TSTP Solution File: PUZ133+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : PUZ133+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:54:57 EDT 2024
% Result : Theorem 8.02s 1.67s
% Output : CNFRefutation 8.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 137 ( 27 unt; 0 def)
% Number of atoms : 467 ( 159 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 555 ( 225 ~; 244 |; 69 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 201 ( 0 sgn 91 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( queens_p
=> ! [X0,X1] :
( ( le(X1,n)
& le(s(X0),X1)
& le(X0,n)
& le(s(n0),X0) )
=> ( minus(p(X0),X0) != minus(p(X1),X1)
& plus(p(X0),X0) != plus(p(X1),X1)
& p(X0) != p(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_p) ).
fof(f2,axiom,
! [X0] : perm(X0) = minus(s(n),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation) ).
fof(f3,axiom,
( ! [X0,X1] :
( ( ( le(s(X0),X1)
<=> le(s(perm(X1)),perm(X0)) )
& le(X1,n)
& le(s(X0),X1)
& le(X0,n)
& le(s(n0),X0) )
=> ( minus(q(X0),X0) != minus(q(X1),X1)
& plus(q(X0),X0) != plus(q(X1),X1)
& q(X0) != q(X1) ) )
=> queens_q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_q) ).
fof(f4,conjecture,
( ( ! [X0] : q(X0) = p(perm(X0))
& queens_p )
=> queens_q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_sym) ).
fof(f5,negated_conjecture,
~ ( ( ! [X0] : q(X0) = p(perm(X0))
& queens_p )
=> queens_q ),
inference(negated_conjecture,[],[f4]) ).
fof(f6,axiom,
! [X0] :
( ( le(X0,n)
& le(s(n0),X0) )
=> ( le(perm(X0),n)
& le(s(n0),perm(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation_range) ).
fof(f7,axiom,
! [X1,X0] : minus(X0,X1) = minus(perm(X1),perm(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation_another_one) ).
fof(f8,axiom,
! [X2,X3,X4] :
( ( le(X3,X4)
& le(X2,X3) )
=> le(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',le_trans) ).
fof(f9,axiom,
! [X2] : le(X2,s(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_le) ).
fof(f10,axiom,
! [X0,X1,X5,X6] :
( plus(X0,X1) = plus(X5,X6)
<=> minus(X0,X5) = minus(X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1) ).
fof(f11,axiom,
! [X0,X1,X5,X6] :
( minus(X0,X1) = minus(X5,X6)
<=> minus(X0,X5) = minus(X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus1) ).
fof(f12,plain,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
inference(rectify,[],[f7]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( le(X1,X2)
& le(X0,X1) )
=> le(X0,X2) ),
inference(rectify,[],[f8]) ).
fof(f14,plain,
! [X0] : le(X0,s(X0)),
inference(rectify,[],[f9]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( plus(X0,X1) = plus(X2,X3)
<=> minus(X0,X2) = minus(X3,X1) ),
inference(rectify,[],[f10]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( minus(X0,X1) = minus(X2,X3)
<=> minus(X0,X2) = minus(X1,X3) ),
inference(rectify,[],[f11]) ).
fof(f17,plain,
( ! [X0,X1] :
( ( minus(p(X0),X0) != minus(p(X1),X1)
& plus(p(X0),X0) != plus(p(X1),X1)
& p(X0) != p(X1) )
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0) )
| ~ queens_p ),
inference(ennf_transformation,[],[f1]) ).
fof(f18,plain,
( ! [X0,X1] :
( ( minus(p(X0),X0) != minus(p(X1),X1)
& plus(p(X0),X0) != plus(p(X1),X1)
& p(X0) != p(X1) )
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0) )
| ~ queens_p ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( queens_q
| ? [X0,X1] :
( ( minus(q(X0),X0) = minus(q(X1),X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| q(X0) = q(X1) )
& ( le(s(X0),X1)
<=> le(s(perm(X1)),perm(X0)) )
& le(X1,n)
& le(s(X0),X1)
& le(X0,n)
& le(s(n0),X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f20,plain,
( queens_q
| ? [X0,X1] :
( ( minus(q(X0),X0) = minus(q(X1),X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| q(X0) = q(X1) )
& ( le(s(X0),X1)
<=> le(s(perm(X1)),perm(X0)) )
& le(X1,n)
& le(s(X0),X1)
& le(X0,n)
& le(s(n0),X0) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( ~ queens_q
& ! [X0] : q(X0) = p(perm(X0))
& queens_p ),
inference(ennf_transformation,[],[f5]) ).
fof(f22,plain,
( ~ queens_q
& ! [X0] : q(X0) = p(perm(X0))
& queens_p ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0] :
( ( le(perm(X0),n)
& le(s(n0),perm(X0)) )
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f24,plain,
! [X0] :
( ( le(perm(X0),n)
& le(s(n0),perm(X0)) )
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( le(X0,X2)
| ~ le(X1,X2)
| ~ le(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f26,plain,
! [X0,X1,X2] :
( le(X0,X2)
| ~ le(X1,X2)
| ~ le(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( queens_q
| ? [X0,X1] :
( ( minus(q(X0),X0) = minus(q(X1),X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| q(X0) = q(X1) )
& ( le(s(X0),X1)
| ~ le(s(perm(X1)),perm(X0)) )
& ( le(s(perm(X1)),perm(X0))
| ~ le(s(X0),X1) )
& le(X1,n)
& le(s(X0),X1)
& le(X0,n)
& le(s(n0),X0) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f28,plain,
( queens_q
| ? [X0,X1] :
( ( minus(q(X0),X0) = minus(q(X1),X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| q(X0) = q(X1) )
& ( le(s(X0),X1)
| ~ le(s(perm(X1)),perm(X0)) )
& ( le(s(perm(X1)),perm(X0))
| ~ le(s(X0),X1) )
& le(X1,n)
& le(s(X0),X1)
& le(X0,n)
& le(s(n0),X0) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
( ? [X0,X1] :
( ( minus(q(X0),X0) = minus(q(X1),X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| q(X0) = q(X1) )
& ( le(s(X0),X1)
| ~ le(s(perm(X1)),perm(X0)) )
& ( le(s(perm(X1)),perm(X0))
| ~ le(s(X0),X1) )
& le(X1,n)
& le(s(X0),X1)
& le(X0,n)
& le(s(n0),X0) )
=> ( ( minus(q(sK0),sK0) = minus(q(sK1),sK1)
| plus(q(sK0),sK0) = plus(q(sK1),sK1)
| q(sK0) = q(sK1) )
& ( le(s(sK0),sK1)
| ~ le(s(perm(sK1)),perm(sK0)) )
& ( le(s(perm(sK1)),perm(sK0))
| ~ le(s(sK0),sK1) )
& le(sK1,n)
& le(s(sK0),sK1)
& le(sK0,n)
& le(s(n0),sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
( queens_q
| ( ( minus(q(sK0),sK0) = minus(q(sK1),sK1)
| plus(q(sK0),sK0) = plus(q(sK1),sK1)
| q(sK0) = q(sK1) )
& ( le(s(sK0),sK1)
| ~ le(s(perm(sK1)),perm(sK0)) )
& ( le(s(perm(sK1)),perm(sK0))
| ~ le(s(sK0),sK1) )
& le(sK1,n)
& le(s(sK0),sK1)
& le(sK0,n)
& le(s(n0),sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f28,f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ( plus(X0,X1) = plus(X2,X3)
| minus(X0,X2) != minus(X3,X1) )
& ( minus(X0,X2) = minus(X3,X1)
| plus(X0,X1) != plus(X2,X3) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ( minus(X0,X1) = minus(X2,X3)
| minus(X0,X2) != minus(X1,X3) )
& ( minus(X0,X2) = minus(X1,X3)
| minus(X0,X1) != minus(X2,X3) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X0,X1] :
( p(X0) != p(X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ queens_p ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X0,X1] :
( plus(p(X0),X0) != plus(p(X1),X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ queens_p ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0,X1] :
( minus(p(X0),X0) != minus(p(X1),X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ queens_p ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0] : perm(X0) = minus(s(n),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f37,plain,
( queens_q
| le(s(n0),sK0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f38,plain,
( queens_q
| le(sK0,n) ),
inference(cnf_transformation,[],[f30]) ).
fof(f39,plain,
( queens_q
| le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f40,plain,
( queens_q
| le(sK1,n) ),
inference(cnf_transformation,[],[f30]) ).
fof(f41,plain,
( queens_q
| le(s(perm(sK1)),perm(sK0))
| ~ le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f43,plain,
( queens_q
| minus(q(sK0),sK0) = minus(q(sK1),sK1)
| plus(q(sK0),sK0) = plus(q(sK1),sK1)
| q(sK0) = q(sK1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f44,plain,
queens_p,
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0] : q(X0) = p(perm(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
~ queens_q,
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X0] :
( le(s(n0),perm(X0))
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X0] :
( le(perm(X0),n)
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
inference(cnf_transformation,[],[f12]) ).
fof(f50,plain,
! [X2,X0,X1] :
( le(X0,X2)
| ~ le(X1,X2)
| ~ le(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f51,plain,
! [X0] : le(X0,s(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( minus(X0,X2) = minus(X3,X1)
| plus(X0,X1) != plus(X2,X3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( plus(X0,X1) = plus(X2,X3)
| minus(X0,X2) != minus(X3,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( minus(X0,X2) = minus(X1,X3)
| minus(X0,X1) != minus(X2,X3) ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
! [X0] : q(X0) = p(minus(s(n),X0)),
inference(definition_unfolding,[],[f45,f36]) ).
fof(f57,plain,
( queens_q
| minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| plus(p(minus(s(n),sK0)),sK0) = plus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(definition_unfolding,[],[f43,f56,f56,f56,f56,f56,f56]) ).
fof(f59,plain,
( queens_q
| le(s(minus(s(n),sK1)),minus(s(n),sK0))
| ~ le(s(sK0),sK1) ),
inference(definition_unfolding,[],[f41,f36,f36]) ).
fof(f60,plain,
! [X0] :
( le(minus(s(n),X0),n)
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(definition_unfolding,[],[f48,f36]) ).
fof(f61,plain,
! [X0] :
( le(s(n0),minus(s(n),X0))
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(definition_unfolding,[],[f47,f36]) ).
fof(f62,plain,
! [X0,X1] : minus(X1,X0) = minus(minus(s(n),X0),minus(s(n),X1)),
inference(definition_unfolding,[],[f49,f36,f36]) ).
cnf(c_49,plain,
( minus(p(X0),X0) != minus(p(X1),X1)
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n)
| ~ queens_p ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_50,plain,
( plus(p(X0),X0) != plus(p(X1),X1)
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n)
| ~ queens_p ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_51,plain,
( p(X0) != p(X1)
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n)
| ~ queens_p ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_52,negated_conjecture,
( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| plus(p(minus(s(n),sK0)),sK0) = plus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1))
| queens_q ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_54,plain,
( ~ le(s(sK0),sK1)
| le(s(minus(s(n),sK1)),minus(s(n),sK0))
| queens_q ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_55,plain,
( le(sK1,n)
| queens_q ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_56,plain,
( le(s(sK0),sK1)
| queens_q ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_57,plain,
( le(sK0,n)
| queens_q ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_58,plain,
( le(s(n0),sK0)
| queens_q ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_59,negated_conjecture,
~ queens_q,
inference(cnf_transformation,[],[f46]) ).
cnf(c_60,negated_conjecture,
queens_p,
inference(cnf_transformation,[],[f44]) ).
cnf(c_61,plain,
( ~ le(s(n0),X0)
| ~ le(X0,n)
| le(minus(s(n),X0),n) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_62,plain,
( ~ le(s(n0),X0)
| ~ le(X0,n)
| le(s(n0),minus(s(n),X0)) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_63,plain,
minus(minus(s(n),X0),minus(s(n),X1)) = minus(X1,X0),
inference(cnf_transformation,[],[f62]) ).
cnf(c_64,plain,
( ~ le(X0,X1)
| ~ le(X1,X2)
| le(X0,X2) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_65,plain,
le(X0,s(X0)),
inference(cnf_transformation,[],[f51]) ).
cnf(c_66,plain,
( minus(X0,X1) != minus(X2,X3)
| plus(X0,X3) = plus(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_67,plain,
( plus(X0,X1) != plus(X2,X3)
| minus(X0,X2) = minus(X3,X1) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_69,plain,
( minus(X0,X1) != minus(X2,X3)
| minus(X0,X2) = minus(X1,X3) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_87,plain,
le(s(minus(s(n),sK1)),minus(s(n),sK0)),
inference(global_subsumption_just,[status(thm)],[c_54,c_59,c_56,c_54]) ).
cnf(c_91,plain,
( ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| p(X0) != p(X1) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_60,c_51]) ).
cnf(c_92,plain,
( p(X0) != p(X1)
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n) ),
inference(renaming,[status(thm)],[c_91]) ).
cnf(c_94,plain,
( ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| plus(p(X0),X0) != plus(p(X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_60,c_50]) ).
cnf(c_95,plain,
( plus(p(X0),X0) != plus(p(X1),X1)
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n) ),
inference(renaming,[status(thm)],[c_94]) ).
cnf(c_97,plain,
( ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| minus(p(X0),X0) != minus(p(X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_60,c_49]) ).
cnf(c_98,plain,
( minus(p(X0),X0) != minus(p(X1),X1)
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n) ),
inference(renaming,[status(thm)],[c_97]) ).
cnf(c_100,plain,
( p(minus(s(n),sK0)) = p(minus(s(n),sK1))
| plus(p(minus(s(n),sK0)),sK0) = plus(p(minus(s(n),sK1)),sK1)
| minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_59,c_52]) ).
cnf(c_101,negated_conjecture,
( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| plus(p(minus(s(n),sK0)),sK0) = plus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(renaming,[status(thm)],[c_100]) ).
cnf(c_282,negated_conjecture,
( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| plus(p(minus(s(n),sK0)),sK0) = plus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(subtyping,[status(esa)],[c_101]) ).
cnf(c_283,plain,
( minus(p(X0_13),X0_13) != minus(p(X1_13),X1_13)
| ~ le(s(X0_13),X1_13)
| ~ le(s(n0),X0_13)
| ~ le(X0_13,n)
| ~ le(X1_13,n) ),
inference(subtyping,[status(esa)],[c_98]) ).
cnf(c_284,plain,
( plus(p(X0_13),X0_13) != plus(p(X1_13),X1_13)
| ~ le(s(X0_13),X1_13)
| ~ le(s(n0),X0_13)
| ~ le(X0_13,n)
| ~ le(X1_13,n) ),
inference(subtyping,[status(esa)],[c_95]) ).
cnf(c_285,plain,
( p(X0_13) != p(X1_13)
| ~ le(s(X0_13),X1_13)
| ~ le(s(n0),X0_13)
| ~ le(X0_13,n)
| ~ le(X1_13,n) ),
inference(subtyping,[status(esa)],[c_92]) ).
cnf(c_286,plain,
le(s(minus(s(n),sK1)),minus(s(n),sK0)),
inference(subtyping,[status(esa)],[c_87]) ).
cnf(c_291,plain,
( minus(X0_13,X1_13) != minus(X2_13,X3_13)
| minus(X0_13,X2_13) = minus(X1_13,X3_13) ),
inference(subtyping,[status(esa)],[c_69]) ).
cnf(c_292,plain,
( plus(X0_13,X1_13) != plus(X2_13,X3_13)
| minus(X0_13,X2_13) = minus(X3_13,X1_13) ),
inference(subtyping,[status(esa)],[c_67]) ).
cnf(c_293,plain,
( minus(X0_13,X1_13) != minus(X2_13,X3_13)
| plus(X0_13,X3_13) = plus(X1_13,X2_13) ),
inference(subtyping,[status(esa)],[c_66]) ).
cnf(c_294,plain,
le(X0_13,s(X0_13)),
inference(subtyping,[status(esa)],[c_65]) ).
cnf(c_295,plain,
( ~ le(X0_13,X1_13)
| ~ le(X1_13,X2_13)
| le(X0_13,X2_13) ),
inference(subtyping,[status(esa)],[c_64]) ).
cnf(c_296,plain,
minus(minus(s(n),X0_13),minus(s(n),X1_13)) = minus(X1_13,X0_13),
inference(subtyping,[status(esa)],[c_63]) ).
cnf(c_297,plain,
( ~ le(s(n0),X0_13)
| ~ le(X0_13,n)
| le(s(n0),minus(s(n),X0_13)) ),
inference(subtyping,[status(esa)],[c_62]) ).
cnf(c_298,plain,
( ~ le(s(n0),X0_13)
| ~ le(X0_13,n)
| le(minus(s(n),X0_13),n) ),
inference(subtyping,[status(esa)],[c_61]) ).
cnf(c_300,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_302,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_306,plain,
( X0_13 != X1_13
| X2_13 != X3_13
| ~ le(X1_13,X3_13)
| le(X0_13,X2_13) ),
theory(equality) ).
cnf(c_572,plain,
( ~ le(X0_13,s(X0_13))
| ~ le(X1_13,X0_13)
| le(X1_13,s(X0_13)) ),
inference(instantiation,[status(thm)],[c_295]) ).
cnf(c_579,plain,
( ~ le(X0_13,s(sK0))
| ~ le(s(sK0),sK1)
| le(X0_13,sK1) ),
inference(instantiation,[status(thm)],[c_295]) ).
cnf(c_588,plain,
( ~ le(s(n0),sK1)
| ~ le(sK1,n)
| le(s(n0),minus(s(n),sK1)) ),
inference(instantiation,[status(thm)],[c_297]) ).
cnf(c_599,plain,
( ~ le(s(n0),sK0)
| ~ le(sK0,n)
| le(minus(s(n),sK0),n) ),
inference(instantiation,[status(thm)],[c_298]) ).
cnf(c_615,plain,
( ~ le(s(n0),sK0)
| ~ le(sK0,s(sK0))
| le(s(n0),s(sK0)) ),
inference(instantiation,[status(thm)],[c_572]) ).
cnf(c_643,plain,
( ~ le(s(X0_13),X1_13)
| le(X0_13,X1_13) ),
inference(superposition,[status(thm)],[c_294,c_295]) ).
cnf(c_690,plain,
( minus(X0_13,X1_13) != minus(X2_13,X3_13)
| minus(X0_13,minus(s(n),X3_13)) = minus(X1_13,minus(s(n),X2_13)) ),
inference(superposition,[status(thm)],[c_296,c_291]) ).
cnf(c_756,plain,
le(minus(s(n),sK1),minus(s(n),sK0)),
inference(superposition,[status(thm)],[c_286,c_643]) ).
cnf(c_843,plain,
( ~ le(X0_13,minus(s(n),X1_13))
| ~ le(minus(s(n),X1_13),n)
| le(X0_13,n) ),
inference(instantiation,[status(thm)],[c_295]) ).
cnf(c_890,plain,
( plus(p(X0_13),X0_13) != plus(p(minus(s(n),X1_13)),minus(s(n),X1_13))
| ~ le(s(X0_13),minus(s(n),X1_13))
| ~ le(minus(s(n),X1_13),n)
| ~ le(s(n0),X0_13)
| ~ le(X0_13,n) ),
inference(instantiation,[status(thm)],[c_284]) ).
cnf(c_981,plain,
( X0_13 != X1_13
| X1_13 = X0_13 ),
inference(resolution,[status(thm)],[c_302,c_300]) ).
cnf(c_1044,plain,
le(sK0,s(sK0)),
inference(instantiation,[status(thm)],[c_294]) ).
cnf(c_1064,plain,
( plus(p(minus(s(n),sK0)),sK0) != plus(X0_13,X1_13)
| minus(p(minus(s(n),sK1)),X0_13) = minus(X1_13,sK1)
| minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(superposition,[status(thm)],[c_282,c_292]) ).
cnf(c_1084,plain,
( minus(X0_13,X1_13) != minus(X2_13,X3_13)
| plus(X0_13,minus(s(n),X2_13)) = plus(X1_13,minus(s(n),X3_13)) ),
inference(superposition,[status(thm)],[c_296,c_293]) ).
cnf(c_1133,plain,
( minus(p(minus(s(n),sK1)),p(minus(s(n),sK0))) = minus(sK0,sK1)
| minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(equality_resolution,[status(thm)],[c_1064]) ).
cnf(c_1189,plain,
( X0_13 != X1_13
| ~ le(X1_13,X2_13)
| le(X0_13,X2_13) ),
inference(resolution,[status(thm)],[c_306,c_300]) ).
cnf(c_1327,plain,
( ~ le(minus(s(n),sK1),minus(s(n),sK0))
| ~ le(minus(s(n),sK0),n)
| le(minus(s(n),sK1),n) ),
inference(instantiation,[status(thm)],[c_843]) ).
cnf(c_1372,plain,
( ~ le(s(n0),s(sK0))
| ~ le(s(sK0),sK1)
| le(s(n0),sK1) ),
inference(instantiation,[status(thm)],[c_579]) ).
cnf(c_1518,plain,
( plus(p(minus(s(n),sK1)),minus(s(n),sK1)) != plus(p(minus(s(n),sK0)),minus(s(n),sK0))
| ~ le(s(minus(s(n),sK1)),minus(s(n),sK0))
| ~ le(s(n0),minus(s(n),sK1))
| ~ le(minus(s(n),sK0),n)
| ~ le(minus(s(n),sK1),n) ),
inference(instantiation,[status(thm)],[c_890]) ).
cnf(c_2747,plain,
( minus(p(minus(s(n),sK1)),minus(s(n),sK1)) != minus(p(X0_13),X0_13)
| ~ le(s(minus(s(n),sK1)),X0_13)
| ~ le(s(n0),minus(s(n),sK1))
| ~ le(minus(s(n),sK1),n)
| ~ le(X0_13,n) ),
inference(instantiation,[status(thm)],[c_283]) ).
cnf(c_2918,plain,
( minus(p(minus(s(n),sK1)),minus(s(n),sK1)) != minus(p(minus(s(n),X0_13)),minus(s(n),X0_13))
| ~ le(s(minus(s(n),sK1)),minus(s(n),X0_13))
| ~ le(s(n0),minus(s(n),sK1))
| ~ le(minus(s(n),X0_13),n)
| ~ le(minus(s(n),sK1),n) ),
inference(instantiation,[status(thm)],[c_2747]) ).
cnf(c_3261,plain,
( minus(p(minus(s(n),sK1)),minus(s(n),sK1)) != minus(p(minus(s(n),sK0)),minus(s(n),sK0))
| ~ le(s(minus(s(n),sK1)),minus(s(n),sK0))
| ~ le(s(n0),minus(s(n),sK1))
| ~ le(minus(s(n),sK0),n)
| ~ le(minus(s(n),sK1),n) ),
inference(instantiation,[status(thm)],[c_2918]) ).
cnf(c_5612,plain,
( minus(p(minus(s(n),sK0)),p(minus(s(n),sK1))) = minus(sK1,sK0)
| minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(resolution,[status(thm)],[c_292,c_282]) ).
cnf(c_6948,plain,
( X0_13 != minus(sK1,sK0)
| minus(p(minus(s(n),sK0)),p(minus(s(n),sK1))) = X0_13
| minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(resolution,[status(thm)],[c_5612,c_302]) ).
cnf(c_7656,plain,
( minus(p(minus(s(n),sK1)),p(minus(s(n),sK0))) != minus(sK1,sK0)
| plus(p(minus(s(n),sK1)),minus(s(n),sK1)) = plus(p(minus(s(n),sK0)),minus(s(n),sK0)) ),
inference(instantiation,[status(thm)],[c_1084]) ).
cnf(c_7683,plain,
( minus(p(minus(s(n),sK1)),p(minus(s(n),sK0))) != minus(sK0,sK1)
| minus(p(minus(s(n),sK1)),minus(s(n),sK1)) = minus(p(minus(s(n),sK0)),minus(s(n),sK0)) ),
inference(instantiation,[status(thm)],[c_690]) ).
cnf(c_7979,plain,
( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_6948,c_59,c_57,c_55,c_58,c_56,c_54,c_588,c_599,c_615,c_756,c_1044,c_1133,c_1327,c_1372,c_3261,c_7683]) ).
cnf(c_7993,plain,
( minus(p(minus(s(n),sK1)),sK1) = minus(p(minus(s(n),sK0)),sK0)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(resolution,[status(thm)],[c_7979,c_981]) ).
cnf(c_7994,plain,
( ~ le(minus(p(minus(s(n),sK1)),sK1),X0_13)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1))
| le(minus(p(minus(s(n),sK0)),sK0),X0_13) ),
inference(resolution,[status(thm)],[c_7979,c_1189]) ).
cnf(c_8017,plain,
( minus(p(minus(s(n),sK1)),p(minus(s(n),sK0))) = minus(sK1,sK0)
| p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ),
inference(resolution,[status(thm)],[c_7993,c_291]) ).
cnf(c_8025,plain,
p(minus(s(n),sK0)) = p(minus(s(n),sK1)),
inference(global_subsumption_just,[status(thm)],[c_7994,c_59,c_57,c_55,c_58,c_56,c_54,c_588,c_599,c_615,c_756,c_1044,c_1327,c_1372,c_1518,c_7656,c_8017]) ).
cnf(c_8031,plain,
p(minus(s(n),sK1)) = p(minus(s(n),sK0)),
inference(resolution,[status(thm)],[c_8025,c_981]) ).
cnf(c_17533,plain,
( ~ le(s(minus(s(n),sK1)),minus(s(n),sK0))
| ~ le(s(n0),minus(s(n),sK1))
| ~ le(minus(s(n),sK0),n)
| ~ le(minus(s(n),sK1),n) ),
inference(resolution,[status(thm)],[c_285,c_8031]) ).
cnf(c_17534,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17533,c_1372,c_1327,c_1044,c_756,c_615,c_599,c_588,c_54,c_56,c_58,c_55,c_57,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ133+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 21:19:31 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.02/1.67 % SZS status Started for theBenchmark.p
% 8.02/1.67 % SZS status Theorem for theBenchmark.p
% 8.02/1.67
% 8.02/1.67 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 8.02/1.67
% 8.02/1.67 ------ iProver source info
% 8.02/1.67
% 8.02/1.67 git: date: 2024-05-02 19:28:25 +0000
% 8.02/1.67 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 8.02/1.67 git: non_committed_changes: false
% 8.02/1.67
% 8.02/1.67 ------ Parsing...
% 8.02/1.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.02/1.67
% 8.02/1.67 ------ Preprocessing... sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 8.02/1.67
% 8.02/1.67 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 8.02/1.67
% 8.02/1.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.02/1.67 ------ Proving...
% 8.02/1.67 ------ Problem Properties
% 8.02/1.67
% 8.02/1.67
% 8.02/1.67 clauses 17
% 8.02/1.67 conjectures 1
% 8.02/1.67 EPR 3
% 8.02/1.67 Horn 16
% 8.02/1.67 unary 7
% 8.02/1.67 binary 3
% 8.02/1.67 lits 40
% 8.02/1.67 lits eq 13
% 8.02/1.67 fd_pure 0
% 8.02/1.67 fd_pseudo 0
% 8.02/1.67 fd_cond 0
% 8.02/1.67 fd_pseudo_cond 0
% 8.02/1.67 AC symbols 0
% 8.02/1.67
% 8.02/1.67 ------ Input Options Time Limit: Unbounded
% 8.02/1.67
% 8.02/1.67
% 8.02/1.67 ------
% 8.02/1.67 Current options:
% 8.02/1.67 ------
% 8.02/1.67
% 8.02/1.67
% 8.02/1.67
% 8.02/1.67
% 8.02/1.67 ------ Proving...
% 8.02/1.67
% 8.02/1.67
% 8.02/1.67 % SZS status Theorem for theBenchmark.p
% 8.02/1.67
% 8.02/1.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.02/1.68
% 8.02/1.68
%------------------------------------------------------------------------------