%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE082+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:51:34 PM UTC 2026
% Result : Theorem 5.16s 1.10s
% Output : Proof 5.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 15
% Syntax : Number of formulae : 194 ( 185 unt; 0 def)
% Number of atoms : 211 ( 203 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 14 ~; 6 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 308 ( 40 sgn 77 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f7_nnf,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t22,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t33,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t22]) ).
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(t4,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t24,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t34,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t33,t24]) ).
cnf(t326,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t34]) ).
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(t23,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t40,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t23]) ).
fof(f17,conjecture,
! [X0,X1] :
( ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0,X1] :
( addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) != antidomain(multiplication(X0,domain(X1)))
& ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one ) ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
! [X2] :
( addition(antidomain(multiplication(sk0,sk1)),antidomain(multiplication(sk0,domain(sk1)))) != antidomain(multiplication(sk0,domain(sk1)))
& multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f17_nnf]) ).
cnf(c19,plain,
multiplication(domain(X2),antidomain(X2)) = zero,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t13,plain,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t49,plain,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(orient,[status(thm)],[t13]) ).
cnf(t51,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = addition(multiplication(X1,antidomain(X2)),zero),
inference(cp,[status(thm)],[t40,t49]) ).
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(t2,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t27,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t4602,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(step,[status(thm)],[t51,t27]) ).
cnf(t2226,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(orient,[status(thm)],[t4602]) ).
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(t10,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t57,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t2230,plain,
multiplication(X1,antidomain(X2)) = multiplication(addition(domain(X2),X1),antidomain(X2)),
inference(cp,[status(thm)],[t2226,t57]) ).
cnf(t4002,plain,
multiplication(addition(domain(X1),X2),antidomain(X1)) = multiplication(X2,antidomain(X1)),
inference(orient,[status(thm)],[t2230]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t18,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t62,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
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(t1,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t26,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t66,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t62,t26]) ).
cnf(t153,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t66]) ).
cnf(t157,plain,
addition(X1,X2) = addition(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t153,t57]) ).
cnf(t181,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(orient,[status(thm)],[t157]) ).
cnf(c18,plain,
addition(domain(X2),antidomain(X2)) = one,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t11,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t80,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(orient,[status(thm)],[t11]) ).
cnf(t82,plain,
addition(domain(X1),addition(antidomain(X1),X2)) = addition(one,X2),
inference(cp,[status(thm)],[t62,t80]) ).
cnf(t1022,plain,
addition(domain(X1),addition(antidomain(X1),X2)) = addition(one,X2),
inference(orient,[status(thm)],[t82]) ).
cnf(t1039,plain,
addition(addition(antidomain(X1),X2),domain(X1)) = addition(addition(antidomain(X1),X2),addition(one,X2)),
inference(cp,[status(thm)],[t181,t1022]) ).
cnf(t4574,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(addition(antidomain(X1),X2),addition(one,X2)),
inference(step,[status(thm)],[t1039,t62]) ).
cnf(t4575,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(antidomain(X1),addition(X2,addition(one,X2))),
inference(step,[status(thm)],[t4574,t62]) ).
cnf(t4576,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(antidomain(X1),addition(X2,one)),
inference(step,[status(thm)],[t4575,t181]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t20,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t29,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t19,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t102,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t159,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t102,t153]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t4531,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t159,t28]) ).
cnf(t160,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t4531]) ).
cnf(t165,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t160,t57]) ).
cnf(t166,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t165]) ).
cnf(t169,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t166,t62]) ).
cnf(t464,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t169]) ).
cnf(t168,plain,
true = leq(antidomain(X1),one),
inference(cp,[status(thm)],[t166,t80]) ).
cnf(t174,plain,
leq(antidomain(X1),one) = true,
inference(orient,[status(thm)],[t168]) ).
cnf(t175,plain,
one = ifeq(true,true,addition(antidomain(X1),one),one),
inference(cp,[status(thm)],[t29,t174]) ).
cnf(t4532,plain,
one = addition(antidomain(X1),one),
inference(step,[status(thm)],[t175,t28]) ).
cnf(t4533,plain,
one = addition(one,antidomain(X1)),
inference(step,[status(thm)],[t4532,t57]) ).
cnf(t177,plain,
addition(one,antidomain(X1)) = one,
inference(orient,[status(thm)],[t4533]) ).
cnf(t477,plain,
true = leq(antidomain(X1),addition(X2,one)),
inference(cp,[status(thm)],[t464,t177]) ).
cnf(t499,plain,
leq(antidomain(X1),addition(X2,one)) = true,
inference(orient,[status(thm)],[t477]) ).
cnf(t501,plain,
addition(X1,one) = ifeq(true,true,addition(antidomain(X2),addition(X1,one)),addition(X1,one)),
inference(cp,[status(thm)],[t29,t499]) ).
cnf(t4554,plain,
addition(X1,one) = addition(antidomain(X2),addition(X1,one)),
inference(step,[status(thm)],[t501,t28]) ).
cnf(t530,plain,
addition(antidomain(X1),addition(X2,one)) = addition(X2,one),
inference(orient,[status(thm)],[t4554]) ).
cnf(t4577,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(X2,one),
inference(step,[status(thm)],[t4576,t530]) ).
cnf(t1070,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(X2,one),
inference(orient,[status(thm)],[t4577]) ).
fof(f16,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain5) ).
fof(f16_nnf,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c17,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t15,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t73,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t15]) ).
cnf(t1077,plain,
addition(domain(X1),one) = addition(antidomain(X2),domain(addition(X1,X2))),
inference(cp,[status(thm)],[t1070,t73]) ).
cnf(t4614,plain,
addition(one,domain(X1)) = addition(antidomain(X2),domain(addition(X1,X2))),
inference(step,[status(thm)],[t1077,t57]) ).
fof(f14,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f14_nnf,plain,
! [X0] : addition(domain(X0),one) = one,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0] : addition(domain(X0),one) = one,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t8,plain,
addition(domain(X1),one) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t4521,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t8,t57]) ).
cnf(t77,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t4521]) ).
cnf(t4615,plain,
one = addition(antidomain(X2),domain(addition(X1,X2))),
inference(step,[status(thm)],[t4614,t77]) ).
cnf(t2585,plain,
addition(antidomain(X1),domain(addition(X2,X1))) = one,
inference(orient,[status(thm)],[t4615]) ).
cnf(t2616,plain,
one = addition(antidomain(multiplication(X1,X2)),domain(multiplication(X1,addition(one,X2)))),
inference(cp,[status(thm)],[t2585,t326]) ).
fof(f13,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f13_nnf,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t16,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t83,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t16]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f12,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f12_nnf,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi13,axiom,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t14,plain,
leq(X1,multiplication(domain(X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi13]) ).
cnf(t96,plain,
leq(X1,multiplication(domain(X1),X1)) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t97,plain,
true = leq(one,domain(one)),
inference(cp,[status(thm)],[t96,t24]) ).
cnf(t125,plain,
leq(one,domain(one)) = true,
inference(orient,[status(thm)],[t97]) ).
cnf(t126,plain,
domain(one) = ifeq(true,true,addition(one,domain(one)),domain(one)),
inference(cp,[status(thm)],[t29,t125]) ).
cnf(t4525,plain,
domain(one) = addition(one,domain(one)),
inference(step,[status(thm)],[t126,t28]) ).
cnf(t4526,plain,
domain(one) = one,
inference(step,[status(thm)],[t4525,t77]) ).
cnf(t128,plain,
domain(one) = one,
inference(orient,[status(thm)],[t4526]) ).
cnf(t130,plain,
domain(addition(one,X1)) = addition(one,domain(X1)),
inference(cp,[status(thm)],[t73,t128]) ).
cnf(t4528,plain,
domain(addition(one,X1)) = one,
inference(step,[status(thm)],[t130,t77]) ).
cnf(t134,plain,
domain(addition(one,X1)) = one,
inference(orient,[status(thm)],[t4528]) ).
cnf(t140,plain,
domain(multiplication(X1,addition(one,X2))) = domain(multiplication(X1,one)),
inference(cp,[status(thm)],[t83,t134]) ).
cnf(t4544,plain,
domain(multiplication(X1,addition(one,X2))) = domain(X1),
inference(step,[status(thm)],[t140,t24]) ).
cnf(t298,plain,
domain(multiplication(X1,addition(one,X2))) = domain(X1),
inference(orient,[status(thm)],[t4544]) ).
cnf(t4616,plain,
one = addition(antidomain(multiplication(X1,X2)),domain(X1)),
inference(step,[status(thm)],[t2616,t298]) ).
cnf(t4617,plain,
one = addition(domain(X1),antidomain(multiplication(X1,X2))),
inference(step,[status(thm)],[t4616,t57]) ).
cnf(t2651,plain,
addition(domain(X1),antidomain(multiplication(X1,X2))) = one,
inference(orient,[status(thm)],[t4617]) ).
cnf(t4004,plain,
multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)) = multiplication(one,antidomain(X1)),
inference(cp,[status(thm)],[t4002,t2651]) ).
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(t6,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t25,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t4646,plain,
multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)) = antidomain(X1),
inference(step,[status(thm)],[t4004,t25]) ).
cnf(t4274,plain,
multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t4646]) ).
cnf(t17,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t46,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(orient,[status(thm)],[t17]) ).
cnf(t42,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t40,t25]) ).
cnf(t336,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t42]) ).
cnf(t4546,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t46,t336]) ).
cnf(t4547,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t4546,t77]) ).
cnf(t4548,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t4547,t25]) ).
cnf(t348,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t4548]) ).
cnf(t349,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t348]) ).
cnf(t4288,plain,
antidomain(domain(X1)) = multiplication(antidomain(X1),antidomain(domain(X1))),
inference(cp,[status(thm)],[t4274,t349]) ).
cnf(t4320,plain,
multiplication(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
inference(orient,[status(thm)],[t4288]) ).
cnf(t4330,plain,
multiplication(antidomain(X1),addition(one,antidomain(domain(X1)))) = addition(antidomain(X1),antidomain(domain(X1))),
inference(cp,[status(thm)],[t326,t4320]) ).
cnf(t4647,plain,
multiplication(antidomain(X1),one) = addition(antidomain(X1),antidomain(domain(X1))),
inference(step,[status(thm)],[t4330,t177]) ).
cnf(t4648,plain,
antidomain(X1) = addition(antidomain(X1),antidomain(domain(X1))),
inference(step,[status(thm)],[t4647,t24]) ).
cnf(t85,plain,
domain(multiplication(one,X1)) = domain(domain(X1)),
inference(cp,[status(thm)],[t83,t25]) ).
cnf(t4523,plain,
domain(X1) = domain(domain(X1)),
inference(step,[status(thm)],[t85,t25]) ).
cnf(t117,plain,
domain(domain(X1)) = domain(X1),
inference(orient,[status(thm)],[t4523]) ).
cnf(t118,plain,
one = addition(domain(X1),antidomain(domain(X1))),
inference(cp,[status(thm)],[t80,t117]) ).
cnf(t190,plain,
addition(domain(X1),antidomain(domain(X1))) = one,
inference(orient,[status(thm)],[t118]) ).
cnf(t4010,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = multiplication(one,antidomain(X1)),
inference(cp,[status(thm)],[t4002,t190]) ).
cnf(t4642,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = antidomain(X1),
inference(step,[status(thm)],[t4010,t25]) ).
cnf(t4174,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t4642]) ).
cnf(t4187,plain,
multiplication(antidomain(domain(X1)),addition(one,antidomain(X1))) = addition(antidomain(domain(X1)),antidomain(X1)),
inference(cp,[status(thm)],[t326,t4174]) ).
cnf(t4643,plain,
multiplication(antidomain(domain(X1)),one) = addition(antidomain(domain(X1)),antidomain(X1)),
inference(step,[status(thm)],[t4187,t177]) ).
cnf(t4644,plain,
antidomain(domain(X1)) = addition(antidomain(domain(X1)),antidomain(X1)),
inference(step,[status(thm)],[t4643,t24]) ).
cnf(t4645,plain,
antidomain(domain(X1)) = addition(antidomain(X1),antidomain(domain(X1))),
inference(step,[status(thm)],[t4644,t57]) ).
cnf(t4208,plain,
addition(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
inference(orient,[status(thm)],[t4645]) ).
cnf(t4649,plain,
antidomain(X1) = antidomain(domain(X1)),
inference(step,[status(thm)],[t4648,t4208]) ).
cnf(t4353,plain,
antidomain(domain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t4649]) ).
cnf(t4361,plain,
antidomain(multiplication(X1,domain(X2))) = antidomain(domain(multiplication(X1,X2))),
inference(cp,[status(thm)],[t4353,t83]) ).
cnf(t4652,plain,
antidomain(multiplication(X1,domain(X2))) = antidomain(multiplication(X1,X2)),
inference(step,[status(thm)],[t4361,t4353]) ).
cnf(t4465,plain,
antidomain(multiplication(X1,domain(X2))) = antidomain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t4652]) ).
cnf(c20,plain,
addition(antidomain(multiplication(sk0,sk1)),antidomain(multiplication(sk0,domain(sk1)))) != antidomain(multiplication(sk0,domain(sk1))),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
addition(antidomain(multiplication(sk0,sk1)),antidomain(multiplication(sk0,domain(sk1)))) != antidomain(multiplication(sk0,domain(sk1))),
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
addition(antidomain(multiplication(sk0,sk1)),antidomain(multiplication(sk0,sk1))) != antidomain(multiplication(sk0,domain(sk1))),
inference(rw,[status(thm)],[goal_0,t4465]) ).
cnf(g0_1,plain,
antidomain(multiplication(sk0,sk1)) != antidomain(multiplication(sk0,domain(sk1))),
inference(rw,[status(thm)],[g0_0,t26]) ).
cnf(g0_2,plain,
antidomain(multiplication(sk0,sk1)) != antidomain(multiplication(sk0,sk1)),
inference(rw,[status(thm)],[g0_1,t4465]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE082+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Wed Sep 23 18:52:37 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.16/1.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/1.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------