(addition(X1,c(sk2)),sk2) = multiplication(X1,sk2),
inference(orient,[status(thm)],[t121684]) ).
cnf(t1275,plain,
multiplication(sk2,sk2) = multiplication(one,sk2),
inference(cp,[status(thm)],[t1274,t402]) ).
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(t8,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t261,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t121685,plain,
multiplication(sk2,sk2) = sk2,
inference(step,[status(thm)],[t1275,t261]) ).
cnf(t1289,plain,
multiplication(sk2,sk2) = sk2,
inference(orient,[status(thm)],[t121685]) ).
cnf(t1295,plain,
multiplication(sk2,addition(sk2,X1)) = addition(sk2,multiplication(sk2,X1)),
inference(cp,[status(thm)],[t485,t1289]) ).
cnf(t121686,plain,
multiplication(sk2,addition(sk2,X1)) = multiplication(sk2,addition(one,X1)),
inference(step,[status(thm)],[t1295,t1082]) ).
cnf(t1312,plain,
multiplication(sk2,addition(one,X1)) = multiplication(sk2,addition(sk2,X1)),
inference(orient,[status(thm)],[t121686]) ).
cnf(t122209,plain,
addition(one,multiplication(sk2,X1)) = addition(one,multiplication(sk2,addition(sk2,X1))),
inference(step,[status(thm)],[t1096,t1312]) ).
cnf(t8782,plain,
addition(one,multiplication(sk2,addition(sk2,X1))) = addition(one,multiplication(sk2,X1)),
inference(orient,[status(thm)],[t122209]) ).
cnf(h4,plain,
complement(sk0(sk2),sk2) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi23]) ).
cnf(t24,plain,
multiplication(sk2,sk0(sk2)) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h4]) ).
cnf(t535,plain,
multiplication(sk2,sk0(sk2)) = zero,
inference(orient,[status(thm)],[t24]) ).
cnf(t538,plain,
multiplication(sk2,addition(X1,sk0(sk2))) = addition(multiplication(sk2,X1),zero),
inference(cp,[status(thm)],[t485,t535]) ).
cnf(t121727,plain,
multiplication(sk2,addition(X1,sk0(sk2))) = multiplication(sk2,X1),
inference(step,[status(thm)],[t538,t259]) ).
cnf(t1853,plain,
multiplication(sk2,addition(X1,sk0(sk2))) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t121727]) ).
cnf(t1855,plain,
multiplication(sk2,X1) = multiplication(sk2,addition(sk0(sk2),X1)),
inference(cp,[status(thm)],[t1853,t372]) ).
cnf(t2345,plain,
multiplication(sk2,addition(sk0(sk2),X1)) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t1855]) ).
cnf(t15,plain,
addition(sk2,sk0(sk2)) = one,
inference(hyper_resolution,[status(thm)],[hi17,h4]) ).
cnf(t432,plain,
addition(sk2,sk0(sk2)) = one,
inference(orient,[status(thm)],[t15]) ).
cnf(t434,plain,
addition(sk2,addition(sk0(sk2),X1)) = addition(one,X1),
inference(cp,[status(thm)],[t378,t432]) ).
cnf(t1180,plain,
addition(sk2,addition(sk0(sk2),X1)) = addition(one,X1),
inference(orient,[status(thm)],[t434]) ).
cnf(t1189,plain,
addition(addition(sk0(sk2),X1),sk2) = addition(addition(sk0(sk2),X1),addition(one,X1)),
inference(cp,[status(thm)],[t814,t1180]) ).
cnf(t122035,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(addition(sk0(sk2),X1),addition(one,X1)),
inference(step,[status(thm)],[t1189,t378]) ).
cnf(t122036,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(sk0(sk2),addition(X1,addition(one,X1))),
inference(step,[status(thm)],[t122035,t378]) ).
cnf(t122037,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(sk0(sk2),addition(X1,one)),
inference(step,[status(thm)],[t122036,t814]) ).
cnf(t753,plain,
true = leq(sk0(sk2),one),
inference(cp,[status(thm)],[t748,t432]) ).
cnf(t766,plain,
leq(sk0(sk2),one) = true,
inference(orient,[status(thm)],[t753]) ).
cnf(t767,plain,
one = ifeq(true,true,addition(sk0(sk2),one),one),
inference(cp,[status(thm)],[t264,t766]) ).
cnf(t121652,plain,
one = addition(sk0(sk2),one),
inference(step,[status(thm)],[t767,t262]) ).
cnf(t121653,plain,
one = addition(one,sk0(sk2)),
inference(step,[status(thm)],[t121652,t372]) ).
cnf(t781,plain,
addition(one,sk0(sk2)) = one,
inference(orient,[status(thm)],[t121653]) ).
cnf(t2556,plain,
true = leq(sk0(sk2),addition(X1,one)),
inference(cp,[status(thm)],[t2515,t781]) ).
cnf(t2614,plain,
leq(sk0(sk2),addition(X1,one)) = true,
inference(orient,[status(thm)],[t2556]) ).
cnf(t2616,plain,
addition(X1,one) = ifeq(true,true,addition(sk0(sk2),addition(X1,one)),addition(X1,one)),
inference(cp,[status(thm)],[t264,t2614]) ).
cnf(t121777,plain,
addition(X1,one) = addition(sk0(sk2),addition(X1,one)),
inference(step,[status(thm)],[t2616,t262]) ).
cnf(t2734,plain,
addition(sk0(sk2),addition(X1,one)) = addition(X1,one),
inference(orient,[status(thm)],[t121777]) ).
cnf(t122038,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(X1,one),
inference(step,[status(thm)],[t122037,t2734]) ).
cnf(t5366,plain,
addition(sk0(sk2),addition(X1,sk2)) = addition(X1,one),
inference(orient,[status(thm)],[t122038]) ).
cnf(t5379,plain,
multiplication(sk2,addition(X1,sk2)) = multiplication(sk2,addition(X1,one)),
inference(cp,[status(thm)],[t2345,t5366]) ).
cnf(t5419,plain,
multiplication(sk2,addition(X1,one)) = multiplication(sk2,addition(X1,sk2)),
inference(orient,[status(thm)],[t5379]) ).
cnf(h23,plain,
complement(sk1,or(c(sk1),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi22,hi29]) ).
cnf(t73,plain,
addition(or(c(sk1),false),sk1) = one,
inference(hyper_resolution,[status(thm)],[hi17,h23]) ).
cnf(t121584,plain,
addition(sk1,or(c(sk1),false)) = one,
inference(step,[status(thm)],[t73,t372]) ).
cnf(t121585,plain,
addition(sk1,c(sk1)) = one,
inference(step,[status(thm)],[t121584,t256]) ).
cnf(t422,plain,
addition(sk1,c(sk1)) = one,
inference(orient,[status(thm)],[t121585]) ).
cnf(t694,plain,
addition(sk1,c(sk1)) = addition(sk1,one),
inference(cp,[status(thm)],[t692,t422]) ).
cnf(t121641,plain,
one = addition(sk1,one),
inference(step,[status(thm)],[t694,t422]) ).
cnf(t709,plain,
addition(sk1,one) = one,
inference(orient,[status(thm)],[t121641]) ).
cnf(t5420,plain,
multiplication(sk2,addition(sk1,sk2)) = multiplication(sk2,one),
inference(cp,[status(thm)],[t5419,t709]) ).
cnf(t122042,plain,
multiplication(sk2,addition(sk2,sk1)) = multiplication(sk2,one),
inference(step,[status(thm)],[t5420,t372]) ).
cnf(t122043,plain,
multiplication(sk2,addition(sk2,sk1)) = sk2,
inference(step,[status(thm)],[t122042,t260]) ).
cnf(t5434,plain,
multiplication(sk2,addition(sk2,sk1)) = sk2,
inference(orient,[status(thm)],[t122043]) ).
cnf(t8786,plain,
addition(one,multiplication(sk2,sk1)) = addition(one,sk2),
inference(cp,[status(thm)],[t8782,t5434]) ).
cnf(t122210,plain,
addition(one,multiplication(sk2,sk1)) = addition(sk2,one),
inference(step,[status(thm)],[t8786,t372]) ).
cnf(t122211,plain,
addition(one,multiplication(sk2,sk1)) = one,
inference(step,[status(thm)],[t122210,t722]) ).
cnf(t8841,plain,
addition(one,multiplication(sk2,sk1)) = one,
inference(orient,[status(thm)],[t122211]) ).
cnf(t21248,plain,
true = leq(multiplication(multiplication(sk2,sk1),X1),multiplication(one,X1)),
inference(cp,[status(thm)],[t20897,t8841]) ).
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(t164,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t493,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t164]) ).
cnf(t122671,plain,
true = leq(multiplication(sk2,multiplication(sk1,X1)),multiplication(one,X1)),
inference(step,[status(thm)],[t21248,t493]) ).
cnf(t122672,plain,
true = leq(multiplication(sk2,multiplication(sk1,X1)),X1),
inference(step,[status(thm)],[t122671,t261]) ).
cnf(t21451,plain,
leq(multiplication(sk2,multiplication(sk1,X1)),X1) = true,
inference(orient,[status(thm)],[t122672]) ).
cnf(t21483,plain,
X1 = ifeq(true,true,addition(multiplication(sk2,multiplication(sk1,X1)),X1),X1),
inference(cp,[status(thm)],[t264,t21451]) ).
cnf(t122687,plain,
X1 = addition(multiplication(sk2,multiplication(sk1,X1)),X1),
inference(step,[status(thm)],[t21483,t262]) ).
cnf(t122688,plain,
X1 = addition(X1,multiplication(sk2,multiplication(sk1,X1))),
inference(step,[status(thm)],[t122687,t372]) ).
cnf(t21857,plain,
addition(X1,multiplication(sk2,multiplication(sk1,X1))) = X1,
inference(orient,[status(thm)],[t122688]) ).
cnf(t21942,plain,
true = leq(multiplication(sk2,multiplication(sk1,X1)),addition(X2,X1)),
inference(cp,[status(thm)],[t2515,t21857]) ).
cnf(t52844,plain,
leq(multiplication(sk2,multiplication(sk1,X1)),addition(X2,X1)) = true,
inference(orient,[status(thm)],[t21942]) ).
cnf(t100,plain,
multiplication(or(c(sk1),false),sk1) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h23]) ).
cnf(t121605,plain,
multiplication(c(sk1),sk1) = zero,
inference(step,[status(thm)],[t100,t256]) ).
cnf(t519,plain,
multiplication(c(sk1),sk1) = zero,
inference(orient,[status(thm)],[t121605]) ).
cnf(t524,plain,
multiplication(addition(X1,c(sk1)),sk1) = addition(multiplication(X1,sk1),zero),
inference(cp,[status(thm)],[t477,t519]) ).
cnf(t121710,plain,
multiplication(addition(X1,c(sk1)),sk1) = multiplication(X1,sk1),
inference(step,[status(thm)],[t524,t259]) ).
cnf(t1642,plain,
multiplication(addition(X1,c(sk1)),sk1) = multiplication(X1,sk1),
inference(orient,[status(thm)],[t121710]) ).
cnf(t1643,plain,
multiplication(sk1,sk1) = multiplication(one,sk1),
inference(cp,[status(thm)],[t1642,t422]) ).
cnf(t121711,plain,
multiplication(sk1,sk1) = sk1,
inference(step,[status(thm)],[t1643,t261]) ).
cnf(t1657,plain,
multiplication(sk1,sk1) = sk1,
inference(orient,[status(thm)],[t121711]) ).
cnf(t52882,plain,
true = leq(multiplication(sk2,sk1),addition(X1,sk1)),
inference(cp,[status(thm)],[t52844,t1657]) ).
cnf(t53074,plain,
leq(multiplication(sk2,sk1),addition(X1,sk1)) = true,
inference(orient,[status(thm)],[t52882]) ).
cnf(t53076,plain,
true = leq(multiplication(sk2,sk1),addition(sk1,X1)),
inference(cp,[status(thm)],[t53074,t372]) ).
cnf(t53081,plain,
leq(multiplication(sk2,sk1),addition(sk1,X1)) = true,
inference(orient,[status(thm)],[t53076]) ).
cnf(t53088,plain,
addition(sk1,X1) = ifeq(true,true,addition(addition(sk1,X1),multiplication(sk2,sk1)),addition(sk1,X1)),
inference(cp,[status(thm)],[t7445,t53081]) ).
cnf(t123161,plain,
addition(sk1,X1) = addition(addition(sk1,X1),multiplication(sk2,sk1)),
inference(step,[status(thm)],[t53088,t262]) ).
cnf(t123162,plain,
addition(sk1,X1) = addition(sk1,addition(X1,multiplication(sk2,sk1))),
inference(step,[status(thm)],[t123161,t378]) ).
cnf(t53232,plain,
addition(sk1,addition(X1,multiplication(sk2,sk1))) = addition(sk1,X1),
inference(orient,[status(thm)],[t123162]) ).
cnf(t53242,plain,
addition(sk1,multiplication(sk2,X1)) = addition(sk1,multiplication(sk2,addition(X1,sk1))),
inference(cp,[status(thm)],[t53232,t485]) ).
cnf(t53569,plain,
addition(sk1,multiplication(sk2,addition(X1,sk1))) = addition(sk1,multiplication(sk2,X1)),
inference(orient,[status(thm)],[t53242]) ).
cnf(t120811,plain,
multiplication(addition(sk1,sk2),addition(sk3,sk1)) = addition(sk1,multiplication(sk2,sk3)),
inference(cp,[status(thm)],[t120807,t53569]) ).
cnf(t123956,plain,
multiplication(addition(sk2,sk1),addition(sk3,sk1)) = addition(sk1,multiplication(sk2,sk3)),
inference(step,[status(thm)],[t120811,t372]) ).
cnf(t121434,plain,
multiplication(addition(sk2,sk1),addition(sk3,sk1)) = addition(sk1,multiplication(sk2,sk3)),
inference(orient,[status(thm)],[t123956]) ).
cnf(c25,plain,
addition(sk1,multiplication(sk2,sk3)) != multiplication(addition(sk1,sk2),addition(sk1,sk3)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(addition(sk1,sk2),addition(sk1,sk3)) != addition(sk1,multiplication(sk2,sk3)),
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(g0_0,plain,
multiplication(addition(sk2,sk1),addition(sk1,sk3)) != addition(sk1,multiplication(sk2,sk3)),
inference(rw,[status(thm)],[goal_0,t372]) ).
cnf(g0_1,plain,
multiplication(addition(sk2,sk1),addition(sk3,sk1)) != addition(sk1,multiplication(sk2,sk3)),
inference(rw,[status(thm)],[g0_0,t372]) ).
cnf(g0_2,plain,
addition(sk1,multiplication(sk2,sk3)) != addition(sk1,multiplication(sk2,sk3)),
inference(rw,[status(thm)],[g0_1,t121434]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE020+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.38 % Computer : n017.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Wed Sep 23 18:32:44 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 199.70/28.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 199.70/28.63 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------