%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PUZ133+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 8.20s 1.71s
% Output : CNFRefutation 8.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 122 ( 23 unt; 0 def)
% Number of atoms : 409 ( 137 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 491 ( 204 ~; 218 |; 56 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 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 : 171 ( 0 sgn 163 !; 8 ?; 93 :)
% 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(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,[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/sandbox/benchmark/theBenchmark.p',permutation_range) ).
fof(f7,axiom,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation_another_one) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( le(X1,X2)
& le(X0,X1) )
=> le(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',le_trans) ).
fof(f9,axiom,
! [X0] : le(X0,s(X0)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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(f16,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(f17,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,[],[f16]) ).
fof(f18,plain,
( ! [X0] : q(X0) = p(perm(X0))
& queens_p
& ~ queens_q ),
inference(ennf_transformation,[],[f5]) ).
fof(f19,plain,
( ! [X0] : q(X0) = p(perm(X0))
& queens_p
& ~ queens_q ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| ( le(perm(X0),n)
& le(s(n0),perm(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f21,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| ( le(perm(X0),n)
& le(s(n0),perm(X0)) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ le(X1,X2)
| ~ le(X0,X1)
| le(X0,X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ le(X1,X2)
| ~ le(X0,X1)
| le(X0,X2) ),
inference(flattening,[],[f22]) ).
fof(f24,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,[],[f17]) ).
fof(f25,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,[],[f24]) ).
fof(f26,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)],[f25]) ).
fof(f27,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(f28,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(f29,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(f30,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(f31,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(f33,plain,
( ~ le(s(sK0),sK1)
| le(s(perm(sK1)),perm(sK0))
| queens_q ),
inference(cnf_transformation,[],[f26]) ).
fof(f34,plain,
( ~ le(s(perm(sK1)),perm(sK0))
| le(s(sK0),sK1)
| queens_q ),
inference(cnf_transformation,[],[f26]) ).
fof(f35,plain,
( le(sK1,n)
| queens_q ),
inference(cnf_transformation,[],[f26]) ).
fof(f36,plain,
( le(s(sK0),sK1)
| queens_q ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
( le(sK0,n)
| queens_q ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
( le(s(n0),sK0)
| queens_q ),
inference(cnf_transformation,[],[f26]) ).
fof(f39,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,[],[f26]) ).
fof(f40,plain,
! [X0] : q(X0) = p(perm(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
queens_p,
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
~ queens_q,
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| le(perm(X0),n) ),
inference(cnf_transformation,[],[f21]) ).
fof(f44,plain,
! [X0] :
( ~ le(X0,n)
| ~ le(s(n0),X0)
| le(s(n0),perm(X0)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ le(X1,X2)
| ~ le(X0,X1)
| le(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X0] : le(X0,s(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( plus(X0,X1) != plus(X2,X3)
| minus(X0,X2) = minus(X3,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( minus(X0,X2) != minus(X3,X1)
| plus(X0,X1) = plus(X2,X3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( minus(X0,X1) != minus(X2,X3)
| minus(X0,X2) = minus(X1,X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
( minus(p(perm(sK0)),sK0) = minus(p(perm(sK1)),sK1)
| plus(p(perm(sK0)),sK0) = plus(p(perm(sK1)),sK1)
| p(perm(sK0)) = p(perm(sK1))
| queens_q ),
inference(definition_unfolding,[],[f39,f40,f40,f40,f40,f40,f40]) ).
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,[],[f31]) ).
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,[],[f30]) ).
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,[],[f29]) ).
tcf(c_53,negated_conjecture,
( queens_q
| ( p(perm(sK0)) = p(perm(sK1)) )
| ( minus(p(perm(sK0)),sK0) = minus(p(perm(sK1)),sK1) )
| ( plus(p(perm(sK0)),sK0) = plus(p(perm(sK1)),sK1) ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_54,plain,
( queens_q
| le(s(n0),sK0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_55,plain,
( queens_q
| le(sK0,n) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
( queens_q
| le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
( queens_q
| le(sK1,n) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
( queens_q
| le(s(sK0),sK1)
| ~ le(s(perm(sK1)),perm(sK0)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,plain,
( queens_q
| le(s(perm(sK1)),perm(sK0))
| ~ le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_60,negated_conjecture,
~ queens_q,
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,negated_conjecture,
queens_p,
inference(cnf_transformation,[],[f41]) ).
tcf(c_62,plain,
! [X0: $i] :
( le(s(n0),perm(X0))
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_63,plain,
! [X0: $i] :
( le(perm(X0),n)
| ~ le(X0,n)
| ~ le(s(n0),X0) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : minus(perm(X0),perm(X1)) = minus(X1,X0),
inference(cnf_transformation,[],[f45]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( le(X0,X2)
| ~ le(X1,X2)
| ~ le(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_66,plain,
! [X0: $i] : le(X0,s(X0)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( plus(X0,X3) = plus(X1,X2) )
| ( minus(X0,X1) != minus(X2,X3) ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( minus(X0,X2) = minus(X3,X1) )
| ( plus(X0,X1) != plus(X2,X3) ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( minus(X0,X2) = minus(X1,X3) )
| ( minus(X0,X1) != minus(X2,X3) ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_89,plain,
le(s(perm(sK1)),perm(sK0)),
inference(global_subsumption_just,[status(thm)],[c_59,c_60,c_56,c_59]) ).
tcf(c_91,plain,
le(s(sK0),sK1),
inference(global_subsumption_just,[status(thm)],[c_58,c_60,c_56]) ).
tcf(c_93,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_61,c_49]) ).
tcf(c_94,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_93]) ).
tcf(c_96,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_61,c_51]) ).
tcf(c_97,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_96]) ).
tcf(c_99,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_61,c_50]) ).
tcf(c_100,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_99]) ).
tcf(c_102,plain,
( ( plus(p(perm(sK0)),sK0) = plus(p(perm(sK1)),sK1) )
| ( minus(p(perm(sK0)),sK0) = minus(p(perm(sK1)),sK1) )
| ( p(perm(sK0)) = p(perm(sK1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_60,c_53]) ).
tcf(c_103,negated_conjecture,
( ( p(perm(sK0)) = p(perm(sK1)) )
| ( minus(p(perm(sK0)),sK0) = minus(p(perm(sK1)),sK1) )
| ( plus(p(perm(sK0)),sK0) = plus(p(perm(sK1)),sK1) ) ),
inference(renaming,[status(thm)],[c_102]) ).
tcf(c_298,negated_conjecture,
( ( p(perm(sK0)) = p(perm(sK1)) )
| ( minus(p(perm(sK0)),sK0) = minus(p(perm(sK1)),sK1) )
| ( plus(p(perm(sK0)),sK0) = plus(p(perm(sK1)),sK1) ) ),
inference(subtyping,[status(esa)],[c_103]) ).
tcf(c_299,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( ~ le(X1_iProver_p_1,n)
| ~ le(X0_iProver_p_1,n)
| ~ le(s(n0),X0_iProver_p_1)
| ~ le(s(X0_iProver_p_1),X1_iProver_p_1)
| ( plus(p(X0_iProver_p_1),X0_iProver_p_1) != plus(p(X1_iProver_p_1),X1_iProver_p_1) ) ),
inference(subtyping,[status(esa)],[c_100]) ).
tcf(c_300,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( ~ le(X1_iProver_p_1,n)
| ~ le(X0_iProver_p_1,n)
| ~ le(s(n0),X0_iProver_p_1)
| ~ le(s(X0_iProver_p_1),X1_iProver_p_1)
| ( minus(p(X0_iProver_p_1),X0_iProver_p_1) != minus(p(X1_iProver_p_1),X1_iProver_p_1) ) ),
inference(subtyping,[status(esa)],[c_97]) ).
tcf(c_301,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( ~ le(X1_iProver_p_1,n)
| ~ le(X0_iProver_p_1,n)
| ~ le(s(n0),X0_iProver_p_1)
| ~ le(s(X0_iProver_p_1),X1_iProver_p_1)
| ( p(X0_iProver_p_1) != p(X1_iProver_p_1) ) ),
inference(subtyping,[status(esa)],[c_94]) ).
tcf(c_302,plain,
le(s(perm(sK1)),perm(sK0)),
inference(subtyping,[status(esa)],[c_89]) ).
tcf(c_304,plain,
le(s(sK0),sK1),
inference(subtyping,[status(esa)],[c_91]) ).
tcf(c_307,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1,X2_iProver_p_1: iProver_p_1,X3_iProver_p_1: iProver_p_1] :
( ( minus(X0_iProver_p_1,X2_iProver_p_1) = minus(X1_iProver_p_1,X3_iProver_p_1) )
| ( minus(X0_iProver_p_1,X1_iProver_p_1) != minus(X2_iProver_p_1,X3_iProver_p_1) ) ),
inference(subtyping,[status(esa)],[c_70]) ).
tcf(c_308,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1,X2_iProver_p_1: iProver_p_1,X3_iProver_p_1: iProver_p_1] :
( ( minus(X0_iProver_p_1,X2_iProver_p_1) = minus(X3_iProver_p_1,X1_iProver_p_1) )
| ( plus(X0_iProver_p_1,X1_iProver_p_1) != plus(X2_iProver_p_1,X3_iProver_p_1) ) ),
inference(subtyping,[status(esa)],[c_68]) ).
tcf(c_309,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1,X2_iProver_p_1: iProver_p_1,X3_iProver_p_1: iProver_p_1] :
( ( plus(X0_iProver_p_1,X3_iProver_p_1) = plus(X1_iProver_p_1,X2_iProver_p_1) )
| ( minus(X0_iProver_p_1,X1_iProver_p_1) != minus(X2_iProver_p_1,X3_iProver_p_1) ) ),
inference(subtyping,[status(esa)],[c_67]) ).
tcf(c_310,plain,
! [X0_iProver_p_1: iProver_p_1] : le(X0_iProver_p_1,s(X0_iProver_p_1)),
inference(subtyping,[status(esa)],[c_66]) ).
tcf(c_311,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1,X2_iProver_p_1: iProver_p_1] :
( le(X0_iProver_p_1,X2_iProver_p_1)
| ~ le(X1_iProver_p_1,X2_iProver_p_1)
| ~ le(X0_iProver_p_1,X1_iProver_p_1) ),
inference(subtyping,[status(esa)],[c_65]) ).
tcf(c_312,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] : minus(perm(X0_iProver_p_1),perm(X1_iProver_p_1)) = minus(X1_iProver_p_1,X0_iProver_p_1),
inference(subtyping,[status(esa)],[c_64]) ).
tcf(c_313,plain,
! [X0_iProver_p_1: iProver_p_1] :
( le(perm(X0_iProver_p_1),n)
| ~ le(X0_iProver_p_1,n)
| ~ le(s(n0),X0_iProver_p_1) ),
inference(subtyping,[status(esa)],[c_63]) ).
tcf(c_314,plain,
! [X0_iProver_p_1: iProver_p_1] :
( le(s(n0),perm(X0_iProver_p_1))
| ~ le(X0_iProver_p_1,n)
| ~ le(s(n0),X0_iProver_p_1) ),
inference(subtyping,[status(esa)],[c_62]) ).
tcf(c_318,plain,
! [X0_iProver_p_1: iProver_p_1] : X0_iProver_p_1 = X0_iProver_p_1,
theory(equality) ).
tcf(c_320,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1,X2_iProver_p_1: iProver_p_1] :
( ( X2_iProver_p_1 = X0_iProver_p_1 )
| ( X2_iProver_p_1 != X1_iProver_p_1 )
| ( X0_iProver_p_1 != X1_iProver_p_1 ) ),
theory(equality) ).
tcf(c_629,plain,
( le(perm(sK0),n)
| ~ le(sK0,n)
| ~ le(s(n0),sK0) ),
inference(instantiation,[status(thm)],[c_313]) ).
tcf(c_641,plain,
( le(s(n0),perm(sK1))
| ~ le(sK1,n)
| ~ le(s(n0),sK1) ),
inference(instantiation,[status(thm)],[c_314]) ).
tcf(c_686,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( le(X0_iProver_p_1,X1_iProver_p_1)
| ~ le(s(X0_iProver_p_1),X1_iProver_p_1) ),
inference(superposition,[status(thm)],[c_310,c_311]) ).
tcf(c_739,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1,X2_iProver_p_1: iProver_p_1,X3_iProver_p_1: iProver_p_1] :
( ( minus(X0_iProver_p_1,perm(X3_iProver_p_1)) = minus(X1_iProver_p_1,perm(X2_iProver_p_1)) )
| ( minus(X0_iProver_p_1,X1_iProver_p_1) != minus(X2_iProver_p_1,X3_iProver_p_1) ) ),
inference(superposition,[status(thm)],[c_312,c_307]) ).
tcf(c_755,plain,
( ~ le(perm(sK1),n)
| ~ le(perm(sK0),n)
| ~ le(s(n0),perm(sK1))
| ~ le(s(perm(sK1)),perm(sK0))
| ( p(perm(sK1)) != p(perm(sK0)) ) ),
inference(instantiation,[status(thm)],[c_301]) ).
tcf(c_768,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1,X2_iProver_p_1: iProver_p_1] :
( le(s(X0_iProver_p_1),X2_iProver_p_1)
| ~ le(X1_iProver_p_1,X2_iProver_p_1)
| ~ le(s(X0_iProver_p_1),X1_iProver_p_1) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_821,plain,
le(sK0,sK1),
inference(superposition,[status(thm)],[c_304,c_686]) ).
tcf(c_822,plain,
le(perm(sK1),perm(sK0)),
inference(superposition,[status(thm)],[c_302,c_686]) ).
tcf(c_907,plain,
! [X0_iProver_p_1: iProver_p_1] :
( le(perm(sK1),X0_iProver_p_1)
| ~ le(perm(sK0),X0_iProver_p_1) ),
inference(superposition,[status(thm)],[c_822,c_311]) ).
tcf(c_908,plain,
( le(perm(sK1),n)
| ~ le(perm(sK0),n) ),
inference(instantiation,[status(thm)],[c_907]) ).
tcf(c_928,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( ~ le(X0_iProver_p_1,n)
| ~ le(s(n0),X0_iProver_p_1)
| ~ le(perm(X1_iProver_p_1),n)
| ~ le(s(X0_iProver_p_1),perm(X1_iProver_p_1))
| ( plus(p(X0_iProver_p_1),X0_iProver_p_1) != plus(p(perm(X1_iProver_p_1)),perm(X1_iProver_p_1)) ) ),
inference(instantiation,[status(thm)],[c_299]) ).
tcf(c_933,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( ~ le(X0_iProver_p_1,n)
| ~ le(s(n0),X0_iProver_p_1)
| ~ le(perm(X1_iProver_p_1),n)
| ~ le(s(X0_iProver_p_1),perm(X1_iProver_p_1))
| ( minus(p(X0_iProver_p_1),X0_iProver_p_1) != minus(p(perm(X1_iProver_p_1)),perm(X1_iProver_p_1)) ) ),
inference(instantiation,[status(thm)],[c_300]) ).
tcf(c_939,plain,
! [X0_iProver_p_1: iProver_p_1] :
( le(s(n0),X0_iProver_p_1)
| ~ le(sK0,X0_iProver_p_1)
| ~ le(s(n0),sK0) ),
inference(instantiation,[status(thm)],[c_768]) ).
tcf(c_1086,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( ( X1_iProver_p_1 = X0_iProver_p_1 )
| ( X0_iProver_p_1 != X1_iProver_p_1 ) ),
inference(resolution,[status(thm)],[c_320,c_318]) ).
tcf(c_1109,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( ( p(perm(sK0)) = p(perm(sK1)) )
| ( minus(p(perm(sK0)),sK0) = minus(p(perm(sK1)),sK1) )
| ( minus(p(perm(sK1)),X0_iProver_p_1) = minus(X1_iProver_p_1,sK1) )
| ( plus(p(perm(sK0)),sK0) != plus(X0_iProver_p_1,X1_iProver_p_1) ) ),
inference(superposition,[status(thm)],[c_298,c_308]) ).
tcf(c_1117,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1,X2_iProver_p_1: iProver_p_1,X3_iProver_p_1: iProver_p_1] :
( ( plus(X0_iProver_p_1,perm(X2_iProver_p_1)) = plus(X1_iProver_p_1,perm(X3_iProver_p_1)) )
| ( minus(X0_iProver_p_1,X1_iProver_p_1) != minus(X2_iProver_p_1,X3_iProver_p_1) ) ),
inference(superposition,[status(thm)],[c_312,c_309]) ).
tcf(c_1242,plain,
( ( p(perm(sK0)) = p(perm(sK1)) )
| ( minus(p(perm(sK0)),sK0) = minus(p(perm(sK1)),sK1) )
| ( minus(p(perm(sK1)),p(perm(sK0))) = minus(sK0,sK1) ) ),
inference(equality_resolution,[status(thm)],[c_1109]) ).
tcf(c_1440,plain,
( ~ le(perm(sK1),n)
| ~ le(perm(sK0),n)
| ~ le(s(n0),perm(sK1))
| ~ le(s(perm(sK1)),perm(sK0))
| ( plus(p(perm(sK1)),perm(sK1)) != plus(p(perm(sK0)),perm(sK0)) ) ),
inference(instantiation,[status(thm)],[c_928]) ).
tcf(c_1442,plain,
( ~ le(perm(sK1),n)
| ~ le(perm(sK0),n)
| ~ le(s(n0),perm(sK1))
| ~ le(s(perm(sK1)),perm(sK0))
| ( minus(p(perm(sK1)),perm(sK1)) != minus(p(perm(sK0)),perm(sK0)) ) ),
inference(instantiation,[status(thm)],[c_933]) ).
tcf(c_1515,plain,
( le(s(n0),sK1)
| ~ le(sK0,sK1)
| ~ le(s(n0),sK0) ),
inference(instantiation,[status(thm)],[c_939]) ).
tcf(c_5225,plain,
( ( p(perm(sK0)) = p(perm(sK1)) )
| ( plus(p(perm(sK0)),sK0) = plus(p(perm(sK1)),sK1) )
| ( minus(p(perm(sK0)),p(perm(sK1))) = minus(sK0,sK1) ) ),
inference(resolution,[status(thm)],[c_307,c_298]) ).
tcf(c_5635,plain,
( ( minus(p(perm(sK1)),perm(sK1)) = minus(p(perm(sK0)),perm(sK0)) )
| ( minus(p(perm(sK1)),p(perm(sK0))) != minus(sK0,sK1) ) ),
inference(instantiation,[status(thm)],[c_739]) ).
tcf(c_5681,plain,
( ( plus(p(perm(sK1)),perm(sK1)) = plus(p(perm(sK0)),perm(sK0)) )
| ( minus(p(perm(sK1)),p(perm(sK0))) != minus(sK1,sK0) ) ),
inference(instantiation,[status(thm)],[c_1117]) ).
tcf(c_6099,negated_conjecture,
( ( p(perm(sK0)) = p(perm(sK1)) )
| ( minus(p(perm(sK0)),sK0) = minus(p(perm(sK1)),sK1) ) ),
inference(global_subsumption_just,[status(thm)],[c_298,c_60,c_57,c_55,c_56,c_54,c_59,c_629,c_641,c_821,c_908,c_1242,c_1442,c_1515,c_5635]) ).
tcf(c_6170,plain,
! [X0_iProver_p_1: iProver_p_1,X1_iProver_p_1: iProver_p_1] :
( ( p(perm(sK0)) = p(perm(sK1)) )
| ( minus(p(perm(sK1)),X0_iProver_p_1) = minus(sK1,X1_iProver_p_1) )
| ( minus(p(perm(sK0)),sK0) != minus(X0_iProver_p_1,X1_iProver_p_1) ) ),
inference(superposition,[status(thm)],[c_6099,c_307]) ).
tcf(c_6178,plain,
( ( p(perm(sK0)) = p(perm(sK1)) )
| ( minus(p(perm(sK1)),p(perm(sK0))) = minus(sK1,sK0) ) ),
inference(equality_resolution,[status(thm)],[c_6170]) ).
tcf(c_6815,plain,
p(perm(sK0)) = p(perm(sK1)),
inference(global_subsumption_just,[status(thm)],[c_5225,c_60,c_57,c_55,c_56,c_54,c_59,c_629,c_641,c_821,c_908,c_1440,c_1515,c_5681,c_6178]) ).
tcf(c_6821,plain,
p(perm(sK1)) = p(perm(sK0)),
inference(resolution,[status(thm)],[c_6815,c_1086]) ).
tcf(c_6824,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6821,c_1515,c_908,c_821,c_755,c_641,c_629,c_59,c_54,c_56,c_55,c_57,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ133+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 06:59:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 8.20/1.71 % SZS status Started for theBenchmark.p
% 8.20/1.71 % SZS status Theorem for theBenchmark.p
% 8.20/1.71
% 8.20/1.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.20/1.71
% 8.20/1.71 % ------ iProver source info
% 8.20/1.71
% 8.20/1.71 % git: date: 2026-07-19 20:42:38 +0200
% 8.20/1.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.20/1.71 % git: non_committed_changes: false
% 8.20/1.71
% 8.20/1.71 % ------ Parsing...
% 8.20/1.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.20/1.71
% 8.20/1.71 % ------ 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 %
% 8.20/1.71
% 8.20/1.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.20/1.71
% 8.20/1.71 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.20/1.71 % ------ Proving...
% 8.20/1.71 % ------ Problem Properties
% 8.20/1.71
% 8.20/1.71 %
% 8.20/1.71 % clauses 18
% 8.20/1.71 % conjectures 1
% 8.20/1.71 % EPR 3
% 8.20/1.71 % Horn 17
% 8.20/1.71 % unary 7
% 8.20/1.71 % binary 3
% 8.20/1.71 % lits 43
% 8.20/1.71 % lits eq 14
% 8.20/1.71 % fd_pure 0
% 8.20/1.71 % fd_pseudo 0
% 8.20/1.71 % fd_cond 0
% 8.20/1.71 % fd_pseudo_cond 0
% 8.20/1.71 % AC symbols 0
% 8.20/1.71
% 8.20/1.71 % ------ Input Options Time Limit: Unbounded
% 8.20/1.71
% 8.20/1.71
% 8.20/1.71 % ------
% 8.20/1.71 % Current options:
% 8.20/1.71 % ------
% 8.20/1.71
% 8.20/1.71
% 8.20/1.71 %
% 8.20/1.71
% 8.20/1.71 % ------ Proving...
% 8.20/1.71 %
% 8.20/1.71
% 8.20/1.71 % SZS status Theorem for theBenchmark.p
% 8.20/1.71
% 8.20/1.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.20/1.71
% 8.20/1.71
%------------------------------------------------------------------------------