%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE080+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 : n016.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 01:51:33 PM UTC 2026
% Result : Theorem 7.51s 1.51s
% Output : Proof 7.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 17
% Syntax : Number of formulae : 292 ( 283 unt; 0 def)
% Number of atoms : 309 ( 301 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 12 ~; 6 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 422 ( 45 sgn 78 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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]) ).
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(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(t9874,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t46,t336]) ).
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]) ).
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(t9849,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t8,t57]) ).
cnf(t77,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t9849]) ).
cnf(t9875,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t9874,t77]) ).
cnf(t9876,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t9875,t25]) ).
cnf(t348,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t9876]) ).
cnf(t349,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t348]) ).
cnf(t356,plain,
multiplication(domain(X1),addition(one,X1)) = addition(domain(X1),X1),
inference(cp,[status(thm)],[t326,t349]) ).
cnf(t9891,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(step,[status(thm)],[t356,t57]) ).
cnf(t680,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(orient,[status(thm)],[t9891]) ).
cnf(t700,plain,
addition(X1,domain(X1)) = multiplication(domain(X1),addition(X1,one)),
inference(cp,[status(thm)],[t680,t57]) ).
cnf(t726,plain,
multiplication(domain(X1),addition(X1,one)) = addition(X1,domain(X1)),
inference(orient,[status(thm)],[t700]) ).
fof(f17,conjecture,
! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> antidomain(antidomain(X0)) = domain(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> antidomain(antidomain(X0)) = domain(X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0] :
( antidomain(antidomain(X0)) != domain(X0)
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
! [X1] :
( antidomain(antidomain(sk0)) != domain(sk0)
& multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f17_nnf]) ).
cnf(c19,plain,
multiplication(domain(X1),antidomain(X1)) = 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(t9930,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)],[t9930]) ).
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(X1),antidomain(X1)) = 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(t9902,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(addition(antidomain(X1),X2),addition(one,X2)),
inference(step,[status(thm)],[t1039,t62]) ).
cnf(t9903,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(antidomain(X1),addition(X2,addition(one,X2))),
inference(step,[status(thm)],[t9902,t62]) ).
cnf(t9904,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(antidomain(X1),addition(X2,one)),
inference(step,[status(thm)],[t9903,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(t9859,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)],[t9859]) ).
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(t9860,plain,
one = addition(antidomain(X1),one),
inference(step,[status(thm)],[t175,t28]) ).
cnf(t9861,plain,
one = addition(one,antidomain(X1)),
inference(step,[status(thm)],[t9860,t57]) ).
cnf(t177,plain,
addition(one,antidomain(X1)) = one,
inference(orient,[status(thm)],[t9861]) ).
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(t9882,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)],[t9882]) ).
cnf(t9905,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(X2,one),
inference(step,[status(thm)],[t9904,t530]) ).
cnf(t1070,plain,
addition(antidomain(X1),addition(X2,domain(X1))) = addition(X2,one),
inference(orient,[status(thm)],[t9905]) ).
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(t9942,plain,
addition(one,domain(X1)) = addition(antidomain(X2),domain(addition(X1,X2))),
inference(step,[status(thm)],[t1077,t57]) ).
cnf(t9943,plain,
one = addition(antidomain(X2),domain(addition(X1,X2))),
inference(step,[status(thm)],[t9942,t77]) ).
cnf(t2585,plain,
addition(antidomain(X1),domain(addition(X2,X1))) = one,
inference(orient,[status(thm)],[t9943]) ).
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]) ).
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(t9853,plain,
domain(one) = addition(one,domain(one)),
inference(step,[status(thm)],[t126,t28]) ).
cnf(t9854,plain,
domain(one) = one,
inference(step,[status(thm)],[t9853,t77]) ).
cnf(t128,plain,
domain(one) = one,
inference(orient,[status(thm)],[t9854]) ).
cnf(t130,plain,
domain(addition(one,X1)) = addition(one,domain(X1)),
inference(cp,[status(thm)],[t73,t128]) ).
cnf(t9856,plain,
domain(addition(one,X1)) = one,
inference(step,[status(thm)],[t130,t77]) ).
cnf(t134,plain,
domain(addition(one,X1)) = one,
inference(orient,[status(thm)],[t9856]) ).
cnf(t140,plain,
domain(multiplication(X1,addition(one,X2))) = domain(multiplication(X1,one)),
inference(cp,[status(thm)],[t83,t134]) ).
cnf(t9872,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)],[t9872]) ).
cnf(t9944,plain,
one = addition(antidomain(multiplication(X1,X2)),domain(X1)),
inference(step,[status(thm)],[t2616,t298]) ).
cnf(t9945,plain,
one = addition(domain(X1),antidomain(multiplication(X1,X2))),
inference(step,[status(thm)],[t9944,t57]) ).
cnf(t2651,plain,
addition(domain(X1),antidomain(multiplication(X1,X2))) = one,
inference(orient,[status(thm)],[t9945]) ).
cnf(t4004,plain,
multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)) = multiplication(one,antidomain(X1)),
inference(cp,[status(thm)],[t4002,t2651]) ).
cnf(t9974,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)],[t9974]) ).
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(t9975,plain,
multiplication(antidomain(X1),one) = addition(antidomain(X1),antidomain(domain(X1))),
inference(step,[status(thm)],[t4330,t177]) ).
cnf(t9976,plain,
antidomain(X1) = addition(antidomain(X1),antidomain(domain(X1))),
inference(step,[status(thm)],[t9975,t24]) ).
cnf(t85,plain,
domain(multiplication(one,X1)) = domain(domain(X1)),
inference(cp,[status(thm)],[t83,t25]) ).
cnf(t9851,plain,
domain(X1) = domain(domain(X1)),
inference(step,[status(thm)],[t85,t25]) ).
cnf(t117,plain,
domain(domain(X1)) = domain(X1),
inference(orient,[status(thm)],[t9851]) ).
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(t9970,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)],[t9970]) ).
cnf(t4187,plain,
multiplication(antidomain(domain(X1)),addition(one,antidomain(X1))) = addition(antidomain(domain(X1)),antidomain(X1)),
inference(cp,[status(thm)],[t326,t4174]) ).
cnf(t9971,plain,
multiplication(antidomain(domain(X1)),one) = addition(antidomain(domain(X1)),antidomain(X1)),
inference(step,[status(thm)],[t4187,t177]) ).
cnf(t9972,plain,
antidomain(domain(X1)) = addition(antidomain(domain(X1)),antidomain(X1)),
inference(step,[status(thm)],[t9971,t24]) ).
cnf(t9973,plain,
antidomain(domain(X1)) = addition(antidomain(X1),antidomain(domain(X1))),
inference(step,[status(thm)],[t9972,t57]) ).
cnf(t4208,plain,
addition(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
inference(orient,[status(thm)],[t9973]) ).
cnf(t9977,plain,
antidomain(X1) = antidomain(domain(X1)),
inference(step,[status(thm)],[t9976,t4208]) ).
cnf(t4353,plain,
antidomain(domain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t9977]) ).
cnf(t4361,plain,
antidomain(multiplication(X1,domain(X2))) = antidomain(domain(multiplication(X1,X2))),
inference(cp,[status(thm)],[t4353,t83]) ).
cnf(t9980,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)],[t9980]) ).
cnf(t119,plain,
domain(addition(domain(X1),X2)) = addition(domain(X1),domain(X2)),
inference(cp,[status(thm)],[t73,t117]) ).
cnf(t9865,plain,
domain(addition(domain(X1),X2)) = domain(addition(X1,X2)),
inference(step,[status(thm)],[t119,t73]) ).
cnf(t225,plain,
domain(addition(domain(X1),X2)) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t9865]) ).
cnf(t227,plain,
domain(addition(X1,antidomain(X1))) = domain(one),
inference(cp,[status(thm)],[t225,t80]) ).
cnf(t9866,plain,
domain(addition(X1,antidomain(X1))) = one,
inference(step,[status(thm)],[t227,t128]) ).
cnf(t242,plain,
domain(addition(X1,antidomain(X1))) = one,
inference(orient,[status(thm)],[t9866]) ).
cnf(t249,plain,
domain(multiplication(X1,addition(X2,antidomain(X2)))) = domain(multiplication(X1,one)),
inference(cp,[status(thm)],[t83,t242]) ).
cnf(t9893,plain,
domain(multiplication(X1,addition(X2,antidomain(X2)))) = domain(X1),
inference(step,[status(thm)],[t249,t24]) ).
cnf(t741,plain,
domain(multiplication(X1,addition(X2,antidomain(X2)))) = domain(X1),
inference(orient,[status(thm)],[t9893]) ).
cnf(t36,plain,
multiplication(X1,X2) = ifeq(leq(multiplication(X1,X3),multiplication(X1,X2)),true,multiplication(X1,addition(X3,X2)),multiplication(X1,X2)),
inference(cp,[status(thm)],[t29,t33]) ).
cnf(t814,plain,
ifeq(leq(multiplication(X1,X2),multiplication(X1,X3)),true,multiplication(X1,addition(X2,X3)),multiplication(X1,X3)) = multiplication(X1,X3),
inference(orient,[status(thm)],[t36]) ).
cnf(t825,plain,
multiplication(domain(X1),X2) = ifeq(leq(zero,multiplication(domain(X1),X2)),true,multiplication(domain(X1),addition(antidomain(X1),X2)),multiplication(domain(X1),X2)),
inference(cp,[status(thm)],[t814,t49]) ).
cnf(t58,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t57,t27]) ).
cnf(t112,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t58]) ).
cnf(t114,plain,
true = ifeq(X1,X1,leq(zero,X1),true),
inference(cp,[status(thm)],[t102,t112]) ).
cnf(t9850,plain,
true = leq(zero,X1),
inference(step,[status(thm)],[t114,t28]) ).
cnf(t116,plain,
leq(zero,X1) = true,
inference(orient,[status(thm)],[t9850]) ).
cnf(t9938,plain,
multiplication(domain(X1),X2) = ifeq(true,true,multiplication(domain(X1),addition(antidomain(X1),X2)),multiplication(domain(X1),X2)),
inference(step,[status(thm)],[t825,t116]) ).
cnf(t9939,plain,
multiplication(domain(X1),X2) = multiplication(domain(X1),addition(antidomain(X1),X2)),
inference(step,[status(thm)],[t9938,t28]) ).
cnf(t2474,plain,
multiplication(domain(X1),addition(antidomain(X1),X2)) = multiplication(domain(X1),X2),
inference(orient,[status(thm)],[t9939]) ).
cnf(t2499,plain,
domain(domain(X1)) = domain(multiplication(domain(X1),antidomain(antidomain(X1)))),
inference(cp,[status(thm)],[t741,t2474]) ).
cnf(t9940,plain,
domain(X1) = domain(multiplication(domain(X1),antidomain(antidomain(X1)))),
inference(step,[status(thm)],[t2499,t117]) ).
cnf(t2500,plain,
domain(multiplication(domain(X1),antidomain(antidomain(X1)))) = domain(X1),
inference(orient,[status(thm)],[t9940]) ).
cnf(t2228,plain,
multiplication(domain(X1),antidomain(X2)) = multiplication(domain(addition(X1,X2)),antidomain(X2)),
inference(cp,[status(thm)],[t2226,t73]) ).
cnf(t7228,plain,
multiplication(domain(addition(X1,X2)),antidomain(X2)) = multiplication(domain(X1),antidomain(X2)),
inference(orient,[status(thm)],[t2228]) ).
cnf(t7236,plain,
multiplication(domain(X1),antidomain(antidomain(X1))) = multiplication(one,antidomain(antidomain(X1))),
inference(cp,[status(thm)],[t7228,t242]) ).
cnf(t10023,plain,
multiplication(domain(X1),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(step,[status(thm)],[t7236,t25]) ).
cnf(t7317,plain,
multiplication(domain(X1),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(orient,[status(thm)],[t10023]) ).
cnf(t10025,plain,
domain(antidomain(antidomain(X1))) = domain(X1),
inference(step,[status(thm)],[t2500,t7317]) ).
cnf(t7358,plain,
domain(antidomain(antidomain(X1))) = domain(X1),
inference(rw,[status(thm)],[t10025]) ).
cnf(t7412,plain,
domain(antidomain(antidomain(X1))) = domain(X1),
inference(orient,[status(thm)],[t7358]) ).
cnf(t7424,plain,
antidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(X1,domain(X2))),
inference(cp,[status(thm)],[t4465,t7412]) ).
cnf(t10034,plain,
antidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
inference(step,[status(thm)],[t7424,t4465]) ).
cnf(t7826,plain,
antidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t10034]) ).
cnf(t698,plain,
addition(antidomain(X1),domain(antidomain(X1))) = multiplication(domain(antidomain(X1)),one),
inference(cp,[status(thm)],[t680,t177]) ).
cnf(t9892,plain,
addition(antidomain(X1),domain(antidomain(X1))) = domain(antidomain(X1)),
inference(step,[status(thm)],[t698,t24]) ).
cnf(t708,plain,
addition(antidomain(X1),domain(antidomain(X1))) = domain(antidomain(X1)),
inference(orient,[status(thm)],[t9892]) ).
cnf(t2227,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = multiplication(domain(antidomain(X1)),antidomain(antidomain(X1))),
inference(cp,[status(thm)],[t2226,t708]) ).
cnf(t9931,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
inference(step,[status(thm)],[t2227,t49]) ).
cnf(t2253,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
inference(orient,[status(thm)],[t9931]) ).
cnf(t4354,plain,
antidomain(multiplication(domain(X1),antidomain(antidomain(X1)))) = antidomain(domain(X1)),
inference(cp,[status(thm)],[t4353,t2500]) ).
cnf(t9985,plain,
antidomain(multiplication(domain(X1),antidomain(antidomain(X1)))) = antidomain(X1),
inference(step,[status(thm)],[t4354,t4353]) ).
cnf(t4693,plain,
antidomain(multiplication(domain(X1),antidomain(antidomain(X1)))) = antidomain(X1),
inference(orient,[status(thm)],[t9985]) ).
cnf(t10024,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(step,[status(thm)],[t4693,t7317]) ).
cnf(t7357,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[t10024]) ).
cnf(t7359,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(orient,[status(thm)],[t7357]) ).
cnf(t7384,plain,
zero = multiplication(antidomain(antidomain(X1)),antidomain(X1)),
inference(cp,[status(thm)],[t2253,t7359]) ).
cnf(t7465,plain,
multiplication(antidomain(antidomain(X1)),antidomain(X1)) = zero,
inference(orient,[status(thm)],[t7384]) ).
cnf(t7828,plain,
antidomain(multiplication(antidomain(antidomain(antidomain(X1))),X1)) = antidomain(zero),
inference(cp,[status(thm)],[t7826,t7465]) ).
cnf(t10035,plain,
antidomain(multiplication(antidomain(X1),X1)) = antidomain(zero),
inference(step,[status(thm)],[t7828,t7359]) ).
fof(f15,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f15_nnf,plain,
domain(zero) = zero,
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c16,plain,
domain(zero) = zero,
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t0,plain,
domain(zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t92,plain,
domain(zero) = zero,
inference(orient,[status(thm)],[t0]) ).
cnf(t93,plain,
one = addition(zero,antidomain(zero)),
inference(cp,[status(thm)],[t80,t92]) ).
cnf(t9852,plain,
one = antidomain(zero),
inference(step,[status(thm)],[t93,t112]) ).
cnf(t124,plain,
antidomain(zero) = one,
inference(orient,[status(thm)],[t9852]) ).
cnf(t10036,plain,
antidomain(multiplication(antidomain(X1),X1)) = one,
inference(step,[status(thm)],[t10035,t124]) ).
cnf(t7932,plain,
antidomain(multiplication(antidomain(X1),X1)) = one,
inference(orient,[status(thm)],[t10036]) ).
cnf(t7952,plain,
zero = multiplication(domain(multiplication(antidomain(X1),X1)),one),
inference(cp,[status(thm)],[t49,t7932]) ).
cnf(t10037,plain,
zero = domain(multiplication(antidomain(X1),X1)),
inference(step,[status(thm)],[t7952,t24]) ).
cnf(t7979,plain,
domain(multiplication(antidomain(X1),X1)) = zero,
inference(orient,[status(thm)],[t10037]) ).
cnf(t7998,plain,
addition(multiplication(antidomain(X1),X1),domain(multiplication(antidomain(X1),X1))) = multiplication(zero,addition(multiplication(antidomain(X1),X1),one)),
inference(cp,[status(thm)],[t726,t7979]) ).
cnf(t10038,plain,
addition(multiplication(antidomain(X1),X1),zero) = multiplication(zero,addition(multiplication(antidomain(X1),X1),one)),
inference(step,[status(thm)],[t7998,t7979]) ).
cnf(t10039,plain,
multiplication(antidomain(X1),X1) = multiplication(zero,addition(multiplication(antidomain(X1),X1),one)),
inference(step,[status(thm)],[t10038,t27]) ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f10_nnf,plain,
! [A] : multiplication(zero,A) = zero,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : multiplication(zero,A) = zero,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t7,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t55,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t7]) ).
cnf(t10040,plain,
multiplication(antidomain(X1),X1) = zero,
inference(step,[status(thm)],[t10039,t55]) ).
cnf(t8024,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t10040]) ).
cnf(t7847,plain,
antidomain(multiplication(domain(antidomain(X1)),X1)) = antidomain(zero),
inference(cp,[status(thm)],[t7826,t49]) ).
cnf(t10041,plain,
antidomain(multiplication(domain(antidomain(X1)),X1)) = one,
inference(step,[status(thm)],[t7847,t124]) ).
cnf(t8086,plain,
antidomain(multiplication(domain(antidomain(X1)),X1)) = one,
inference(orient,[status(thm)],[t10041]) ).
cnf(t8105,plain,
zero = multiplication(one,multiplication(domain(antidomain(X1)),X1)),
inference(cp,[status(thm)],[t8024,t8086]) ).
cnf(t10042,plain,
zero = multiplication(domain(antidomain(X1)),X1),
inference(step,[status(thm)],[t8105,t25]) ).
cnf(t8135,plain,
multiplication(domain(antidomain(X1)),X1) = zero,
inference(orient,[status(thm)],[t10042]) ).
cnf(t8155,plain,
multiplication(addition(domain(antidomain(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(cp,[status(thm)],[t40,t8135]) ).
cnf(t10070,plain,
multiplication(addition(domain(antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(step,[status(thm)],[t8155,t112]) ).
cnf(t9689,plain,
multiplication(addition(domain(antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(orient,[status(thm)],[t10070]) ).
cnf(t9695,plain,
multiplication(antidomain(antidomain(X1)),X1) = multiplication(one,X1),
inference(cp,[status(thm)],[t9689,t80]) ).
cnf(t10071,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(step,[status(thm)],[t9695,t25]) ).
cnf(t9761,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(orient,[status(thm)],[t10071]) ).
cnf(t9780,plain,
domain(X1) = multiplication(antidomain(antidomain(X1)),domain(X1)),
inference(cp,[status(thm)],[t9761,t4353]) ).
cnf(t8048,plain,
multiplication(antidomain(X1),addition(X2,X1)) = addition(multiplication(antidomain(X1),X2),zero),
inference(cp,[status(thm)],[t33,t8024]) ).
cnf(t10063,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(step,[status(thm)],[t8048,t27]) ).
cnf(t9480,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(orient,[status(thm)],[t10063]) ).
cnf(t9522,plain,
multiplication(antidomain(antidomain(X1)),domain(X1)) = multiplication(antidomain(antidomain(X1)),one),
inference(cp,[status(thm)],[t9480,t80]) ).
cnf(t10064,plain,
multiplication(antidomain(antidomain(X1)),domain(X1)) = antidomain(antidomain(X1)),
inference(step,[status(thm)],[t9522,t24]) ).
cnf(t9547,plain,
multiplication(antidomain(antidomain(X1)),domain(X1)) = antidomain(antidomain(X1)),
inference(orient,[status(thm)],[t10064]) ).
cnf(t10072,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(step,[status(thm)],[t9780,t9547]) ).
cnf(t9801,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t10072]) ).
cnf(c20,plain,
antidomain(antidomain(sk0)) != domain(sk0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
antidomain(antidomain(sk0)) != domain(sk0),
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
domain(sk0) != domain(sk0),
inference(rw,[status(thm)],[goal_0,t9801]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE080+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 18:56:56 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.51/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.51/1.51 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------