%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PUZ133+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 02:33:01 PM UTC 2026
% Result : Theorem 4.86s 1.75s
% Output : CNFRefutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 134 ( 27 unt; 0 def)
% Number of atoms : 445 ( 167 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 532 ( 221 ~; 242 |; 56 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 191 ( 0 sgn 183 !; 8 ?; 106 :)
% 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/sandbox2/benchmark/theBenchmark.p',queens_p) ).
fof(f2,axiom,
! [X0] : perm(X0) = minus(s(n),X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',queens_q) ).
fof(f4,conjecture,
( ( ! [X0] : q(X0) = p(perm(X0))
& queens_p )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_sym) ).
fof(f5,negated_conjecture,
~ ( ( ! [X0] : q(X0) = p(perm(X0))
& queens_p )
=> queens_q ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,axiom,
! [X0] :
( ( le(X0,n)
& le(s(n0),X0) )
=> ( le(perm(X0),n)
& le(s(n0),perm(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation_range) ).
fof(f7,axiom,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation_another_one) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( le(X1,X2)
& le(X0,X1) )
=> le(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',le_trans) ).
fof(f9,axiom,
! [X0] : le(X0,s(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_le) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( plus(X0,X1) = plus(X2,X3)
<=> minus(X0,X2) = minus(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( minus(X0,X1) = minus(X2,X3)
<=> minus(X0,X2) = minus(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus1) ).
fof(f12,plain,
( ~ 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) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
( ~ 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) ) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ? [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 ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,plain,
( ? [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 ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
( ! [X0] : q(X0) = p(perm(X0))
& queens_p
& ~ queens_q ),
inference(ennf_transformation,[],[f5]) ).
fof(f17,plain,
( ! [X0] : q(X0) = p(perm(X0))
& queens_p
& ~ queens_q ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| ( le(perm(X0),n)
& le(s(n0),perm(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| ( le(perm(X0),n)
& le(s(n0),perm(X0)) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ le(X1,X2)
| ~ le(X0,X1)
| le(X0,X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ le(X1,X2)
| ~ le(X0,X1)
| le(X0,X2) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
( ? [X0,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(X0),X0) = minus(q(X1),X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| q(X0) = q(X1) ) )
| queens_q ),
inference(nnf_transformation,[],[f15]) ).
fof(f23,plain,
( ? [X0,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(X0),X0) = minus(q(X1),X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| q(X0) = q(X1) ) )
| queens_q ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( ( ( ~ 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)
& ( minus(q(sK0),sK0) = minus(q(sK1),sK1)
| plus(q(sK0),sK0) = plus(q(sK1),sK1)
| q(sK0) = q(sK1) ) )
| queens_q ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).
fof(f25,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,[],[f10]) ).
fof(f26,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,[],[f11]) ).
fof(f27,plain,
! [X0,X1] :
( ~ queens_p
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| minus(p(X0),X0) != minus(p(X1),X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( ~ queens_p
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| plus(p(X0),X0) != plus(p(X1),X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( ~ queens_p
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| p(X0) != p(X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X0] : perm(X0) = minus(s(n),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f31,plain,
( ~ le(s(sK0),sK1)
| le(s(perm(sK1)),perm(sK0))
| queens_q ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
( le(sK1,n)
| queens_q ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
( le(s(sK0),sK1)
| queens_q ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
( le(sK0,n)
| queens_q ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
( le(s(n0),sK0)
| queens_q ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
( minus(q(sK0),sK0) = minus(q(sK1),sK1)
| plus(q(sK0),sK0) = plus(q(sK1),sK1)
| q(sK0) = q(sK1)
| queens_q ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X0] : q(X0) = p(perm(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f39,plain,
queens_p,
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
~ queens_q,
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| le(perm(X0),n) ),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| le(s(n0),perm(X0)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ le(X1,X2)
| ~ le(X0,X1)
| le(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0] : le(X0,s(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( plus(X0,X1) != plus(X2,X3)
| minus(X0,X2) = minus(X3,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( minus(X0,X2) != minus(X3,X1)
| plus(X0,X1) = plus(X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( minus(X0,X1) != minus(X2,X3)
| minus(X0,X2) = minus(X1,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f50,plain,
! [X0] : q(X0) = p(minus(s(n),X0)),
inference(definition_unfolding,[],[f38,f30]) ).
fof(f51,plain,
( 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(definition_unfolding,[],[f37,f50,f50,f50,f50,f50,f50]) ).
fof(f53,plain,
( ~ le(s(sK0),sK1)
| le(s(minus(s(n),sK1)),minus(s(n),sK0))
| queens_q ),
inference(definition_unfolding,[],[f31,f30,f30]) ).
fof(f54,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| le(s(n0),minus(s(n),X0)) ),
inference(definition_unfolding,[],[f42,f30]) ).
fof(f55,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| le(minus(s(n),X0),n) ),
inference(definition_unfolding,[],[f41,f30]) ).
fof(f56,plain,
! [X0,X1] : minus(X1,X0) = minus(minus(s(n),X0),minus(s(n),X1)),
inference(definition_unfolding,[],[f43,f30,f30]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ queens_p
| ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| ( p(X0) != p(X1) ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ~ queens_p
| ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| ( plus(p(X0),X0) != plus(p(X1),X1) ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ~ queens_p
| ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| ( minus(p(X0),X0) != minus(p(X1),X1) ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,negated_conjecture,
( queens_q
| ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( 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) ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_53,plain,
( queens_q
| le(s(n0),sK0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_54,plain,
( queens_q
| le(sK0,n) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
( queens_q
| le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_56,plain,
( queens_q
| le(sK1,n) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_58,plain,
( queens_q
| le(s(minus(s(n),sK1)),minus(s(n),sK0))
| ~ le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_59,negated_conjecture,
~ queens_q,
inference(cnf_transformation,[],[f40]) ).
tcf(c_60,negated_conjecture,
queens_p,
inference(cnf_transformation,[],[f39]) ).
tcf(c_61,plain,
! [X0: $i] :
( le(s(n0),minus(s(n),X0))
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_62,plain,
! [X0: $i] :
( le(minus(s(n),X0),n)
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : minus(minus(s(n),X0),minus(s(n),X1)) = minus(X1,X0),
inference(cnf_transformation,[],[f56]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( le(X0,X2)
| ~ le(X1,X2)
| ~ le(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i] : le(X0,s(X0)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( plus(X0,X3) = plus(X1,X2) )
| ( minus(X0,X1) != minus(X2,X3) ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( minus(X0,X2) = minus(X3,X1) )
| ( plus(X0,X1) != plus(X2,X3) ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( minus(X0,X2) = minus(X1,X3) )
| ( minus(X0,X1) != minus(X2,X3) ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_87,plain,
le(s(minus(s(n),sK1)),minus(s(n),sK0)),
inference(global_subsumption_just,[status(thm)],[c_58,c_59,c_55,c_58]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ( p(X0) != p(X1) )
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_60,c_49]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| ( p(X0) != p(X1) ) ),
inference(renaming,[status(thm)],[c_91]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( ( minus(p(X0),X0) != minus(p(X1),X1) )
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_60,c_51]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| ( minus(p(X0),X0) != minus(p(X1),X1) ) ),
inference(renaming,[status(thm)],[c_94]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( ( plus(p(X0),X0) != plus(p(X1),X1) )
| ~ le(s(X0),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(X1,n) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_60,c_50]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ~ le(X1,n)
| ~ le(X0,n)
| ~ le(s(n0),X0)
| ~ le(s(X0),X1)
| ( plus(p(X0),X0) != plus(p(X1),X1) ) ),
inference(renaming,[status(thm)],[c_97]) ).
tcf(c_100,plain,
( ( 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) )
| ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_59,c_52]) ).
tcf(c_101,negated_conjecture,
( ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( 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) ) ),
inference(renaming,[status(thm)],[c_100]) ).
tcf(c_282,negated_conjecture,
( ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( 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) ) ),
inference(subtyping,[status(esa)],[c_101]) ).
tcf(c_283,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ~ le(X1_iProver_minus_1,n)
| ~ le(X0_iProver_minus_1,n)
| ~ le(s(n0),X0_iProver_minus_1)
| ~ le(s(X0_iProver_minus_1),X1_iProver_minus_1)
| ( plus(p(X0_iProver_minus_1),X0_iProver_minus_1) != plus(p(X1_iProver_minus_1),X1_iProver_minus_1) ) ),
inference(subtyping,[status(esa)],[c_98]) ).
tcf(c_284,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ~ le(X1_iProver_minus_1,n)
| ~ le(X0_iProver_minus_1,n)
| ~ le(s(n0),X0_iProver_minus_1)
| ~ le(s(X0_iProver_minus_1),X1_iProver_minus_1)
| ( minus(p(X0_iProver_minus_1),X0_iProver_minus_1) != minus(p(X1_iProver_minus_1),X1_iProver_minus_1) ) ),
inference(subtyping,[status(esa)],[c_95]) ).
tcf(c_285,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ~ le(X1_iProver_minus_1,n)
| ~ le(X0_iProver_minus_1,n)
| ~ le(s(n0),X0_iProver_minus_1)
| ~ le(s(X0_iProver_minus_1),X1_iProver_minus_1)
| ( p(X0_iProver_minus_1) != p(X1_iProver_minus_1) ) ),
inference(subtyping,[status(esa)],[c_92]) ).
tcf(c_286,plain,
le(s(minus(s(n),sK1)),minus(s(n),sK0)),
inference(subtyping,[status(esa)],[c_87]) ).
tcf(c_291,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1,X2_iProver_minus_1: iProver_minus_1,X3_iProver_minus_1: iProver_minus_1] :
( ( minus(X0_iProver_minus_1,X2_iProver_minus_1) = minus(X1_iProver_minus_1,X3_iProver_minus_1) )
| ( minus(X0_iProver_minus_1,X1_iProver_minus_1) != minus(X2_iProver_minus_1,X3_iProver_minus_1) ) ),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_292,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1,X2_iProver_minus_1: iProver_minus_1,X3_iProver_minus_1: iProver_minus_1] :
( ( minus(X0_iProver_minus_1,X2_iProver_minus_1) = minus(X3_iProver_minus_1,X1_iProver_minus_1) )
| ( plus(X0_iProver_minus_1,X1_iProver_minus_1) != plus(X2_iProver_minus_1,X3_iProver_minus_1) ) ),
inference(subtyping,[status(esa)],[c_67]) ).
tcf(c_293,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1,X2_iProver_minus_1: iProver_minus_1,X3_iProver_minus_1: iProver_minus_1] :
( ( plus(X0_iProver_minus_1,X3_iProver_minus_1) = plus(X1_iProver_minus_1,X2_iProver_minus_1) )
| ( minus(X0_iProver_minus_1,X1_iProver_minus_1) != minus(X2_iProver_minus_1,X3_iProver_minus_1) ) ),
inference(subtyping,[status(esa)],[c_66]) ).
tcf(c_294,plain,
! [X0_iProver_minus_1: iProver_minus_1] : le(X0_iProver_minus_1,s(X0_iProver_minus_1)),
inference(subtyping,[status(esa)],[c_65]) ).
tcf(c_295,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1,X2_iProver_minus_1: iProver_minus_1] :
( le(X0_iProver_minus_1,X2_iProver_minus_1)
| ~ le(X1_iProver_minus_1,X2_iProver_minus_1)
| ~ le(X0_iProver_minus_1,X1_iProver_minus_1) ),
inference(subtyping,[status(esa)],[c_64]) ).
tcf(c_296,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] : minus(minus(s(n),X0_iProver_minus_1),minus(s(n),X1_iProver_minus_1)) = minus(X1_iProver_minus_1,X0_iProver_minus_1),
inference(subtyping,[status(esa)],[c_63]) ).
tcf(c_297,plain,
! [X0_iProver_minus_1: iProver_minus_1] :
( le(minus(s(n),X0_iProver_minus_1),n)
| ~ le(X0_iProver_minus_1,n)
| ~ le(s(n0),X0_iProver_minus_1) ),
inference(subtyping,[status(esa)],[c_62]) ).
tcf(c_298,plain,
! [X0_iProver_minus_1: iProver_minus_1] :
( le(s(n0),minus(s(n),X0_iProver_minus_1))
| ~ le(X0_iProver_minus_1,n)
| ~ le(s(n0),X0_iProver_minus_1) ),
inference(subtyping,[status(esa)],[c_61]) ).
tcf(c_301,plain,
! [X0_iProver_minus_1: iProver_minus_1] : X0_iProver_minus_1 = X0_iProver_minus_1,
theory(equality) ).
tcf(c_303,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1,X2_iProver_minus_1: iProver_minus_1] :
( ( X2_iProver_minus_1 = X0_iProver_minus_1 )
| ( X2_iProver_minus_1 != X1_iProver_minus_1 )
| ( X0_iProver_minus_1 != X1_iProver_minus_1 ) ),
theory(equality) ).
tcf(c_572,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( le(X1_iProver_minus_1,s(X0_iProver_minus_1))
| ~ le(X1_iProver_minus_1,X0_iProver_minus_1)
| ~ le(X0_iProver_minus_1,s(X0_iProver_minus_1)) ),
inference(instantiation,[status(thm)],[c_295]) ).
tcf(c_583,plain,
! [X0_iProver_minus_1: iProver_minus_1] :
( le(X0_iProver_minus_1,sK1)
| ~ le(s(sK0),sK1)
| ~ le(X0_iProver_minus_1,s(sK0)) ),
inference(instantiation,[status(thm)],[c_295]) ).
tcf(c_588,plain,
( le(minus(s(n),sK0),n)
| ~ le(sK0,n)
| ~ le(s(n0),sK0) ),
inference(instantiation,[status(thm)],[c_297]) ).
tcf(c_599,plain,
( le(s(n0),minus(s(n),sK1))
| ~ le(sK1,n)
| ~ le(s(n0),sK1) ),
inference(instantiation,[status(thm)],[c_298]) ).
tcf(c_611,plain,
( le(s(n0),s(sK0))
| ~ le(sK0,s(sK0))
| ~ le(s(n0),sK0) ),
inference(instantiation,[status(thm)],[c_572]) ).
tcf(c_643,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( le(X0_iProver_minus_1,X1_iProver_minus_1)
| ~ le(s(X0_iProver_minus_1),X1_iProver_minus_1) ),
inference(superposition,[status(thm)],[c_294,c_295]) ).
tcf(c_688,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1,X2_iProver_minus_1: iProver_minus_1,X3_iProver_minus_1: iProver_minus_1] :
( ( minus(X0_iProver_minus_1,minus(s(n),X3_iProver_minus_1)) = minus(X1_iProver_minus_1,minus(s(n),X2_iProver_minus_1)) )
| ( minus(X0_iProver_minus_1,X1_iProver_minus_1) != minus(X2_iProver_minus_1,X3_iProver_minus_1) ) ),
inference(superposition,[status(thm)],[c_296,c_291]) ).
tcf(c_689,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] : minus(X0_iProver_minus_1,X0_iProver_minus_1) = minus(X1_iProver_minus_1,X1_iProver_minus_1),
inference(equality_resolution,[status(thm)],[c_291]) ).
tcf(c_721,plain,
( ~ le(minus(s(n),sK1),n)
| ~ le(minus(s(n),sK0),n)
| ~ le(s(n0),minus(s(n),sK1))
| ~ le(s(minus(s(n),sK1)),minus(s(n),sK0))
| ( p(minus(s(n),sK1)) != p(minus(s(n),sK0)) ) ),
inference(instantiation,[status(thm)],[c_285]) ).
tcf(c_738,plain,
le(minus(s(n),sK1),minus(s(n),sK0)),
inference(superposition,[status(thm)],[c_286,c_643]) ).
tcf(c_810,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( le(X0_iProver_minus_1,n)
| ~ le(minus(s(n),X1_iProver_minus_1),n)
| ~ le(X0_iProver_minus_1,minus(s(n),X1_iProver_minus_1)) ),
inference(instantiation,[status(thm)],[c_295]) ).
tcf(c_887,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ~ le(X0_iProver_minus_1,n)
| ~ le(s(n0),X0_iProver_minus_1)
| ~ le(minus(s(n),X1_iProver_minus_1),n)
| ~ le(s(X0_iProver_minus_1),minus(s(n),X1_iProver_minus_1))
| ( plus(p(X0_iProver_minus_1),X0_iProver_minus_1) != plus(p(minus(s(n),X1_iProver_minus_1)),minus(s(n),X1_iProver_minus_1)) ) ),
inference(instantiation,[status(thm)],[c_283]) ).
tcf(c_892,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ~ le(X0_iProver_minus_1,n)
| ~ le(s(n0),X0_iProver_minus_1)
| ~ le(minus(s(n),X1_iProver_minus_1),n)
| ~ le(s(X0_iProver_minus_1),minus(s(n),X1_iProver_minus_1))
| ( minus(p(X0_iProver_minus_1),X0_iProver_minus_1) != minus(p(minus(s(n),X1_iProver_minus_1)),minus(s(n),X1_iProver_minus_1)) ) ),
inference(instantiation,[status(thm)],[c_284]) ).
tcf(c_1012,plain,
le(sK0,s(sK0)),
inference(instantiation,[status(thm)],[c_294]) ).
tcf(c_1066,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) )
| ( minus(p(minus(s(n),sK1)),X0_iProver_minus_1) = minus(X1_iProver_minus_1,sK1) )
| ( plus(p(minus(s(n),sK0)),sK0) != plus(X0_iProver_minus_1,X1_iProver_minus_1) ) ),
inference(superposition,[status(thm)],[c_282,c_292]) ).
tcf(c_1093,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1,X2_iProver_minus_1: iProver_minus_1,X3_iProver_minus_1: iProver_minus_1] :
( ( plus(X0_iProver_minus_1,minus(s(n),X2_iProver_minus_1)) = plus(X1_iProver_minus_1,minus(s(n),X3_iProver_minus_1)) )
| ( minus(X0_iProver_minus_1,X1_iProver_minus_1) != minus(X2_iProver_minus_1,X3_iProver_minus_1) ) ),
inference(superposition,[status(thm)],[c_296,c_293]) ).
tcf(c_1167,plain,
( ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) )
| ( minus(p(minus(s(n),sK1)),p(minus(s(n),sK1))) = minus(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_282,c_1066]) ).
tcf(c_1168,plain,
( ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) )
| ( minus(p(minus(s(n),sK1)),p(minus(s(n),sK0))) = minus(sK0,sK1) ) ),
inference(equality_resolution,[status(thm)],[c_1066]) ).
tcf(c_1248,plain,
( le(minus(s(n),sK1),n)
| ~ le(minus(s(n),sK0),n)
| ~ le(minus(s(n),sK1),minus(s(n),sK0)) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1315,plain,
( le(s(n0),sK1)
| ~ le(s(sK0),sK1)
| ~ le(s(n0),s(sK0)) ),
inference(instantiation,[status(thm)],[c_583]) ).
tcf(c_1352,plain,
( ~ le(minus(s(n),sK1),n)
| ~ le(minus(s(n),sK0),n)
| ~ le(s(n0),minus(s(n),sK1))
| ~ le(s(minus(s(n),sK1)),minus(s(n),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_887]) ).
tcf(c_1376,plain,
( ~ le(minus(s(n),sK1),n)
| ~ le(minus(s(n),sK0),n)
| ~ le(s(n0),minus(s(n),sK1))
| ~ le(s(minus(s(n),sK1)),minus(s(n),sK0))
| ( 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_892]) ).
tcf(c_1459,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) )
| ( minus(X0_iProver_minus_1,p(minus(s(n),sK1))) = minus(X1_iProver_minus_1,p(minus(s(n),sK1))) )
| ( minus(X0_iProver_minus_1,X1_iProver_minus_1) != minus(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_1167,c_291]) ).
tcf(c_2616,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ( p(minus(s(n),sK1)) = p(X1_iProver_minus_1) )
| ( p(X1_iProver_minus_1) != X0_iProver_minus_1 )
| ( p(minus(s(n),sK1)) != X0_iProver_minus_1 ) ),
inference(instantiation,[status(thm)],[c_303]) ).
tcf(c_2919,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ( p(minus(s(n),sK1)) = p(X1_iProver_minus_1) )
| ( p(X1_iProver_minus_1) != p(X0_iProver_minus_1) )
| ( p(minus(s(n),sK1)) != p(X0_iProver_minus_1) ) ),
inference(instantiation,[status(thm)],[c_2616]) ).
tcf(c_3886,plain,
p(minus(s(n),sK1)) = p(minus(s(n),sK1)),
inference(instantiation,[status(thm)],[c_301]) ).
tcf(c_4047,plain,
! [X0_iProver_minus_1: iProver_minus_1] :
( ( p(minus(s(n),sK1)) = p(X0_iProver_minus_1) )
| ( p(X0_iProver_minus_1) != p(minus(s(n),sK1)) )
| ( p(minus(s(n),sK1)) != p(minus(s(n),sK1)) ) ),
inference(instantiation,[status(thm)],[c_2919]) ).
tcf(c_5705,plain,
( ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) )
| ( minus(p(minus(s(n),sK1)),p(minus(s(n),sK1))) = minus(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_282,c_1066]) ).
tcf(c_5734,plain,
! [X0_iProver_minus_1: iProver_minus_1] :
( ( minus(X0_iProver_minus_1,X0_iProver_minus_1) = minus(sK1,sK1) )
| ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) ) ),
inference(superposition,[status(thm)],[c_689,c_5705]) ).
tcf(c_5735,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1,X2_iProver_minus_1: iProver_minus_1] :
( ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) )
| ( minus(X1_iProver_minus_1,p(minus(s(n),sK1))) = minus(X2_iProver_minus_1,p(minus(s(n),sK1))) )
| ( minus(X0_iProver_minus_1,X0_iProver_minus_1) != minus(X1_iProver_minus_1,X2_iProver_minus_1) ) ),
inference(superposition,[status(thm)],[c_689,c_1459]) ).
tcf(c_5821,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ( minus(X1_iProver_minus_1,X1_iProver_minus_1) = minus(sK1,sK1) )
| ( p(minus(s(n),sK0)) = p(minus(s(n),sK1)) )
| ( minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1) )
| ( minus(p(minus(s(n),sK1)),p(minus(s(n),sK1))) = minus(sK1,p(minus(s(n),sK1))) )
| ( minus(p(minus(s(n),sK0)),sK0) != minus(X0_iProver_minus_1,X0_iProver_minus_1) ) ),
inference(superposition,[status(thm)],[c_5734,c_5735]) ).
tcf(c_7434,plain,
( ( minus(p(minus(s(n),sK1)),minus(s(n),sK1)) = minus(p(minus(s(n),sK0)),minus(s(n),sK0)) )
| ( minus(p(minus(s(n),sK1)),p(minus(s(n),sK0))) != minus(sK0,sK1) ) ),
inference(instantiation,[status(thm)],[c_688]) ).
tcf(c_7490,plain,
( ( plus(p(minus(s(n),sK1)),minus(s(n),sK1)) = plus(p(minus(s(n),sK0)),minus(s(n),sK0)) )
| ( minus(p(minus(s(n),sK1)),p(minus(s(n),sK0))) != minus(sK1,sK0) ) ),
inference(instantiation,[status(thm)],[c_1093]) ).
tcf(c_8931,plain,
( ( p(minus(s(n),sK1)) = p(minus(s(n),sK0)) )
| ( p(minus(s(n),sK1)) != p(minus(s(n),sK1)) )
| ( p(minus(s(n),sK0)) != p(minus(s(n),sK1)) ) ),
inference(instantiation,[status(thm)],[c_4047]) ).
tcf(c_9007,plain,
minus(p(minus(s(n),sK0)),sK0) = minus(p(minus(s(n),sK1)),sK1),
inference(global_subsumption_just,[status(thm)],[c_5821,c_59,c_56,c_54,c_55,c_53,c_58,c_588,c_599,c_611,c_721,c_738,c_1012,c_1168,c_1248,c_1315,c_1376,c_3886,c_7434,c_8931]) ).
tcf(c_9016,plain,
! [X0_iProver_minus_1: iProver_minus_1,X1_iProver_minus_1: iProver_minus_1] :
( ( minus(p(minus(s(n),sK1)),X0_iProver_minus_1) = minus(sK1,X1_iProver_minus_1) )
| ( minus(p(minus(s(n),sK0)),sK0) != minus(X0_iProver_minus_1,X1_iProver_minus_1) ) ),
inference(superposition,[status(thm)],[c_9007,c_291]) ).
tcf(c_9092,plain,
minus(p(minus(s(n),sK1)),p(minus(s(n),sK0))) = minus(sK1,sK0),
inference(equality_resolution,[status(thm)],[c_9016]) ).
tcf(c_9093,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9092,c_7490,c_1352,c_1315,c_1248,c_1012,c_738,c_611,c_599,c_588,c_58,c_53,c_55,c_54,c_56,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ133+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 06:57:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 4.86/1.75 % SZS status Started for theBenchmark.p
% 4.86/1.75 % SZS status Theorem for theBenchmark.p
% 4.86/1.75
% 4.86/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.86/1.75
% 4.86/1.75 % ------ iProver source info
% 4.86/1.75
% 4.86/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 4.86/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.86/1.75 % git: non_committed_changes: false
% 4.86/1.75
% 4.86/1.75 % ------ Parsing...
% 4.86/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.86/1.75
% 4.86/1.75 % ------ 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 %
% 4.86/1.75
% 4.86/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.86/1.75
% 4.86/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.86/1.75 % ------ Proving...
% 4.86/1.75 % ------ Problem Properties
% 4.86/1.75
% 4.86/1.75 %
% 4.86/1.75 % clauses 17
% 4.86/1.75 % conjectures 1
% 4.86/1.75 % EPR 3
% 4.86/1.75 % Horn 16
% 4.86/1.75 % unary 7
% 4.86/1.75 % binary 3
% 4.86/1.75 % lits 40
% 4.86/1.75 % lits eq 13
% 4.86/1.75 % fd_pure 0
% 4.86/1.75 % fd_pseudo 0
% 4.86/1.75 % fd_cond 0
% 4.86/1.75 % fd_pseudo_cond 0
% 4.86/1.75 % AC symbols 0
% 4.86/1.75
% 4.86/1.75 % ------ Input Options Time Limit: Unbounded
% 4.86/1.75
% 4.86/1.75
% 4.86/1.75 % ------
% 4.86/1.75 % Current options:
% 4.86/1.75 % ------
% 4.86/1.75
% 4.86/1.75
% 4.86/1.75 %
% 4.86/1.75
% 4.86/1.75 % ------ Proving...
% 4.86/1.75 %
% 4.86/1.75
% 4.86/1.75 % SZS status Theorem for theBenchmark.p
% 4.86/1.75
% 4.86/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.86/1.75
% 4.86/1.75
%------------------------------------------------------------------------------