%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE015+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 : n026.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 120.65s 16.65s
% Output : Proof 120.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of formulae : 225 ( 203 unt; 0 def)
% Number of atoms : 281 ( 234 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 96 ( 40 ~; 29 |; 20 &)
% ( 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 : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 239 ( 11 sgn 84 !; 4 ?)
% 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(t78,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)],[t78]) ).
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]) ).
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(t103,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)],[t103]) ).
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] :
( ( test(X0)
& test(X1) )
=> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1] :
( multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) != zero
& test(X0)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( multiplication(multiplication(addition(sk1,sk2),c(sk1)),c(sk2)) != zero
& test(sk1)
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f16_nnf]) ).
cnf(c23,plain,
test(sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi23,negated_conjecture,
test(sk1) = 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(sk1,addition(c(sk1),c(sk1))) = 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(t47,plain,
multiplication(addition(c(sk1),c(sk1)),sk1) = 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(t89959,plain,
multiplication(c(sk1),sk1) = zero,
inference(step,[status(thm)],[t47,t256]) ).
cnf(t334,plain,
multiplication(c(sk1),sk1) = zero,
inference(orient,[status(thm)],[t89959]) ).
cnf(t336,plain,
multiplication(c(sk1),addition(X1,sk1)) = addition(multiplication(c(sk1),X1),zero),
inference(cp,[status(thm)],[t326,t334]) ).
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(t90195,plain,
multiplication(c(sk1),addition(X1,sk1)) = multiplication(c(sk1),X1),
inference(step,[status(thm)],[t336,t257]) ).
cnf(t2710,plain,
multiplication(c(sk1),addition(X1,sk1)) = multiplication(c(sk1),X1),
inference(orient,[status(thm)],[t90195]) ).
cnf(t2712,plain,
multiplication(c(sk1),X1) = multiplication(c(sk1),addition(sk1,X1)),
inference(cp,[status(thm)],[t2710,t268]) ).
cnf(t3134,plain,
multiplication(c(sk1),addition(sk1,X1)) = multiplication(c(sk1),X1),
inference(orient,[status(thm)],[t2712]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t73,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t616,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t73]) ).
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(t77,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t567,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t77]) ).
cnf(t0,plain,
test(sk1) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t447,plain,
test(sk1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t569,plain,
true = ifeq(true,true,complement(sk0(sk1),sk1),true),
inference(cp,[status(thm)],[t567,t447]) ).
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(t90057,plain,
true = complement(sk0(sk1),sk1),
inference(step,[status(thm)],[t569,t262]) ).
cnf(t673,plain,
complement(sk0(sk1),sk1) = true,
inference(orient,[status(thm)],[t90057]) ).
cnf(t674,plain,
one = ifeq(true,true,addition(sk1,sk0(sk1)),one),
inference(cp,[status(thm)],[t616,t673]) ).
cnf(t90065,plain,
one = addition(sk1,sk0(sk1)),
inference(step,[status(thm)],[t674,t262]) ).
cnf(t714,plain,
addition(sk1,sk0(sk1)) = one,
inference(orient,[status(thm)],[t90065]) ).
cnf(t3141,plain,
multiplication(c(sk1),sk0(sk1)) = multiplication(c(sk1),one),
inference(cp,[status(thm)],[t3134,t714]) ).
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(t104,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)],[t104]) ).
cnf(t75,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t396,plain,
ifeq(complement(X1,X2),true,multiplication(X2,X1),zero) = zero,
inference(orient,[status(thm)],[t75]) ).
cnf(t676,plain,
zero = ifeq(true,true,multiplication(sk1,sk0(sk1)),zero),
inference(cp,[status(thm)],[t396,t673]) ).
cnf(t90067,plain,
zero = multiplication(sk1,sk0(sk1)),
inference(step,[status(thm)],[t676,t262]) ).
cnf(t728,plain,
multiplication(sk1,sk0(sk1)) = zero,
inference(orient,[status(thm)],[t90067]) ).
cnf(t733,plain,
multiplication(addition(sk1,X1),sk0(sk1)) = addition(zero,multiplication(X1,sk0(sk1))),
inference(cp,[status(thm)],[t320,t728]) ).
cnf(t269,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t268,t257]) ).
cnf(t643,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t269]) ).
cnf(t90216,plain,
multiplication(addition(sk1,X1),sk0(sk1)) = multiplication(X1,sk0(sk1)),
inference(step,[status(thm)],[t733,t643]) ).
cnf(t2988,plain,
multiplication(addition(sk1,X1),sk0(sk1)) = multiplication(X1,sk0(sk1)),
inference(orient,[status(thm)],[t90216]) ).
cnf(hi2,axiom,
addition(X0,zero) = X0,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t23,plain,
complement(sk1,addition(c(sk1),zero)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23,hi2]) ).
cnf(t90012,plain,
complement(sk1,c(sk1)) = true,
inference(step,[status(thm)],[t23,t257]) ).
cnf(t459,plain,
complement(sk1,c(sk1)) = true,
inference(orient,[status(thm)],[t90012]) ).
cnf(t620,plain,
one = ifeq(true,true,addition(c(sk1),sk1),one),
inference(cp,[status(thm)],[t616,t459]) ).
cnf(t90060,plain,
one = addition(c(sk1),sk1),
inference(step,[status(thm)],[t620,t262]) ).
cnf(t90061,plain,
one = addition(sk1,c(sk1)),
inference(step,[status(thm)],[t90060,t268]) ).
cnf(t686,plain,
addition(sk1,c(sk1)) = one,
inference(orient,[status(thm)],[t90061]) ).
cnf(t2994,plain,
multiplication(c(sk1),sk0(sk1)) = multiplication(one,sk0(sk1)),
inference(cp,[status(thm)],[t2988,t686]) ).
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(t90217,plain,
multiplication(c(sk1),sk0(sk1)) = sk0(sk1),
inference(step,[status(thm)],[t2994,t261]) ).
cnf(t3010,plain,
multiplication(c(sk1),sk0(sk1)) = sk0(sk1),
inference(orient,[status(thm)],[t90217]) ).
cnf(t90219,plain,
sk0(sk1) = multiplication(c(sk1),one),
inference(step,[status(thm)],[t3141,t3010]) ).
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(t90220,plain,
sk0(sk1) = c(sk1),
inference(step,[status(thm)],[t90219,t260]) ).
cnf(t3155,plain,
c(sk1) = sk0(sk1),
inference(orient,[status(thm)],[t90220]) ).
cnf(t729,plain,
multiplication(sk1,multiplication(sk0(sk1),X1)) = multiplication(zero,X1),
inference(cp,[status(thm)],[t596,t728]) ).
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(t344,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t8]) ).
cnf(t90118,plain,
multiplication(sk1,multiplication(sk0(sk1),X1)) = zero,
inference(step,[status(thm)],[t729,t344]) ).
cnf(t1030,plain,
multiplication(sk1,multiplication(sk0(sk1),X1)) = zero,
inference(orient,[status(thm)],[t90118]) ).
cnf(t1036,plain,
multiplication(addition(X1,sk1),multiplication(sk0(sk1),X2)) = addition(multiplication(X1,multiplication(sk0(sk1),X2)),zero),
inference(cp,[status(thm)],[t320,t1030]) ).
cnf(t91491,plain,
multiplication(addition(X1,sk1),multiplication(sk0(sk1),X2)) = multiplication(X1,multiplication(sk0(sk1),X2)),
inference(step,[status(thm)],[t1036,t257]) ).
cnf(t89820,plain,
multiplication(addition(X1,sk1),multiplication(sk0(sk1),X2)) = multiplication(X1,multiplication(sk0(sk1),X2)),
inference(orient,[status(thm)],[t91491]) ).
cnf(c22,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
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(t48,plain,
multiplication(addition(c(sk2),c(sk2)),sk2) = zero,
inference(hyper_resolution,[status(thm)],[hi15,h7]) ).
cnf(t89960,plain,
multiplication(c(sk2),sk2) = zero,
inference(step,[status(thm)],[t48,t256]) ).
cnf(t339,plain,
multiplication(c(sk2),sk2) = zero,
inference(orient,[status(thm)],[t89960]) ).
cnf(t341,plain,
multiplication(c(sk2),addition(X1,sk2)) = addition(multiplication(c(sk2),X1),zero),
inference(cp,[status(thm)],[t326,t339]) ).
cnf(t90196,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(step,[status(thm)],[t341,t257]) ).
cnf(t2724,plain,
multiplication(c(sk2),addition(X1,sk2)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t90196]) ).
cnf(t2726,plain,
multiplication(c(sk2),X1) = multiplication(c(sk2),addition(sk2,X1)),
inference(cp,[status(thm)],[t2724,t268]) ).
cnf(t3329,plain,
multiplication(c(sk2),addition(sk2,X1)) = multiplication(c(sk2),X1),
inference(orient,[status(thm)],[t2726]) ).
cnf(t1,plain,
test(sk2) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t449,plain,
test(sk2) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t568,plain,
true = ifeq(true,true,complement(sk0(sk2),sk2),true),
inference(cp,[status(thm)],[t567,t449]) ).
cnf(t90056,plain,
true = complement(sk0(sk2),sk2),
inference(step,[status(thm)],[t568,t262]) ).
cnf(t666,plain,
complement(sk0(sk2),sk2) = true,
inference(orient,[status(thm)],[t90056]) ).
cnf(t667,plain,
one = ifeq(true,true,addition(sk2,sk0(sk2)),one),
inference(cp,[status(thm)],[t616,t666]) ).
cnf(t90062,plain,
one = addition(sk2,sk0(sk2)),
inference(step,[status(thm)],[t667,t262]) ).
cnf(t692,plain,
addition(sk2,sk0(sk2)) = one,
inference(orient,[status(thm)],[t90062]) ).
cnf(t3336,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(c(sk2),one),
inference(cp,[status(thm)],[t3329,t692]) ).
cnf(t669,plain,
zero = ifeq(true,true,multiplication(sk2,sk0(sk2)),zero),
inference(cp,[status(thm)],[t396,t666]) ).
cnf(t90064,plain,
zero = multiplication(sk2,sk0(sk2)),
inference(step,[status(thm)],[t669,t262]) ).
cnf(t706,plain,
multiplication(sk2,sk0(sk2)) = zero,
inference(orient,[status(thm)],[t90064]) ).
cnf(t711,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = addition(zero,multiplication(X1,sk0(sk2))),
inference(cp,[status(thm)],[t320,t706]) ).
cnf(t90206,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(step,[status(thm)],[t711,t643]) ).
cnf(t2854,plain,
multiplication(addition(sk2,X1),sk0(sk2)) = multiplication(X1,sk0(sk2)),
inference(orient,[status(thm)],[t90206]) ).
cnf(t24,plain,
complement(sk2,addition(c(sk2),zero)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi22,hi2]) ).
cnf(t90013,plain,
complement(sk2,c(sk2)) = true,
inference(step,[status(thm)],[t24,t257]) ).
cnf(t460,plain,
complement(sk2,c(sk2)) = true,
inference(orient,[status(thm)],[t90013]) ).
cnf(t619,plain,
one = ifeq(true,true,addition(c(sk2),sk2),one),
inference(cp,[status(thm)],[t616,t460]) ).
cnf(t90058,plain,
one = addition(c(sk2),sk2),
inference(step,[status(thm)],[t619,t262]) ).
cnf(t90059,plain,
one = addition(sk2,c(sk2)),
inference(step,[status(thm)],[t90058,t268]) ).
cnf(t680,plain,
addition(sk2,c(sk2)) = one,
inference(orient,[status(thm)],[t90059]) ).
cnf(t2860,plain,
multiplication(c(sk2),sk0(sk2)) = multiplication(one,sk0(sk2)),
inference(cp,[status(thm)],[t2854,t680]) ).
cnf(t90207,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(step,[status(thm)],[t2860,t261]) ).
cnf(t2876,plain,
multiplication(c(sk2),sk0(sk2)) = sk0(sk2),
inference(orient,[status(thm)],[t90207]) ).
cnf(t90242,plain,
sk0(sk2) = multiplication(c(sk2),one),
inference(step,[status(thm)],[t3336,t2876]) ).
cnf(t90243,plain,
sk0(sk2) = c(sk2),
inference(step,[status(thm)],[t90242,t260]) ).
cnf(t3350,plain,
c(sk2) = sk0(sk2),
inference(orient,[status(thm)],[t90243]) ).
cnf(t343,plain,
multiplication(addition(X1,c(sk2)),sk2) = addition(multiplication(X1,sk2),zero),
inference(cp,[status(thm)],[t320,t339]) ).
cnf(t90129,plain,
multiplication(addition(X1,c(sk2)),sk2) = multiplication(X1,sk2),
inference(step,[status(thm)],[t343,t257]) ).
cnf(t1284,plain,
multiplication(addition(X1,c(sk2)),sk2) = multiplication(X1,sk2),
inference(orient,[status(thm)],[t90129]) ).
cnf(t1285,plain,
multiplication(sk2,sk2) = multiplication(one,sk2),
inference(cp,[status(thm)],[t1284,t680]) ).
cnf(t90130,plain,
multiplication(sk2,sk2) = sk2,
inference(step,[status(thm)],[t1285,t261]) ).
cnf(t1299,plain,
multiplication(sk2,sk2) = sk2,
inference(orient,[status(thm)],[t90130]) ).
cnf(t1305,plain,
multiplication(sk2,addition(sk2,X1)) = addition(sk2,multiplication(sk2,X1)),
inference(cp,[status(thm)],[t326,t1299]) ).
cnf(t328,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t326,t260]) ).
cnf(t1061,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t328]) ).
cnf(t90131,plain,
multiplication(sk2,addition(sk2,X1)) = multiplication(sk2,addition(one,X1)),
inference(step,[status(thm)],[t1305,t1061]) ).
cnf(t1322,plain,
multiplication(sk2,addition(one,X1)) = multiplication(sk2,addition(sk2,X1)),
inference(orient,[status(thm)],[t90131]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t76,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)],[t76]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t72,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t482,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t72]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t71,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t271,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t71]) ).
cnf(t274,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t271,t256]) ).
cnf(t748,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t274]) ).
cnf(t758,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t482,t748]) ).
cnf(t90088,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t758,t262]) ).
cnf(t775,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t90088]) ).
cnf(t779,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t775,t268]) ).
cnf(t780,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t779]) ).
cnf(t782,plain,
true = leq(sk0(sk1),one),
inference(cp,[status(thm)],[t780,t714]) ).
cnf(t793,plain,
leq(sk0(sk1),one) = true,
inference(orient,[status(thm)],[t782]) ).
cnf(t794,plain,
one = ifeq(true,true,addition(sk0(sk1),one),one),
inference(cp,[status(thm)],[t264,t793]) ).
cnf(t90091,plain,
one = addition(sk0(sk1),one),
inference(step,[status(thm)],[t794,t262]) ).
cnf(t90092,plain,
one = addition(one,sk0(sk1)),
inference(step,[status(thm)],[t90091,t268]) ).
cnf(t808,plain,
addition(one,sk0(sk1)) = one,
inference(orient,[status(thm)],[t90092]) ).
cnf(t1327,plain,
multiplication(sk2,addition(sk2,sk0(sk1))) = multiplication(sk2,one),
inference(cp,[status(thm)],[t1322,t808]) ).
cnf(t90132,plain,
multiplication(sk2,addition(sk2,sk0(sk1))) = sk2,
inference(step,[status(thm)],[t1327,t260]) ).
cnf(t1340,plain,
multiplication(sk2,addition(sk2,sk0(sk1))) = sk2,
inference(orient,[status(thm)],[t90132]) ).
cnf(t1342,plain,
multiplication(sk2,multiplication(addition(sk2,sk0(sk1)),X1)) = multiplication(sk2,X1),
inference(cp,[status(thm)],[t596,t1340]) ).
cnf(t6097,plain,
multiplication(sk2,multiplication(addition(sk2,sk0(sk1)),X1)) = multiplication(sk2,X1),
inference(orient,[status(thm)],[t1342]) ).
cnf(t6098,plain,
multiplication(sk2,sk0(sk2)) = multiplication(sk2,multiplication(sk0(sk1),sk0(sk2))),
inference(cp,[status(thm)],[t6097,t2854]) ).
cnf(t90372,plain,
zero = multiplication(sk2,multiplication(sk0(sk1),sk0(sk2))),
inference(step,[status(thm)],[t6098,t706]) ).
cnf(t6116,plain,
multiplication(sk2,multiplication(sk0(sk1),sk0(sk2))) = zero,
inference(orient,[status(thm)],[t90372]) ).
cnf(c24,plain,
multiplication(multiplication(addition(sk1,sk2),c(sk1)),c(sk2)) != zero,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(multiplication(addition(sk1,sk2),c(sk1)),c(sk2)) != zero,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(g0_0,plain,
multiplication(addition(sk1,sk2),multiplication(c(sk1),c(sk2))) != zero,
inference(rw,[status(thm)],[goal_0,t596]) ).
cnf(g0_1,plain,
multiplication(addition(sk2,sk1),multiplication(c(sk1),c(sk2))) != zero,
inference(rw,[status(thm)],[g0_0,t268]) ).
cnf(g0_2,plain,
multiplication(addition(sk2,sk1),multiplication(sk0(sk1),c(sk2))) != zero,
inference(rw,[status(thm)],[g0_1,t3155]) ).
cnf(g0_3,plain,
multiplication(sk2,multiplication(sk0(sk1),c(sk2))) != zero,
inference(rw,[status(thm)],[g0_2,t89820]) ).
cnf(g0_4,plain,
multiplication(sk2,multiplication(sk0(sk1),sk0(sk2))) != zero,
inference(rw,[status(thm)],[g0_3,t3350]) ).
cnf(g0_5,plain,
zero != zero,
inference(rw,[status(thm)],[g0_4,t6116]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE015+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 18:39:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 120.65/16.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 120.65/16.65 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------