%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE024+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 : n018.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 113.75s 20.24s
% Output : Proof 113.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 14
% Syntax : Number of formulae : 186 ( 169 unt; 0 def)
% Number of atoms : 237 ( 197 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 82 ( 31 ~; 23 |; 20 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 180 ( 10 sgn 71 !; 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(t80,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t593,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t80]) ).
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(t105,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t326,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t105]) ).
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]) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] :
( multiplication(multiplication(X1,X0),c(X2)) != zero
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
& test(X2)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( multiplication(multiplication(sk2,sk1),c(sk3)) != zero
& addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1)
& test(sk3)
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f16_nnf]) ).
cnf(c23,plain,
test(sk3),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi23,negated_conjecture,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
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(hi3,axiom,
addition(X0,X0) = X0,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h6,plain,
complement(sk3,addition(c(sk3),c(sk3))) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi3]) ).
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(t48,plain,
multiplication(addition(c(sk3),c(sk3)),sk3) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h6]) ).
cnf(t2,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t256,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t101784,plain,
multiplication(c(sk3),sk3) = zero,
inference(step,[status(thm)],[t48,t256]) ).
cnf(t337,plain,
multiplication(c(sk3),sk3) = zero,
inference(orient,[status(thm)],[t101784]) ).
cnf(t339,plain,
multiplication(c(sk3),addition(X1,sk3)) = addition(multiplication(c(sk3),X1),zero),
inference(cp,[status(thm)],[t326,t337]) ).
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(t257,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t102016,plain,
multiplication(c(sk3),addition(X1,sk3)) = multiplication(c(sk3),X1),
inference(step,[status(thm)],[t339,t257]) ).
cnf(t2715,plain,
multiplication(c(sk3),addition(X1,sk3)) = multiplication(c(sk3),X1),
inference(orient,[status(thm)],[t102016]) ).
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(t13,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t268,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t2717,plain,
multiplication(c(sk3),X1) = multiplication(c(sk3),addition(sk3,X1)),
inference(cp,[status(thm)],[t2715,t268]) ).
cnf(t3141,plain,
multiplication(c(sk3),addition(sk3,X1)) = multiplication(c(sk3),X1),
inference(orient,[status(thm)],[t2717]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t74,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t612,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t74]) ).
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(t78,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t564,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t78]) ).
cnf(t1,plain,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t443,plain,
test(sk3) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t566,plain,
true = ifeq(true,true,complement(sk0(sk3),sk3),true),
inference(cp,[status(thm)],[t564,t443]) ).
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(t101878,plain,
true = complement(sk0(sk3),sk3),
inference(step,[status(thm)],[t566,t262]) ).
cnf(t670,plain,
complement(sk0(sk3),sk3) = true,
inference(orient,[status(thm)],[t101878]) ).
cnf(t671,plain,
one = ifeq(true,true,addition(sk3,sk0(sk3)),one),
inference(cp,[status(thm)],[t612,t670]) ).
cnf(t101886,plain,
one = addition(sk3,sk0(sk3)),
inference(step,[status(thm)],[t671,t262]) ).
cnf(t711,plain,
addition(sk3,sk0(sk3)) = one,
inference(orient,[status(thm)],[t101886]) ).
cnf(t3148,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(c(sk3),one),
inference(cp,[status(thm)],[t3141,t711]) ).
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(t106,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t320,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t106]) ).
cnf(t76,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t394,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(orient,[status(thm)],[t76]) ).
cnf(t673,plain,
zero = ifeq(true,true,multiplication(sk3,sk0(sk3)),zero),
inference(cp,[status(thm)],[t394,t670]) ).
cnf(t101888,plain,
zero = multiplication(sk3,sk0(sk3)),
inference(step,[status(thm)],[t673,t262]) ).
cnf(t725,plain,
multiplication(sk3,sk0(sk3)) = zero,
inference(orient,[status(thm)],[t101888]) ).
cnf(t730,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = addition(zero,multiplication(X1,sk0(sk3))),
inference(cp,[status(thm)],[t320,t725]) ).
cnf(t269,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t268,t257]) ).
cnf(t640,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t269]) ).
cnf(t102037,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(step,[status(thm)],[t730,t640]) ).
cnf(t2993,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(orient,[status(thm)],[t102037]) ).
cnf(hi2,axiom,
addition(X0,zero) = X0,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t24,plain,
complement(sk3,addition(c(sk3),zero)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi2]) ).
cnf(t101833,plain,
complement(sk3,c(sk3)) = true,
inference(step,[status(thm)],[t24,t257]) ).
cnf(t456,plain,
complement(sk3,c(sk3)) = true,
inference(orient,[status(thm)],[t101833]) ).
cnf(t616,plain,
one = ifeq(true,true,addition(c(sk3),sk3),one),
inference(cp,[status(thm)],[t612,t456]) ).
cnf(t101881,plain,
one = addition(c(sk3),sk3),
inference(step,[status(thm)],[t616,t262]) ).
cnf(t101882,plain,
one = addition(sk3,c(sk3)),
inference(step,[status(thm)],[t101881,t268]) ).
cnf(t683,plain,
addition(sk3,c(sk3)) = one,
inference(orient,[status(thm)],[t101882]) ).
cnf(t2999,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(one,sk0(sk3)),
inference(cp,[status(thm)],[t2993,t683]) ).
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(t102038,plain,
multiplication(c(sk3),sk0(sk3)) = sk0(sk3),
inference(step,[status(thm)],[t2999,t261]) ).
cnf(t3117,plain,
multiplication(c(sk3),sk0(sk3)) = sk0(sk3),
inference(orient,[status(thm)],[t102038]) ).
cnf(t102040,plain,
sk0(sk3) = multiplication(c(sk3),one),
inference(step,[status(thm)],[t3148,t3117]) ).
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(t102041,plain,
sk0(sk3) = c(sk3),
inference(step,[status(thm)],[t102040,t260]) ).
cnf(t3162,plain,
c(sk3) = sk0(sk3),
inference(orient,[status(thm)],[t102041]) ).
cnf(c22,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t0,plain,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t445,plain,
test(sk2) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t565,plain,
true = ifeq(true,true,complement(sk0(sk2),sk2),true),
inference(cp,[status(thm)],[t564,t445]) ).
cnf(t101877,plain,
true = complement(sk0(sk2),sk2),
inference(step,[status(thm)],[t565,t262]) ).
cnf(t663,plain,
complement(sk0(sk2),sk2) = true,
inference(orient,[status(thm)],[t101877]) ).
cnf(t666,plain,
zero = ifeq(true,true,multiplication(sk2,sk0(sk2)),zero),
inference(cp,[status(thm)],[t394,t663]) ).
cnf(t101885,plain,
zero = multiplication(sk2,sk0(sk2)),
inference(step,[status(thm)],[t666,t262]) ).
cnf(t703,plain,
multiplication(sk2,sk0(sk2)) = zero,
inference(orient,[status(thm)],[t101885]) ).
cnf(t704,plain,
multiplication(sk2,multiplication(sk0(sk2),X1)) = multiplication(zero,X1),
inference(cp,[status(thm)],[t593,t703]) ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f10_nnf,plain,
! [A] : multiplication(zero,A) = zero,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : multiplication(zero,A) = zero,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t8,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t347,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t8]) ).
cnf(t101937,plain,
multiplication(sk2,multiplication(sk0(sk2),X1)) = zero,
inference(step,[status(thm)],[t704,t347]) ).
cnf(t1010,plain,
multiplication(sk2,multiplication(sk0(sk2),X1)) = zero,
inference(orient,[status(thm)],[t101937]) ).
cnf(t1014,plain,
multiplication(sk2,addition(X1,multiplication(sk0(sk2),X2))) = addition(multiplication(sk2,X1),zero),
inference(cp,[status(thm)],[t326,t1010]) ).
cnf(t102193,plain,
multiplication(sk2,addition(X1,multiplication(sk0(sk2),X2))) = multiplication(sk2,X1),
inference(step,[status(thm)],[t1014,t257]) ).
cnf(t5983,plain,
multiplication(sk2,addition(X1,multiplication(sk0(sk2),X2))) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t102193]) ).
cnf(c24,plain,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t154,plain,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t332,plain,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(orient,[status(thm)],[t154]) ).
cnf(t102060,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(step,[status(thm)],[t332,t3162]) ).
cnf(t3179,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(rw,[status(thm)],[t102060]) ).
cnf(hi22,negated_conjecture,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h7,plain,
complement(sk2,addition(c(sk2),c(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi22,hi3]) ).
cnf(t47,plain,
multiplication(addition(c(sk2),c(sk2)),sk2) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h7]) ).
cnf(t101785,plain,
multiplication(c(sk2),sk2) = zero,
inference(step,[status(thm)],[t47,t256]) ).
cnf(t342,plain,
multiplication(c(sk2),sk2) = zero,
inference(orient,[status(thm)],[t101785]) ).
cnf(t344,plain,
multiplication(c(sk2),addition(X1,sk2)) = addition(multiplication(c(sk2),X1),zero),
inference(cp,[status(thm)],[t326,t342]) ).
cnf(t102017,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(step,[status(thm)],[t344,t257]) ).
cnf(t2729,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t102017]) ).
cnf(t2731,plain,
multiplication(c(sk2),X1) = multiplication(c(sk2),addition(sk2,X1)),
inference(cp,[status(thm)],[t2729,t268]) ).
cnf(t3338,plain,
multiplication(c(sk2),addition(sk2,X1)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t2731]) ).
cnf(t664,plain,
one = ifeq(true,true,addition(sk2,sk0(sk2)),one),
inference(cp,[status(thm)],[t612,t663]) ).
cnf(t101883,plain,
one = addition(sk2,sk0(sk2)),
inference(step,[status(thm)],[t664,t262]) ).
cnf(t689,plain,
addition(sk2,sk0(sk2)) = one,
inference(orient,[status(thm)],[t101883]) ).
cnf(t3345,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(c(sk2),one),
inference(cp,[status(thm)],[t3338,t689]) ).
cnf(t708,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = addition(zero,multiplication(X1,sk0(sk2))),
inference(cp,[status(thm)],[t320,t703]) ).
cnf(t102027,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(step,[status(thm)],[t708,t640]) ).
cnf(t2859,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(orient,[status(thm)],[t102027]) ).
cnf(t23,plain,
complement(sk2,addition(c(sk2),zero)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi22,hi2]) ).
cnf(t101834,plain,
complement(sk2,c(sk2)) = true,
inference(step,[status(thm)],[t23,t257]) ).
cnf(t457,plain,
complement(sk2,c(sk2)) = true,
inference(orient,[status(thm)],[t101834]) ).
cnf(t615,plain,
one = ifeq(true,true,addition(c(sk2),sk2),one),
inference(cp,[status(thm)],[t612,t457]) ).
cnf(t101879,plain,
one = addition(c(sk2),sk2),
inference(step,[status(thm)],[t615,t262]) ).
cnf(t101880,plain,
one = addition(sk2,c(sk2)),
inference(step,[status(thm)],[t101879,t268]) ).
cnf(t677,plain,
addition(sk2,c(sk2)) = one,
inference(orient,[status(thm)],[t101880]) ).
cnf(t2865,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(one,sk0(sk2)),
inference(cp,[status(thm)],[t2859,t677]) ).
cnf(t102028,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(step,[status(thm)],[t2865,t261]) ).
cnf(t2881,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(orient,[status(thm)],[t102028]) ).
cnf(t102065,plain,
sk0(sk2) = multiplication(c(sk2),one),
inference(step,[status(thm)],[t3345,t2881]) ).
cnf(t102066,plain,
sk0(sk2) = c(sk2),
inference(step,[status(thm)],[t102065,t260]) ).
cnf(t3359,plain,
c(sk2) = sk0(sk2),
inference(orient,[status(thm)],[t102066]) ).
cnf(t103361,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(step,[status(thm)],[t3179,t3359]) ).
cnf(t103362,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = multiplication(sk0(sk2),sk1),
inference(step,[status(thm)],[t103361,t3359]) ).
cnf(t101568,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = multiplication(sk0(sk2),sk1),
inference(orient,[status(thm)],[t103362]) ).
cnf(t101633,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = multiplication(sk2,multiplication(sk0(sk2),sk1)),
inference(cp,[status(thm)],[t5983,t101568]) ).
cnf(t103363,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(step,[status(thm)],[t101633,t1010]) ).
cnf(t101654,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(orient,[status(thm)],[t103363]) ).
cnf(c25,plain,
multiplication(multiplication(sk2,sk1),c(sk3)) != zero,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(multiplication(sk2,sk1),c(sk3)) != zero,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(g0_0,plain,
multiplication(sk2,multiplication(sk1,c(sk3))) != zero,
inference(rw,[status(thm)],[goal_0,t593]) ).
cnf(g0_1,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) != zero,
inference(rw,[status(thm)],[g0_0,t3162]) ).
cnf(g0_2,plain,
zero != zero,
inference(rw,[status(thm)],[g0_1,t101654]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE024+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n018.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Wed Sep 23 18:42:08 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 113.75/20.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 113.75/20.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------