%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 01:51:25 PM UTC 2026
% Result : Theorem 153.04s 36.26s
% Output : Proof 153.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 17
% Syntax : Number of formulae : 220 ( 194 unt; 0 def)
% Number of atoms : 283 ( 230 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 113 ( 50 ~; 36 |; 20 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 247 ( 8 sgn 87 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f7_nnf,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t127,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t377,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t127]) ).
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,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0,X1,X2,X3,X4] :
( addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2))
& test(X4)
& test(X3) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( addition(multiplication(sk4,addition(multiplication(sk4,sk1),multiplication(c(sk4),sk2))),multiplication(c(sk4),sk3)) != addition(multiplication(sk4,sk1),multiplication(c(sk4),sk3))
& test(sk5)
& test(sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4,sk5])],[f18_nnf]) ).
cnf(c24,plain,
test(sk4),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi24,negated_conjecture,
test(sk4) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(hi30,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h24,plain,
complement(sk4,or(c(sk4),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi24,hi30]) ).
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(t54,plain,
multiplication(sk4,or(c(sk4),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(t6839,plain,
multiplication(sk4,c(sk4)) = zero,
inference(step,[status(thm)],[t54,t256]) ).
cnf(t458,plain,
multiplication(sk4,c(sk4)) = zero,
inference(orient,[status(thm)],[t6839]) ).
cnf(t461,plain,
multiplication(sk4,addition(X1,c(sk4))) = addition(multiplication(sk4,X1),zero),
inference(cp,[status(thm)],[t377,t458]) ).
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(t6925,plain,
multiplication(sk4,addition(X1,c(sk4))) = multiplication(sk4,X1),
inference(step,[status(thm)],[t461,t259]) ).
cnf(t1183,plain,
multiplication(sk4,addition(X1,c(sk4))) = multiplication(sk4,X1),
inference(orient,[status(thm)],[t6925]) ).
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(t34,plain,
addition(or(c(sk4),false),sk4) = one,
inference(hyper_resolution,[status(thm)],[hi17,h24]) ).
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(t289,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t15]) ).
cnf(t6804,plain,
addition(sk4,or(c(sk4),false)) = one,
inference(step,[status(thm)],[t34,t289]) ).
cnf(t6805,plain,
addition(sk4,c(sk4)) = one,
inference(step,[status(thm)],[t6804,t256]) ).
cnf(t329,plain,
addition(sk4,c(sk4)) = one,
inference(orient,[status(thm)],[t6805]) ).
cnf(t1184,plain,
multiplication(sk4,sk4) = multiplication(sk4,one),
inference(cp,[status(thm)],[t1183,t329]) ).
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(t6926,plain,
multiplication(sk4,sk4) = sk4,
inference(step,[status(thm)],[t1184,t260]) ).
cnf(t1200,plain,
multiplication(sk4,sk4) = sk4,
inference(orient,[status(thm)],[t6926]) ).
cnf(t1206,plain,
multiplication(sk4,addition(sk4,X1)) = addition(sk4,multiplication(sk4,X1)),
inference(cp,[status(thm)],[t377,t1200]) ).
cnf(t379,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t377,t260]) ).
cnf(t1048,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t379]) ).
cnf(t6927,plain,
multiplication(sk4,addition(sk4,X1)) = multiplication(sk4,addition(one,X1)),
inference(step,[status(thm)],[t1206,t1048]) ).
cnf(t1224,plain,
multiplication(sk4,addition(one,X1)) = multiplication(sk4,addition(sk4,X1)),
inference(orient,[status(thm)],[t6927]) ).
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(t101,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)],[t101]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t97,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t548,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t97]) ).
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(t96,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t299,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t96]) ).
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(t302,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t299,t258]) ).
cnf(t779,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t302]) ).
cnf(t787,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t548,t779]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t6902,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t787,t262]) ).
cnf(t799,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t6902]) ).
cnf(t805,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t799,t289]) ).
cnf(t809,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t805]) ).
cnf(t98,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t393,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t98]) ).
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(t102,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t618,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t102]) ).
cnf(c25,plain,
test(sk5),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t1,plain,
test(sk5) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t531,plain,
test(sk5) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t619,plain,
true = ifeq(true,true,complement(sk0(sk5),sk5),true),
inference(cp,[status(thm)],[t618,t531]) ).
cnf(t6893,plain,
true = complement(sk0(sk5),sk5),
inference(step,[status(thm)],[t619,t262]) ).
cnf(t715,plain,
complement(sk0(sk5),sk5) = true,
inference(orient,[status(thm)],[t6893]) ).
cnf(t718,plain,
one = ifeq(true,true,addition(sk5,sk0(sk5)),one),
inference(cp,[status(thm)],[t393,t715]) ).
cnf(t6897,plain,
one = addition(sk5,sk0(sk5)),
inference(step,[status(thm)],[t718,t262]) ).
cnf(t755,plain,
addition(sk5,sk0(sk5)) = one,
inference(orient,[status(thm)],[t6897]) ).
cnf(t810,plain,
true = leq(sk0(sk5),one),
inference(cp,[status(thm)],[t809,t755]) ).
cnf(t820,plain,
leq(sk0(sk5),one) = true,
inference(orient,[status(thm)],[t810]) ).
cnf(t821,plain,
one = ifeq(true,true,addition(sk0(sk5),one),one),
inference(cp,[status(thm)],[t264,t820]) ).
cnf(t6903,plain,
one = addition(sk0(sk5),one),
inference(step,[status(thm)],[t821,t262]) ).
cnf(t6904,plain,
one = addition(one,sk0(sk5)),
inference(step,[status(thm)],[t6903,t289]) ).
cnf(t826,plain,
addition(one,sk0(sk5)) = one,
inference(orient,[status(thm)],[t6904]) ).
cnf(t1228,plain,
multiplication(sk4,addition(sk4,sk0(sk5))) = multiplication(sk4,one),
inference(cp,[status(thm)],[t1224,t826]) ).
cnf(t6928,plain,
multiplication(sk4,addition(sk4,sk0(sk5))) = sk4,
inference(step,[status(thm)],[t1228,t260]) ).
cnf(t1241,plain,
multiplication(sk4,addition(sk4,sk0(sk5))) = sk4,
inference(orient,[status(thm)],[t6928]) ).
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(t103,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t412,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t103]) ).
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(t128,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t361,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t128]) ).
cnf(t463,plain,
multiplication(addition(X1,sk4),c(sk4)) = addition(multiplication(X1,c(sk4)),zero),
inference(cp,[status(thm)],[t361,t458]) ).
cnf(t7011,plain,
multiplication(addition(X1,sk4),c(sk4)) = multiplication(X1,c(sk4)),
inference(step,[status(thm)],[t463,t259]) ).
cnf(t2504,plain,
multiplication(addition(X1,sk4),c(sk4)) = multiplication(X1,c(sk4)),
inference(orient,[status(thm)],[t7011]) ).
cnf(t2506,plain,
multiplication(X1,c(sk4)) = multiplication(addition(sk4,X1),c(sk4)),
inference(cp,[status(thm)],[t2504,t289]) ).
cnf(t2797,plain,
multiplication(addition(sk4,X1),c(sk4)) = multiplication(X1,c(sk4)),
inference(orient,[status(thm)],[t2506]) ).
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(h112,plain,
test(or(c(sk4),false)) = true,
inference(hyper_resolution,[status(thm)],[hi14,h24]) ).
cnf(h657,plain,
complement(or(c(sk4),false),or(c(or(c(sk4),false)),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,h112,hi30]) ).
cnf(h12585,plain,
test(or(c(or(c(sk4),false)),false)) = true,
inference(hyper_resolution,[status(thm)],[hi14,h657]) ).
cnf(hi13,axiom,
ifeq(test(X0),true,complement(sk0(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h12898,plain,
complement(sk0(or(c(or(c(sk4),false)),false)),or(c(or(c(sk4),false)),false)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h12585]) ).
cnf(t244,plain,
addition(or(c(or(c(sk4),false)),false),sk0(or(c(or(c(sk4),false)),false))) = one,
inference(hyper_resolution,[status(thm)],[hi17,h12898]) ).
cnf(t6812,plain,
addition(c(or(c(sk4),false)),sk0(or(c(or(c(sk4),false)),false))) = one,
inference(step,[status(thm)],[t244,t256]) ).
cnf(t6813,plain,
addition(c(c(sk4)),sk0(or(c(or(c(sk4),false)),false))) = one,
inference(step,[status(thm)],[t6812,t256]) ).
cnf(t6814,plain,
addition(c(c(sk4)),sk0(c(or(c(sk4),false)))) = one,
inference(step,[status(thm)],[t6813,t256]) ).
cnf(t6815,plain,
addition(c(c(sk4)),sk0(c(c(sk4)))) = one,
inference(step,[status(thm)],[t6814,t256]) ).
cnf(t340,plain,
addition(c(c(sk4)),sk0(c(c(sk4)))) = one,
inference(orient,[status(thm)],[t6815]) ).
cnf(c20,plain,
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t231,plain,
ifeq(test(X1),true,ifeq(complement(X1,X2),true,c(X1),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t263,plain,
ifeq(test(X1),true,ifeq(complement(X1,X2),true,c(X1),X2),X2) = X2,
inference(orient,[status(thm)],[t231]) ).
cnf(c18,plain,
( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t252,plain,
ifeq(multiplication(X1,X2),zero,ifeq(multiplication(X2,X1),zero,ifeq(addition(X1,X2),one,complement(X2,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t567,plain,
ifeq(multiplication(X1,X2),zero,ifeq(multiplication(X2,X1),zero,ifeq(addition(X1,X2),one,complement(X2,X1),true),true),true) = true,
inference(orient,[status(thm)],[t252]) ).
cnf(t573,plain,
true = ifeq(zero,zero,ifeq(multiplication(c(sk4),sk4),zero,ifeq(addition(sk4,c(sk4)),one,complement(c(sk4),sk4),true),true),true),
inference(cp,[status(thm)],[t567,t458]) ).
cnf(t6873,plain,
true = ifeq(multiplication(c(sk4),sk4),zero,ifeq(addition(sk4,c(sk4)),one,complement(c(sk4),sk4),true),true),
inference(step,[status(thm)],[t573,t262]) ).
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(t49,plain,
multiplication(or(c(sk4),false),sk4) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h24]) ).
cnf(t6840,plain,
multiplication(c(sk4),sk4) = zero,
inference(step,[status(thm)],[t49,t256]) ).
cnf(t465,plain,
multiplication(c(sk4),sk4) = zero,
inference(orient,[status(thm)],[t6840]) ).
cnf(t6874,plain,
true = ifeq(zero,zero,ifeq(addition(sk4,c(sk4)),one,complement(c(sk4),sk4),true),true),
inference(step,[status(thm)],[t6873,t465]) ).
cnf(t6875,plain,
true = ifeq(addition(sk4,c(sk4)),one,complement(c(sk4),sk4),true),
inference(step,[status(thm)],[t6874,t262]) ).
cnf(t6876,plain,
true = ifeq(one,one,complement(c(sk4),sk4),true),
inference(step,[status(thm)],[t6875,t329]) ).
cnf(t6877,plain,
true = complement(c(sk4),sk4),
inference(step,[status(thm)],[t6876,t262]) ).
cnf(t685,plain,
complement(c(sk4),sk4) = true,
inference(orient,[status(thm)],[t6877]) ).
cnf(t686,plain,
sk4 = ifeq(test(c(sk4)),true,ifeq(true,true,c(c(sk4)),sk4),sk4),
inference(cp,[status(thm)],[t263,t685]) ).
cnf(t28,plain,
test(or(c(sk4),false)) = true,
inference(hyper_resolution,[status(thm)],[hi14,h24]) ).
cnf(t6851,plain,
test(c(sk4)) = true,
inference(step,[status(thm)],[t28,t256]) ).
cnf(t513,plain,
test(c(sk4)) = true,
inference(orient,[status(thm)],[t6851]) ).
cnf(t6878,plain,
sk4 = ifeq(true,true,ifeq(true,true,c(c(sk4)),sk4),sk4),
inference(step,[status(thm)],[t686,t513]) ).
cnf(t6879,plain,
sk4 = ifeq(true,true,c(c(sk4)),sk4),
inference(step,[status(thm)],[t6878,t262]) ).
cnf(t6880,plain,
sk4 = c(c(sk4)),
inference(step,[status(thm)],[t6879,t262]) ).
cnf(t688,plain,
c(c(sk4)) = sk4,
inference(orient,[status(thm)],[t6880]) ).
cnf(t6885,plain,
addition(sk4,sk0(c(c(sk4)))) = one,
inference(step,[status(thm)],[t340,t688]) ).
cnf(t6886,plain,
addition(sk4,sk0(sk4)) = one,
inference(step,[status(thm)],[t6885,t688]) ).
cnf(t702,plain,
addition(sk4,sk0(sk4)) = one,
inference(rw,[status(thm)],[t6886]) ).
cnf(t729,plain,
addition(sk4,sk0(sk4)) = one,
inference(orient,[status(thm)],[t702]) ).
cnf(t2803,plain,
multiplication(sk0(sk4),c(sk4)) = multiplication(one,c(sk4)),
inference(cp,[status(thm)],[t2797,t729]) ).
cnf(t99,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t654,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t99]) ).
cnf(t0,plain,
test(sk4) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t507,plain,
test(sk4) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t620,plain,
true = ifeq(true,true,complement(sk0(sk4),sk4),true),
inference(cp,[status(thm)],[t618,t507]) ).
cnf(t6894,plain,
true = complement(sk0(sk4),sk4),
inference(step,[status(thm)],[t620,t262]) ).
cnf(t722,plain,
complement(sk0(sk4),sk4) = true,
inference(orient,[status(thm)],[t6894]) ).
cnf(t723,plain,
zero = ifeq(true,true,multiplication(sk0(sk4),sk4),zero),
inference(cp,[status(thm)],[t654,t722]) ).
cnf(t6898,plain,
zero = multiplication(sk0(sk4),sk4),
inference(step,[status(thm)],[t723,t262]) ).
cnf(t760,plain,
multiplication(sk0(sk4),sk4) = zero,
inference(orient,[status(thm)],[t6898]) ).
cnf(t763,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = addition(zero,multiplication(sk0(sk4),X1)),
inference(cp,[status(thm)],[t377,t760]) ).
cnf(t294,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t289,t259]) ).
cnf(t669,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t294]) ).
cnf(t7018,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = multiplication(sk0(sk4),X1),
inference(step,[status(thm)],[t763,t669]) ).
cnf(t2602,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = multiplication(sk0(sk4),X1),
inference(orient,[status(thm)],[t7018]) ).
cnf(t2609,plain,
multiplication(sk0(sk4),c(sk4)) = multiplication(sk0(sk4),one),
inference(cp,[status(thm)],[t2602,t329]) ).
cnf(t7020,plain,
multiplication(sk0(sk4),c(sk4)) = sk0(sk4),
inference(step,[status(thm)],[t2609,t260]) ).
cnf(t2633,plain,
multiplication(sk0(sk4),c(sk4)) = sk0(sk4),
inference(orient,[status(thm)],[t7020]) ).
cnf(t7028,plain,
sk0(sk4) = multiplication(one,c(sk4)),
inference(step,[status(thm)],[t2803,t2633]) ).
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(t7029,plain,
sk0(sk4) = c(sk4),
inference(step,[status(thm)],[t7028,t261]) ).
cnf(t2815,plain,
c(sk4) = sk0(sk4),
inference(orient,[status(thm)],[t7029]) ).
cnf(c26,plain,
addition(multiplication(sk4,addition(multiplication(sk4,sk1),multiplication(c(sk4),sk2))),multiplication(c(sk4),sk3)) != addition(multiplication(sk4,sk1),multiplication(c(sk4),sk3)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
addition(multiplication(sk4,addition(multiplication(sk4,sk1),multiplication(c(sk4),sk2))),multiplication(c(sk4),sk3)) != addition(multiplication(sk4,sk1),multiplication(c(sk4),sk3)),
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(g0_0,plain,
addition(multiplication(sk4,addition(multiplication(sk4,sk1),multiplication(c(sk4),sk2))),multiplication(c(sk4),sk3)) != addition(multiplication(multiplication(sk4,addition(sk4,sk0(sk5))),sk1),multiplication(c(sk4),sk3)),
inference(rw,[status(thm)],[goal_0,t1241]) ).
cnf(g0_1,plain,
addition(multiplication(sk4,addition(multiplication(sk4,sk1),multiplication(c(sk4),sk2))),multiplication(c(sk4),sk3)) != addition(multiplication(c(sk4),sk3),multiplication(multiplication(sk4,addition(sk4,sk0(sk5))),sk1)),
inference(rw,[status(thm)],[g0_0,t289]) ).
cnf(g0_2,plain,
addition(multiplication(sk4,addition(multiplication(sk4,sk1),multiplication(c(sk4),sk2))),multiplication(c(sk4),sk3)) != addition(multiplication(c(sk4),sk3),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))),
inference(rw,[status(thm)],[g0_1,t412]) ).
cnf(g0_3,plain,
addition(multiplication(sk4,addition(multiplication(sk4,sk1),multiplication(c(sk4),sk2))),multiplication(c(sk4),sk3)) != addition(multiplication(sk0(sk4),sk3),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))),
inference(rw,[status(thm)],[g0_2,t2815]) ).
cnf(g0_4,plain,
addition(multiplication(c(sk4),sk3),multiplication(sk4,addition(multiplication(sk4,sk1),multiplication(c(sk4),sk2)))) != addition(multiplication(sk0(sk4),sk3),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))),
inference(rw,[status(thm)],[g0_3,t289]) ).
cnf(g0_5,plain,
addition(multiplication(c(sk4),sk3),multiplication(sk4,addition(multiplication(multiplication(sk4,addition(sk4,sk0(sk5))),sk1),multiplication(c(sk4),sk2)))) != addition(multiplication(sk0(sk4),sk3),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))),
inference(rw,[status(thm)],[g0_4,t1241]) ).
cnf(g0_6,plain,
addition(multiplication(c(sk4),sk3),multiplication(sk4,addition(multiplication(c(sk4),sk2),multiplication(multiplication(sk4,addition(sk4,sk0(sk5))),sk1)))) != addition(multiplication(sk0(sk4),sk3),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))),
inference(rw,[status(thm)],[g0_5,t289]) ).
cnf(g0_7,plain,
addition(multiplication(c(sk4),sk3),multiplication(sk4,addition(multiplication(c(sk4),sk2),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))))) != addition(multiplication(sk0(sk4),sk3),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))),
inference(rw,[status(thm)],[g0_6,t412]) ).
cnf(g0_8,plain,
addition(multiplication(sk0(sk4),sk3),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))) != addition(multiplication(sk0(sk4),sk3),multiplication(sk4,multiplication(addition(sk4,sk0(sk5)),sk1))),
inference(rw,[status(thm)],[g0_7]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.43 % CPULimit : 300
% 0.07/15.43 % WCLimit : 300
% 0.07/15.43 % DateTime : Wed Sep 23 18:44:05 UTC 2026
% 0.07/15.43 % CPUTime :
% 0.07/15.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 153.04/36.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 153.04/36.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------