%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE024+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 127.03s 18.22s
% Output : Proof 127.03s
% 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/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(t86,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t596,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t86]) ).
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(t101,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t430,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t101]) ).
fof(f14,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f14_nnf,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c19,plain,
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi19,axiom,
ifeq(test(X0),true,ifeq(c(X0),X1,complement(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
fof(f18,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_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)],[f18]) ).
fof(f18_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)],[f18_neg]) ).
fof(f18_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])],[f18_nnf]) ).
cnf(c25,plain,
test(sk3),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi25,negated_conjecture,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
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(hi3,axiom,
addition(X0,X0) = X0,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h14,plain,
complement(sk3,addition(c(sk3),c(sk3))) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi25,hi3]) ).
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(t54,plain,
multiplication(addition(c(sk3),c(sk3)),sk3) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h14]) ).
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(t102367,plain,
multiplication(c(sk3),sk3) = zero,
inference(step,[status(thm)],[t54,t256]) ).
cnf(t462,plain,
multiplication(c(sk3),sk3) = zero,
inference(orient,[status(thm)],[t102367]) ).
cnf(t464,plain,
multiplication(c(sk3),addition(X1,sk3)) = addition(multiplication(c(sk3),X1),zero),
inference(cp,[status(thm)],[t430,t462]) ).
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(t257,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t102644,plain,
multiplication(c(sk3),addition(X1,sk3)) = multiplication(c(sk3),X1),
inference(step,[status(thm)],[t464,t257]) ).
cnf(t3454,plain,
multiplication(c(sk3),addition(X1,sk3)) = multiplication(c(sk3),X1),
inference(orient,[status(thm)],[t102644]) ).
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(t298,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t15]) ).
cnf(t3456,plain,
multiplication(c(sk3),X1) = multiplication(c(sk3),addition(sk3,X1)),
inference(cp,[status(thm)],[t3454,t298]) ).
cnf(t3864,plain,
multiplication(c(sk3),addition(sk3,X1)) = multiplication(c(sk3),X1),
inference(orient,[status(thm)],[t3456]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t80,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t897,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t80]) ).
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(t84,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t868,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t84]) ).
cnf(t1,plain,
test(sk3) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t715,plain,
test(sk3) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t870,plain,
true = ifeq(true,true,complement(sk0(sk3),sk3),true),
inference(cp,[status(thm)],[t868,t715]) ).
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(t102447,plain,
true = complement(sk0(sk3),sk3),
inference(step,[status(thm)],[t870,t262]) ).
cnf(t959,plain,
complement(sk0(sk3),sk3) = true,
inference(orient,[status(thm)],[t102447]) ).
cnf(t960,plain,
one = ifeq(true,true,addition(sk3,sk0(sk3)),one),
inference(cp,[status(thm)],[t897,t959]) ).
cnf(t102460,plain,
one = addition(sk3,sk0(sk3)),
inference(step,[status(thm)],[t960,t262]) ).
cnf(t1015,plain,
addition(sk3,sk0(sk3)) = one,
inference(orient,[status(thm)],[t102460]) ).
cnf(t3872,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(c(sk3),one),
inference(cp,[status(thm)],[t3864,t1015]) ).
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(t102,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t404,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t102]) ).
cnf(t82,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t537,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(orient,[status(thm)],[t82]) ).
cnf(t962,plain,
zero = ifeq(true,true,multiplication(sk3,sk0(sk3)),zero),
inference(cp,[status(thm)],[t537,t959]) ).
cnf(t102462,plain,
zero = multiplication(sk3,sk0(sk3)),
inference(step,[status(thm)],[t962,t262]) ).
cnf(t1031,plain,
multiplication(sk3,sk0(sk3)) = zero,
inference(orient,[status(thm)],[t102462]) ).
cnf(t1036,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = addition(zero,multiplication(X1,sk0(sk3))),
inference(cp,[status(thm)],[t404,t1031]) ).
cnf(t309,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t298,t257]) ).
cnf(t929,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t309]) ).
cnf(t102665,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(step,[status(thm)],[t1036,t929]) ).
cnf(t3766,plain,
multiplication(addition(sk3,X1),sk0(sk3)) = multiplication(X1,sk0(sk3)),
inference(orient,[status(thm)],[t102665]) ).
cnf(hi2,axiom,
addition(X0,zero) = X0,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t25,plain,
complement(sk3,addition(c(sk3),zero)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi25,hi2]) ).
cnf(t102420,plain,
complement(sk3,c(sk3)) = true,
inference(step,[status(thm)],[t25,t257]) ).
cnf(t735,plain,
complement(sk3,c(sk3)) = true,
inference(orient,[status(thm)],[t102420]) ).
cnf(t901,plain,
one = ifeq(true,true,addition(c(sk3),sk3),one),
inference(cp,[status(thm)],[t897,t735]) ).
cnf(t102455,plain,
one = addition(c(sk3),sk3),
inference(step,[status(thm)],[t901,t262]) ).
cnf(t102456,plain,
one = addition(sk3,c(sk3)),
inference(step,[status(thm)],[t102455,t298]) ).
cnf(t984,plain,
addition(sk3,c(sk3)) = one,
inference(orient,[status(thm)],[t102456]) ).
cnf(t3772,plain,
multiplication(c(sk3),sk0(sk3)) = multiplication(one,sk0(sk3)),
inference(cp,[status(thm)],[t3766,t984]) ).
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(t102666,plain,
multiplication(c(sk3),sk0(sk3)) = sk0(sk3),
inference(step,[status(thm)],[t3772,t261]) ).
cnf(t3790,plain,
multiplication(c(sk3),sk0(sk3)) = sk0(sk3),
inference(orient,[status(thm)],[t102666]) ).
cnf(t102670,plain,
sk0(sk3) = multiplication(c(sk3),one),
inference(step,[status(thm)],[t3872,t3790]) ).
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(t102671,plain,
sk0(sk3) = c(sk3),
inference(step,[status(thm)],[t102670,t260]) ).
cnf(t3887,plain,
c(sk3) = sk0(sk3),
inference(orient,[status(thm)],[t102671]) ).
cnf(c24,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t0,plain,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t721,plain,
test(sk2) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t869,plain,
true = ifeq(true,true,complement(sk0(sk2),sk2),true),
inference(cp,[status(thm)],[t868,t721]) ).
cnf(t102446,plain,
true = complement(sk0(sk2),sk2),
inference(step,[status(thm)],[t869,t262]) ).
cnf(t952,plain,
complement(sk0(sk2),sk2) = true,
inference(orient,[status(thm)],[t102446]) ).
cnf(t955,plain,
zero = ifeq(true,true,multiplication(sk2,sk0(sk2)),zero),
inference(cp,[status(thm)],[t537,t952]) ).
cnf(t102459,plain,
zero = multiplication(sk2,sk0(sk2)),
inference(step,[status(thm)],[t955,t262]) ).
cnf(t1006,plain,
multiplication(sk2,sk0(sk2)) = zero,
inference(orient,[status(thm)],[t102459]) ).
cnf(t1007,plain,
multiplication(sk2,multiplication(sk0(sk2),X1)) = multiplication(zero,X1),
inference(cp,[status(thm)],[t596,t1006]) ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/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(t10,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t474,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t10]) ).
cnf(t102536,plain,
multiplication(sk2,multiplication(sk0(sk2),X1)) = zero,
inference(step,[status(thm)],[t1007,t474]) ).
cnf(t1398,plain,
multiplication(sk2,multiplication(sk0(sk2),X1)) = zero,
inference(orient,[status(thm)],[t102536]) ).
cnf(t1402,plain,
multiplication(sk2,addition(X1,multiplication(sk0(sk2),X2))) = addition(multiplication(sk2,X1),zero),
inference(cp,[status(thm)],[t430,t1398]) ).
cnf(t102939,plain,
multiplication(sk2,addition(X1,multiplication(sk0(sk2),X2))) = multiplication(sk2,X1),
inference(step,[status(thm)],[t1402,t257]) ).
cnf(t8233,plain,
multiplication(sk2,addition(X1,multiplication(sk0(sk2),X2))) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t102939]) ).
cnf(c26,plain,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t148,plain,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t456,plain,
addition(multiplication(sk1,c(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(orient,[status(thm)],[t148]) ).
cnf(t102707,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(step,[status(thm)],[t456,t3887]) ).
cnf(t3928,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(c(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(rw,[status(thm)],[t102707]) ).
cnf(hi24,negated_conjecture,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h15,plain,
complement(sk2,addition(c(sk2),c(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi24,hi3]) ).
cnf(t53,plain,
multiplication(addition(c(sk2),c(sk2)),sk2) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h15]) ).
cnf(t102368,plain,
multiplication(c(sk2),sk2) = zero,
inference(step,[status(thm)],[t53,t256]) ).
cnf(t468,plain,
multiplication(c(sk2),sk2) = zero,
inference(orient,[status(thm)],[t102368]) ).
cnf(t470,plain,
multiplication(c(sk2),addition(X1,sk2)) = addition(multiplication(c(sk2),X1),zero),
inference(cp,[status(thm)],[t430,t468]) ).
cnf(t102645,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(step,[status(thm)],[t470,t257]) ).
cnf(t3469,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t102645]) ).
cnf(t3471,plain,
multiplication(c(sk2),X1) = multiplication(c(sk2),addition(sk2,X1)),
inference(cp,[status(thm)],[t3469,t298]) ).
cnf(t4219,plain,
multiplication(c(sk2),addition(sk2,X1)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t3471]) ).
cnf(t953,plain,
one = ifeq(true,true,addition(sk2,sk0(sk2)),one),
inference(cp,[status(thm)],[t897,t952]) ).
cnf(t102457,plain,
one = addition(sk2,sk0(sk2)),
inference(step,[status(thm)],[t953,t262]) ).
cnf(t990,plain,
addition(sk2,sk0(sk2)) = one,
inference(orient,[status(thm)],[t102457]) ).
cnf(t4227,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(c(sk2),one),
inference(cp,[status(thm)],[t4219,t990]) ).
cnf(t1011,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = addition(zero,multiplication(X1,sk0(sk2))),
inference(cp,[status(thm)],[t404,t1006]) ).
cnf(t102655,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(step,[status(thm)],[t1011,t929]) ).
cnf(t3615,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(orient,[status(thm)],[t102655]) ).
cnf(t24,plain,
complement(sk2,addition(c(sk2),zero)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi24,hi2]) ).
cnf(t102421,plain,
complement(sk2,c(sk2)) = true,
inference(step,[status(thm)],[t24,t257]) ).
cnf(t736,plain,
complement(sk2,c(sk2)) = true,
inference(orient,[status(thm)],[t102421]) ).
cnf(t900,plain,
one = ifeq(true,true,addition(c(sk2),sk2),one),
inference(cp,[status(thm)],[t897,t736]) ).
cnf(t102448,plain,
one = addition(c(sk2),sk2),
inference(step,[status(thm)],[t900,t262]) ).
cnf(t102449,plain,
one = addition(sk2,c(sk2)),
inference(step,[status(thm)],[t102448,t298]) ).
cnf(t966,plain,
addition(sk2,c(sk2)) = one,
inference(orient,[status(thm)],[t102449]) ).
cnf(t3621,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(one,sk0(sk2)),
inference(cp,[status(thm)],[t3615,t966]) ).
cnf(t102656,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(step,[status(thm)],[t3621,t261]) ).
cnf(t3639,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(orient,[status(thm)],[t102656]) ).
cnf(t102718,plain,
sk0(sk2) = multiplication(c(sk2),one),
inference(step,[status(thm)],[t4227,t3639]) ).
cnf(t102719,plain,
sk0(sk2) = c(sk2),
inference(step,[status(thm)],[t102718,t260]) ).
cnf(t4242,plain,
c(sk2) = sk0(sk2),
inference(orient,[status(thm)],[t102719]) ).
cnf(t104049,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = multiplication(c(sk2),sk1),
inference(step,[status(thm)],[t3928,t4242]) ).
cnf(t104050,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = multiplication(sk0(sk2),sk1),
inference(step,[status(thm)],[t104049,t4242]) ).
cnf(t102084,plain,
addition(multiplication(sk1,sk0(sk3)),multiplication(sk0(sk2),sk1)) = multiplication(sk0(sk2),sk1),
inference(orient,[status(thm)],[t104050]) ).
cnf(t102142,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = multiplication(sk2,multiplication(sk0(sk2),sk1)),
inference(cp,[status(thm)],[t8233,t102084]) ).
cnf(t104051,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(step,[status(thm)],[t102142,t1398]) ).
cnf(t102155,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) = zero,
inference(orient,[status(thm)],[t104051]) ).
cnf(c27,plain,
multiplication(multiplication(sk2,sk1),c(sk3)) != zero,
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(multiplication(sk2,sk1),c(sk3)) != zero,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
multiplication(sk2,multiplication(sk1,c(sk3))) != zero,
inference(rw,[status(thm)],[goal_0,t596]) ).
cnf(g0_1,plain,
multiplication(sk2,multiplication(sk1,sk0(sk3))) != zero,
inference(rw,[status(thm)],[g0_0,t3887]) ).
cnf(g0_2,plain,
zero != zero,
inference(rw,[status(thm)],[g0_1,t102155]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE024+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 18:39:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 127.03/18.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 127.03/18.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------