%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:51:26 PM UTC 2026
% Result : Theorem 65.33s 24.97s
% Output : Proof 65.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 15
% Syntax : Number of formulae : 158 ( 136 unt; 0 def)
% Number of atoms : 222 ( 161 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 104 ( 40 ~; 29 |; 28 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 181 ( 4 sgn 73 !; 6 ?)
% 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(t127,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t433,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t127]) ).
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(t15,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t291,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t15]) ).
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(t154,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t385,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t154]) ).
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(f18,conjecture,
! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0,X1,X2,X3] :
( ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( ~ leq(multiplication(multiplication(sk3,addition(sk1,sk2)),c(sk4)),zero)
& leq(multiplication(multiplication(sk3,sk2),c(sk4)),zero)
& leq(multiplication(multiplication(sk3,sk1),c(sk4)),zero)
& test(sk3)
& test(sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4])],[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(hi32,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h26,plain,
complement(sk4,or(c(sk4),false)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi24,hi32]) ).
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(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(t73,plain,
multiplication(sk4,or(c(sk4),false)) = zero,
inference(hyper_resolution,[status(thm)],[hi16,h26]) ).
cnf(t11,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t105298,plain,
multiplication(sk4,c(sk4)) = zero,
inference(step,[status(thm)],[t73,t256]) ).
cnf(t494,plain,
multiplication(sk4,c(sk4)) = zero,
inference(orient,[status(thm)],[t105298]) ).
cnf(t499,plain,
multiplication(addition(X1,sk4),c(sk4)) = addition(multiplication(X1,c(sk4)),zero),
inference(cp,[status(thm)],[t385,t494]) ).
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(t259,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t105530,plain,
multiplication(addition(X1,sk4),c(sk4)) = multiplication(X1,c(sk4)),
inference(step,[status(thm)],[t499,t259]) ).
cnf(t3431,plain,
multiplication(addition(X1,sk4),c(sk4)) = multiplication(X1,c(sk4)),
inference(orient,[status(thm)],[t105530]) ).
cnf(t3433,plain,
multiplication(X1,c(sk4)) = multiplication(addition(sk4,X1),c(sk4)),
inference(cp,[status(thm)],[t3431,t291]) ).
cnf(t4213,plain,
multiplication(addition(sk4,X1),c(sk4)) = multiplication(X1,c(sk4)),
inference(orient,[status(thm)],[t3433]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t122,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t790,plain,
ifeq(complement(X1,X2),true,addition(X2,X1),one) = one,
inference(orient,[status(thm)],[t122]) ).
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(t126,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t731,plain,
ifeq(test(X1),true,complement(sk0(X1),X1),true) = true,
inference(orient,[status(thm)],[t126]) ).
cnf(t1,plain,
test(sk4) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t588,plain,
test(sk4) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t735,plain,
true = ifeq(true,true,complement(sk0(sk4),sk4),true),
inference(cp,[status(thm)],[t731,t588]) ).
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(t105374,plain,
true = complement(sk0(sk4),sk4),
inference(step,[status(thm)],[t735,t262]) ).
cnf(t879,plain,
complement(sk0(sk4),sk4) = true,
inference(orient,[status(thm)],[t105374]) ).
cnf(t880,plain,
one = ifeq(true,true,addition(sk4,sk0(sk4)),one),
inference(cp,[status(thm)],[t790,t879]) ).
cnf(t105378,plain,
one = addition(sk4,sk0(sk4)),
inference(step,[status(thm)],[t880,t262]) ).
cnf(t914,plain,
addition(sk4,sk0(sk4)) = one,
inference(orient,[status(thm)],[t105378]) ).
cnf(t4221,plain,
multiplication(sk0(sk4),c(sk4)) = multiplication(one,c(sk4)),
inference(cp,[status(thm)],[t4213,t914]) ).
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(t153,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t403,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t153]) ).
cnf(t123,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t772,plain,
ifeq(complement(X1,X2),true,multiplication(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t123]) ).
cnf(t881,plain,
zero = ifeq(true,true,multiplication(sk0(sk4),sk4),zero),
inference(cp,[status(thm)],[t772,t879]) ).
cnf(t105379,plain,
zero = multiplication(sk0(sk4),sk4),
inference(step,[status(thm)],[t881,t262]) ).
cnf(t920,plain,
multiplication(sk0(sk4),sk4) = zero,
inference(orient,[status(thm)],[t105379]) ).
cnf(t923,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = addition(zero,multiplication(sk0(sk4),X1)),
inference(cp,[status(thm)],[t403,t920]) ).
cnf(t298,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t291,t259]) ).
cnf(t818,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t298]) ).
cnf(t105543,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = multiplication(sk0(sk4),X1),
inference(step,[status(thm)],[t923,t818]) ).
cnf(t3621,plain,
multiplication(sk0(sk4),addition(sk4,X1)) = multiplication(sk0(sk4),X1),
inference(orient,[status(thm)],[t105543]) ).
cnf(hi17,axiom,
ifeq(complement(X0,X1),true,addition(X1,X0),one) = one,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t37,plain,
addition(or(c(sk4),false),sk4) = one,
inference(hyper_resolution,[status(thm)],[hi17,h26]) ).
cnf(t105253,plain,
addition(sk4,or(c(sk4),false)) = one,
inference(step,[status(thm)],[t37,t291]) ).
cnf(t105254,plain,
addition(sk4,c(sk4)) = one,
inference(step,[status(thm)],[t105253,t256]) ).
cnf(t339,plain,
addition(sk4,c(sk4)) = one,
inference(orient,[status(thm)],[t105254]) ).
cnf(t3627,plain,
multiplication(sk0(sk4),c(sk4)) = multiplication(sk0(sk4),one),
inference(cp,[status(thm)],[t3621,t339]) ).
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(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(t105544,plain,
multiplication(sk0(sk4),c(sk4)) = sk0(sk4),
inference(step,[status(thm)],[t3627,t260]) ).
cnf(t3645,plain,
multiplication(sk0(sk4),c(sk4)) = sk0(sk4),
inference(orient,[status(thm)],[t105544]) ).
cnf(t105616,plain,
sk0(sk4) = multiplication(one,c(sk4)),
inference(step,[status(thm)],[t4221,t3645]) ).
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(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(t105617,plain,
sk0(sk4) = c(sk4),
inference(step,[status(thm)],[t105616,t261]) ).
cnf(t4235,plain,
c(sk4) = sk0(sk4),
inference(orient,[status(thm)],[t105617]) ).
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(hi11,axiom,
ifeq(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(c26,plain,
leq(multiplication(multiplication(sk3,sk1),c(sk4)),zero),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi26,negated_conjecture,
leq(multiplication(multiplication(sk3,sk1),c(sk4)),zero) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t90,plain,
addition(multiplication(multiplication(sk3,sk1),c(sk4)),zero) = zero,
inference(hyper_resolution,[status(thm)],[hi11,hi26]) ).
cnf(t105293,plain,
multiplication(multiplication(sk3,sk1),c(sk4)) = zero,
inference(step,[status(thm)],[t90,t259]) ).
cnf(t421,plain,
multiplication(multiplication(sk3,sk1),c(sk4)) = zero,
inference(orient,[status(thm)],[t105293]) ).
cnf(t105296,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(step,[status(thm)],[t421,t433]) ).
cnf(t444,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(rw,[status(thm)],[t105296]) ).
cnf(t1168,plain,
multiplication(sk3,multiplication(sk1,c(sk4))) = zero,
inference(orient,[status(thm)],[t444]) ).
cnf(t105642,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(step,[status(thm)],[t1168,t4235]) ).
cnf(t4269,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(rw,[status(thm)],[t105642]) ).
cnf(t4385,plain,
multiplication(sk3,multiplication(sk1,sk0(sk4))) = zero,
inference(orient,[status(thm)],[t4269]) ).
cnf(t4392,plain,
multiplication(sk3,addition(X1,multiplication(sk1,sk0(sk4)))) = addition(multiplication(sk3,X1),zero),
inference(cp,[status(thm)],[t403,t4385]) ).
cnf(t105899,plain,
multiplication(sk3,addition(X1,multiplication(sk1,sk0(sk4)))) = multiplication(sk3,X1),
inference(step,[status(thm)],[t4392,t259]) ).
cnf(t8829,plain,
multiplication(sk3,addition(X1,multiplication(sk1,sk0(sk4)))) = multiplication(sk3,X1),
inference(orient,[status(thm)],[t105899]) ).
cnf(t8831,plain,
multiplication(sk3,multiplication(X1,sk0(sk4))) = multiplication(sk3,multiplication(addition(X1,sk1),sk0(sk4))),
inference(cp,[status(thm)],[t8829,t385]) ).
cnf(t105090,plain,
multiplication(sk3,multiplication(addition(X1,sk1),sk0(sk4))) = multiplication(sk3,multiplication(X1,sk0(sk4))),
inference(orient,[status(thm)],[t8831]) ).
cnf(c27,plain,
leq(multiplication(multiplication(sk3,sk2),c(sk4)),zero),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi27,negated_conjecture,
leq(multiplication(multiplication(sk3,sk2),c(sk4)),zero) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t91,plain,
addition(multiplication(multiplication(sk3,sk2),c(sk4)),zero) = zero,
inference(hyper_resolution,[status(thm)],[hi11,hi27]) ).
cnf(t105294,plain,
multiplication(multiplication(sk3,sk2),c(sk4)) = zero,
inference(step,[status(thm)],[t91,t259]) ).
cnf(t427,plain,
multiplication(multiplication(sk3,sk2),c(sk4)) = zero,
inference(orient,[status(thm)],[t105294]) ).
cnf(t105295,plain,
multiplication(sk3,multiplication(sk2,c(sk4))) = zero,
inference(step,[status(thm)],[t427,t433]) ).
cnf(t443,plain,
multiplication(sk3,multiplication(sk2,c(sk4))) = zero,
inference(rw,[status(thm)],[t105295]) ).
cnf(t1157,plain,
multiplication(sk3,multiplication(sk2,c(sk4))) = zero,
inference(orient,[status(thm)],[t443]) ).
cnf(t105643,plain,
multiplication(sk3,multiplication(sk2,sk0(sk4))) = zero,
inference(step,[status(thm)],[t1157,t4235]) ).
cnf(t4270,plain,
multiplication(sk3,multiplication(sk2,sk0(sk4))) = zero,
inference(rw,[status(thm)],[t105643]) ).
cnf(t4501,plain,
multiplication(sk3,multiplication(sk2,sk0(sk4))) = zero,
inference(orient,[status(thm)],[t4270]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t121,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t633,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t121]) ).
cnf(t821,plain,
true = ifeq(X1,X1,leq(zero,X1),true),
inference(cp,[status(thm)],[t633,t818]) ).
cnf(t105346,plain,
true = leq(zero,X1),
inference(step,[status(thm)],[t821,t262]) ).
cnf(t828,plain,
leq(zero,X1) = true,
inference(orient,[status(thm)],[t105346]) ).
cnf(c28,plain,
~ leq(multiplication(multiplication(sk3,addition(sk1,sk2)),c(sk4)),zero),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
leq(multiplication(multiplication(sk3,addition(sk1,sk2)),c(sk4)),zero) != true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(g0_0,plain,
leq(multiplication(sk3,multiplication(addition(sk1,sk2),c(sk4))),zero) != true,
inference(rw,[status(thm)],[goal_0,t433]) ).
cnf(g0_1,plain,
leq(multiplication(sk3,multiplication(addition(sk2,sk1),c(sk4))),zero) != true,
inference(rw,[status(thm)],[g0_0,t291]) ).
cnf(g0_2,plain,
leq(multiplication(sk3,multiplication(addition(sk2,sk1),sk0(sk4))),zero) != true,
inference(rw,[status(thm)],[g0_1,t4235]) ).
cnf(g0_3,plain,
leq(multiplication(sk3,multiplication(sk2,sk0(sk4))),zero) != true,
inference(rw,[status(thm)],[g0_2,t105090]) ).
cnf(g0_4,plain,
leq(zero,zero) != true,
inference(rw,[status(thm)],[g0_3,t4501]) ).
cnf(g0_5,plain,
true != true,
inference(rw,[status(thm)],[g0_4,t828]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/15.95 % Computer : n012.cluster.edu
% 0.04/15.95 % Model : x86_64 x86_64
% 0.04/15.95 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.95 % Memory : 8046.5625MB
% 0.04/15.95 % OS : Linux 6.8.0-71-generic
% 0.04/15.95 % CPULimit : 300
% 0.04/15.95 % WCLimit : 300
% 0.04/15.95 % DateTime : Wed Sep 23 18:43:33 UTC 2026
% 0.04/15.95 % CPUTime :
% 0.04/15.95 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 65.33/24.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.33/24.97 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------