%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE088+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 : n015.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 42.70s 6.02s
% Output : Proof 42.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 15
% Syntax : Number of formulae : 151 ( 142 unt; 0 def)
% Number of atoms : 164 ( 156 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 : 196 ( 15 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(t23,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t50,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t23]) ).
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(t29,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t53,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t50,t29]) ).
cnf(t434,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t53]) ).
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(t22,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t37,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t22]) ).
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(t12,plain,
multiplication(antidomain(X1),X1) = zero,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t58,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t12]) ).
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(t26,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t102,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(orient,[status(thm)],[t26]) ).
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(t9,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t123,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t20782,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(step,[status(thm)],[t102,t123]) ).
cnf(t20783,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = antidomain(multiplication(X1,domain(X2))),
inference(step,[status(thm)],[t20782,t123]) ).
cnf(t127,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = antidomain(multiplication(X1,domain(X2))),
inference(rw,[status(thm)],[t20783]) ).
cnf(t18008,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = antidomain(multiplication(X1,domain(X2))),
inference(orient,[status(thm)],[t127]) ).
fof(f20,conjecture,
! [X0,X1] :
( multiplication(domain(X0),X1) = zero
=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20_neg,negated_conjecture,
~ ! [X0,X1] :
( multiplication(domain(X0),X1) = zero
=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [X0,X1] :
( addition(domain(X0),antidomain(X1)) != antidomain(X1)
& multiplication(domain(X0),X1) = zero ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( addition(domain(sk0),antidomain(sk1)) != antidomain(sk1)
& multiplication(domain(sk0),sk1) = zero ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f20_nnf]) ).
cnf(c21,plain,
multiplication(domain(sk0),sk1) = zero,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t13,plain,
multiplication(domain(sk0),sk1) = zero,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t67,plain,
multiplication(domain(sk0),sk1) = zero,
inference(orient,[status(thm)],[t13]) ).
cnf(t18124,plain,
antidomain(multiplication(domain(sk0),domain(sk1))) = addition(antidomain(zero),antidomain(multiplication(domain(sk0),domain(sk1)))),
inference(cp,[status(thm)],[t18008,t67]) ).
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(t28,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t59,plain,
zero = antidomain(one),
inference(cp,[status(thm)],[t58,t28]) ).
cnf(t162,plain,
antidomain(one) = zero,
inference(orient,[status(thm)],[t59]) ).
cnf(t163,plain,
domain(one) = antidomain(zero),
inference(cp,[status(thm)],[t123,t162]) ).
cnf(t166,plain,
antidomain(zero) = domain(one),
inference(orient,[status(thm)],[t163]) ).
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(t16,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
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(t14,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t73,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t14]) ).
cnf(t20777,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(step,[status(thm)],[t16,t73]) ).
cnf(t115,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(orient,[status(thm)],[t20777]) ).
cnf(t20781,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(step,[status(thm)],[t115,t123]) ).
cnf(t126,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(rw,[status(thm)],[t20781]) ).
cnf(t20793,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(step,[status(thm)],[t126,t73]) ).
cnf(t217,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(orient,[status(thm)],[t20793]) ).
cnf(t221,plain,
one = addition(domain(one),zero),
inference(cp,[status(thm)],[t217,t162]) ).
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(t31,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t20794,plain,
one = domain(one),
inference(step,[status(thm)],[t221,t31]) ).
cnf(t225,plain,
domain(one) = one,
inference(orient,[status(thm)],[t20794]) ).
cnf(t20795,plain,
antidomain(zero) = one,
inference(step,[status(thm)],[t166,t225]) ).
cnf(t226,plain,
antidomain(zero) = one,
inference(orient,[status(thm)],[t20795]) ).
cnf(t21368,plain,
antidomain(multiplication(domain(sk0),domain(sk1))) = addition(one,antidomain(multiplication(domain(sk0),domain(sk1)))),
inference(step,[status(thm)],[t18124,t226]) ).
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(t20,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t33,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(t152,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t19]) ).
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(t18,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t78,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/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(t30,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t81,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t78,t30]) ).
cnf(t230,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t81]) ).
cnf(t237,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t152,t230]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t20803,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t237,t32]) ).
cnf(t246,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t20803]) ).
cnf(t252,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t246,t73]) ).
cnf(t259,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t252]) ).
cnf(t260,plain,
true = leq(antidomain(X1),one),
inference(cp,[status(thm)],[t259,t217]) ).
cnf(t268,plain,
leq(antidomain(X1),one) = true,
inference(orient,[status(thm)],[t260]) ).
cnf(t269,plain,
one = ifeq(true,true,addition(antidomain(X1),one),one),
inference(cp,[status(thm)],[t33,t268]) ).
cnf(t20804,plain,
one = addition(antidomain(X1),one),
inference(step,[status(thm)],[t269,t32]) ).
cnf(t20805,plain,
one = addition(one,antidomain(X1)),
inference(step,[status(thm)],[t20804,t73]) ).
cnf(t274,plain,
addition(one,antidomain(X1)) = one,
inference(orient,[status(thm)],[t20805]) ).
cnf(t21369,plain,
antidomain(multiplication(domain(sk0),domain(sk1))) = one,
inference(step,[status(thm)],[t21368,t274]) ).
cnf(t18282,plain,
antidomain(multiplication(domain(sk0),domain(sk1))) = one,
inference(orient,[status(thm)],[t21369]) ).
cnf(t18291,plain,
zero = multiplication(one,multiplication(domain(sk0),domain(sk1))),
inference(cp,[status(thm)],[t58,t18282]) ).
cnf(t21370,plain,
zero = multiplication(domain(sk0),domain(sk1)),
inference(step,[status(thm)],[t18291,t29]) ).
cnf(t18313,plain,
multiplication(domain(sk0),domain(sk1)) = zero,
inference(orient,[status(thm)],[t21370]) ).
cnf(t18316,plain,
multiplication(domain(sk0),addition(domain(sk1),X1)) = addition(zero,multiplication(domain(sk0),X1)),
inference(cp,[status(thm)],[t37,t18313]) ).
cnf(t74,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t73,t31]) ).
cnf(t168,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t74]) ).
cnf(t21435,plain,
multiplication(domain(sk0),addition(domain(sk1),X1)) = multiplication(domain(sk0),X1),
inference(step,[status(thm)],[t18316,t168]) ).
cnf(t20679,plain,
multiplication(domain(sk0),addition(domain(sk1),X1)) = multiplication(domain(sk0),X1),
inference(orient,[status(thm)],[t21435]) ).
cnf(t20682,plain,
multiplication(domain(sk0),antidomain(sk1)) = multiplication(domain(sk0),one),
inference(cp,[status(thm)],[t20679,t217]) ).
cnf(t21436,plain,
multiplication(domain(sk0),antidomain(sk1)) = domain(sk0),
inference(step,[status(thm)],[t20682,t28]) ).
cnf(t20719,plain,
multiplication(domain(sk0),antidomain(sk1)) = domain(sk0),
inference(orient,[status(thm)],[t21436]) ).
cnf(t20720,plain,
multiplication(addition(one,domain(sk0)),antidomain(sk1)) = addition(antidomain(sk1),domain(sk0)),
inference(cp,[status(thm)],[t434,t20719]) ).
cnf(t232,plain,
addition(domain(X1),antidomain(X1)) = addition(domain(X1),one),
inference(cp,[status(thm)],[t230,t217]) ).
cnf(t20799,plain,
one = addition(domain(X1),one),
inference(step,[status(thm)],[t232,t217]) ).
cnf(t20800,plain,
one = addition(one,domain(X1)),
inference(step,[status(thm)],[t20799,t73]) ).
cnf(t238,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t20800]) ).
cnf(t21437,plain,
multiplication(one,antidomain(sk1)) = addition(antidomain(sk1),domain(sk0)),
inference(step,[status(thm)],[t20720,t238]) ).
cnf(t21438,plain,
antidomain(sk1) = addition(antidomain(sk1),domain(sk0)),
inference(step,[status(thm)],[t21437,t29]) ).
cnf(t21439,plain,
antidomain(sk1) = addition(domain(sk0),antidomain(sk1)),
inference(step,[status(thm)],[t21438,t73]) ).
cnf(t20748,plain,
addition(domain(sk0),antidomain(sk1)) = antidomain(sk1),
inference(orient,[status(thm)],[t21439]) ).
cnf(c22,plain,
addition(domain(sk0),antidomain(sk1)) != antidomain(sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
addition(domain(sk0),antidomain(sk1)) != antidomain(sk1),
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
antidomain(sk1) != antidomain(sk1),
inference(rw,[status(thm)],[goal_0,t20748]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 18:57:10 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 42.70/6.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.70/6.02 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------