%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE090+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 : n020.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 01:51:35 PM UTC 2026
% Result : Theorem 35.97s 5.10s
% Output : Proof 35.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 169 ( 160 unt; 0 def)
% Number of atoms : 182 ( 174 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 6 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 214 ( 20 sgn 70 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t24,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t51,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t24]) ).
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(t30,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t54,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t51,t30]) ).
cnf(t428,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t54]) ).
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(t23,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t38,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t23]) ).
fof(f12,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f12_nnf,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t14,plain,
multiplication(antidomain(X1),X1) = zero,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t59,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t14]) ).
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(t21,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t34,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f13,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f13_nnf,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi14,axiom,
addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t25,plain,
leq(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi14]) ).
fof(f15,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f15_nnf,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c16,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t11,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t119,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t19881,plain,
leq(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = true,
inference(step,[status(thm)],[t25,t119]) ).
cnf(t135,plain,
leq(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = true,
inference(orient,[status(thm)],[t19881]) ).
cnf(t64,plain,
multiplication(antidomain(X1),addition(X2,X1)) = addition(multiplication(antidomain(X1),X2),zero),
inference(cp,[status(thm)],[t38,t59]) ).
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(t1,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t32,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t20028,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(step,[status(thm)],[t64,t32]) ).
cnf(t2218,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(orient,[status(thm)],[t20028]) ).
cnf(t20,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t148,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t20]) ).
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(t19,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t73,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t19]) ).
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(t0,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t31,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t76,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t73,t31]) ).
cnf(t228,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t76]) ).
cnf(t235,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t148,t228]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t19899,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t235,t33]) ).
cnf(t244,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t19899]) ).
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(t68,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t15]) ).
cnf(t250,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t244,t68]) ).
cnf(t258,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t250]) ).
cnf(t261,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t258,t73]) ).
cnf(t1112,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t261]) ).
fof(f20,conjecture,
! [X0,X1] :
( addition(X0,X1) = X1
=> addition(antidomain(X1),antidomain(X0)) = antidomain(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20_neg,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> addition(antidomain(X1),antidomain(X0)) = antidomain(X0) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [X0,X1] :
( addition(antidomain(X1),antidomain(X0)) != antidomain(X0)
& addition(X0,X1) = X1 ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( addition(antidomain(sk1),antidomain(sk0)) != antidomain(sk0)
& addition(sk0,sk1) = sk1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f20_nnf]) ).
cnf(c21,plain,
addition(sk0,sk1) = sk1,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t2,plain,
addition(sk0,sk1) = sk1,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t19873,plain,
addition(sk1,sk0) = sk1,
inference(step,[status(thm)],[t2,t68]) ).
cnf(t111,plain,
addition(sk1,sk0) = sk1,
inference(orient,[status(thm)],[t19873]) ).
cnf(t113,plain,
addition(sk1,addition(sk0,X1)) = addition(sk1,X1),
inference(cp,[status(thm)],[t73,t111]) ).
cnf(t280,plain,
addition(sk1,addition(sk0,X1)) = addition(sk1,X1),
inference(orient,[status(thm)],[t113]) ).
cnf(t281,plain,
addition(sk1,X1) = addition(sk1,addition(X1,sk0)),
inference(cp,[status(thm)],[t280,t68]) ).
cnf(t295,plain,
addition(sk1,addition(X1,sk0)) = addition(sk1,X1),
inference(orient,[status(thm)],[t281]) ).
cnf(t1117,plain,
true = leq(sk0,addition(sk1,X1)),
inference(cp,[status(thm)],[t1112,t295]) ).
cnf(t1150,plain,
leq(sk0,addition(sk1,X1)) = true,
inference(orient,[status(thm)],[t1117]) ).
cnf(t1154,plain,
addition(sk1,X1) = ifeq(true,true,addition(sk0,addition(sk1,X1)),addition(sk1,X1)),
inference(cp,[status(thm)],[t34,t1150]) ).
cnf(t19956,plain,
addition(sk1,X1) = addition(sk0,addition(sk1,X1)),
inference(step,[status(thm)],[t1154,t33]) ).
cnf(t1160,plain,
addition(sk0,addition(sk1,X1)) = addition(sk1,X1),
inference(orient,[status(thm)],[t19956]) ).
cnf(t2225,plain,
multiplication(antidomain(addition(sk1,X1)),sk0) = multiplication(antidomain(addition(sk1,X1)),addition(sk1,X1)),
inference(cp,[status(thm)],[t2218,t1160]) ).
cnf(t20040,plain,
multiplication(antidomain(addition(sk1,X1)),sk0) = zero,
inference(step,[status(thm)],[t2225,t59]) ).
cnf(t2303,plain,
multiplication(antidomain(addition(sk1,X1)),sk0) = zero,
inference(orient,[status(thm)],[t20040]) ).
cnf(t2304,plain,
zero = multiplication(antidomain(sk1),sk0),
inference(cp,[status(thm)],[t2303,t111]) ).
cnf(t2321,plain,
multiplication(antidomain(sk1),sk0) = zero,
inference(orient,[status(thm)],[t2304]) ).
cnf(t2332,plain,
true = leq(antidomain(zero),antidomain(multiplication(antidomain(sk1),domain(sk0)))),
inference(cp,[status(thm)],[t135,t2321]) ).
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(t29,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t60,plain,
zero = antidomain(one),
inference(cp,[status(thm)],[t59,t29]) ).
cnf(t160,plain,
antidomain(one) = zero,
inference(orient,[status(thm)],[t60]) ).
cnf(t161,plain,
domain(one) = antidomain(zero),
inference(cp,[status(thm)],[t119,t160]) ).
cnf(t164,plain,
antidomain(zero) = domain(one),
inference(orient,[status(thm)],[t161]) ).
fof(f14,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f14_nnf,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t17,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t19872,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(step,[status(thm)],[t17,t68]) ).
cnf(t108,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(orient,[status(thm)],[t19872]) ).
cnf(t19877,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(step,[status(thm)],[t108,t119]) ).
cnf(t122,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(rw,[status(thm)],[t19877]) ).
cnf(t19889,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(step,[status(thm)],[t122,t68]) ).
cnf(t215,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(orient,[status(thm)],[t19889]) ).
cnf(t219,plain,
one = addition(domain(one),zero),
inference(cp,[status(thm)],[t215,t160]) ).
cnf(t19890,plain,
one = domain(one),
inference(step,[status(thm)],[t219,t32]) ).
cnf(t223,plain,
domain(one) = one,
inference(orient,[status(thm)],[t19890]) ).
cnf(t19891,plain,
antidomain(zero) = one,
inference(step,[status(thm)],[t164,t223]) ).
cnf(t224,plain,
antidomain(zero) = one,
inference(orient,[status(thm)],[t19891]) ).
cnf(t20229,plain,
true = leq(one,antidomain(multiplication(antidomain(sk1),domain(sk0)))),
inference(step,[status(thm)],[t2332,t224]) ).
cnf(t7873,plain,
leq(one,antidomain(multiplication(antidomain(sk1),domain(sk0)))) = true,
inference(orient,[status(thm)],[t20229]) ).
cnf(t7874,plain,
antidomain(multiplication(antidomain(sk1),domain(sk0))) = ifeq(true,true,addition(one,antidomain(multiplication(antidomain(sk1),domain(sk0)))),antidomain(multiplication(antidomain(sk1),domain(sk0)))),
inference(cp,[status(thm)],[t34,t7873]) ).
cnf(t20230,plain,
antidomain(multiplication(antidomain(sk1),domain(sk0))) = addition(one,antidomain(multiplication(antidomain(sk1),domain(sk0)))),
inference(step,[status(thm)],[t7874,t33]) ).
cnf(t259,plain,
true = leq(antidomain(X1),one),
inference(cp,[status(thm)],[t258,t215]) ).
cnf(t266,plain,
leq(antidomain(X1),one) = true,
inference(orient,[status(thm)],[t259]) ).
cnf(t267,plain,
one = ifeq(true,true,addition(antidomain(X1),one),one),
inference(cp,[status(thm)],[t34,t266]) ).
cnf(t19900,plain,
one = addition(antidomain(X1),one),
inference(step,[status(thm)],[t267,t33]) ).
cnf(t19901,plain,
one = addition(one,antidomain(X1)),
inference(step,[status(thm)],[t19900,t68]) ).
cnf(t272,plain,
addition(one,antidomain(X1)) = one,
inference(orient,[status(thm)],[t19901]) ).
cnf(t20231,plain,
antidomain(multiplication(antidomain(sk1),domain(sk0))) = one,
inference(step,[status(thm)],[t20230,t272]) ).
cnf(t7877,plain,
antidomain(multiplication(antidomain(sk1),domain(sk0))) = one,
inference(orient,[status(thm)],[t20231]) ).
cnf(t7885,plain,
zero = multiplication(one,multiplication(antidomain(sk1),domain(sk0))),
inference(cp,[status(thm)],[t59,t7877]) ).
cnf(t20232,plain,
zero = multiplication(antidomain(sk1),domain(sk0)),
inference(step,[status(thm)],[t7885,t30]) ).
cnf(t7898,plain,
multiplication(antidomain(sk1),domain(sk0)) = zero,
inference(orient,[status(thm)],[t20232]) ).
cnf(t7901,plain,
multiplication(antidomain(sk1),addition(domain(sk0),X1)) = addition(zero,multiplication(antidomain(sk1),X1)),
inference(cp,[status(thm)],[t38,t7898]) ).
cnf(t69,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t68,t32]) ).
cnf(t166,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t69]) ).
cnf(t20554,plain,
multiplication(antidomain(sk1),addition(domain(sk0),X1)) = multiplication(antidomain(sk1),X1),
inference(step,[status(thm)],[t7901,t166]) ).
cnf(t19794,plain,
multiplication(antidomain(sk1),addition(domain(sk0),X1)) = multiplication(antidomain(sk1),X1),
inference(orient,[status(thm)],[t20554]) ).
cnf(t19797,plain,
multiplication(antidomain(sk1),antidomain(sk0)) = multiplication(antidomain(sk1),one),
inference(cp,[status(thm)],[t19794,t215]) ).
cnf(t20555,plain,
multiplication(antidomain(sk1),antidomain(sk0)) = antidomain(sk1),
inference(step,[status(thm)],[t19797,t29]) ).
cnf(t19827,plain,
multiplication(antidomain(sk1),antidomain(sk0)) = antidomain(sk1),
inference(orient,[status(thm)],[t20555]) ).
cnf(t19828,plain,
multiplication(addition(one,antidomain(sk1)),antidomain(sk0)) = addition(antidomain(sk0),antidomain(sk1)),
inference(cp,[status(thm)],[t428,t19827]) ).
cnf(t20556,plain,
multiplication(one,antidomain(sk0)) = addition(antidomain(sk0),antidomain(sk1)),
inference(step,[status(thm)],[t19828,t272]) ).
cnf(t20557,plain,
antidomain(sk0) = addition(antidomain(sk0),antidomain(sk1)),
inference(step,[status(thm)],[t20556,t30]) ).
cnf(t20558,plain,
antidomain(sk0) = addition(antidomain(sk1),antidomain(sk0)),
inference(step,[status(thm)],[t20557,t68]) ).
cnf(t19851,plain,
addition(antidomain(sk1),antidomain(sk0)) = antidomain(sk0),
inference(orient,[status(thm)],[t20558]) ).
cnf(c22,plain,
addition(antidomain(sk1),antidomain(sk0)) != antidomain(sk0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
addition(antidomain(sk1),antidomain(sk0)) != antidomain(sk0),
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
antidomain(sk0) != antidomain(sk0),
inference(rw,[status(thm)],[goal_0,t19851]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE090+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 18:55:18 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 35.97/5.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.97/5.10 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------