%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV116+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 03:16:28 PM UTC 2026
% Result : Theorem 0.85s 6.28s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 64 ( 2 unt; 2 def)
% Number of atoms : 484 ( 80 equ)
% Maximal formula atoms : 42 ( 7 avg)
% Number of connectives : 609 ( 205 ~; 219 |; 165 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-3 aty)
% Number of variables : 129 ( 0 sgn 101 !; 28 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [X8] :
( ( leq(X8,minus(n6,n1))
& leq(n0,X8) )
=> ! [X9] :
( ( leq(X9,minus(n6,n1))
& leq(n0,X9) )
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X6,X7] :
( ( leq(X7,minus(n6,n1))
& leq(X6,minus(n6,n1))
& leq(n0,X7)
& leq(n0,X6) )
=> a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ( leq(X5,minus(n6,n1))
& leq(X4,minus(n6,n1))
& leq(n0,X5)
& leq(n0,X4) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ( leq(X3,minus(n3,n1))
& leq(X2,minus(n3,n1))
& leq(n0,X3)
& leq(n0,X2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ( leq(X1,minus(n6,n1))
& leq(X0,minus(n6,n1))
& leq(n0,X1)
& leq(n0,X0) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [X14,X15] :
( ( leq(X15,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X15)
& leq(n0,X14) )
=> a_select3(pminus_ds1_filter,X14,X15) = a_select3(pminus_ds1_filter,X15,X14) )
& ! [X12,X13] :
( ( leq(X13,minus(n3,n1))
& leq(X12,minus(n3,n1))
& leq(n0,X13)
& leq(n0,X12) )
=> a_select3(r_ds1_filter,X12,X13) = a_select3(r_ds1_filter,X13,X12) )
& ! [X10,X11] :
( ( leq(X11,minus(n6,n1))
& leq(X10,minus(n6,n1))
& leq(n0,X11)
& leq(n0,X10) )
=> a_select3(q_ds1_filter,X10,X11) = a_select3(q_ds1_filter,X11,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0009) ).
fof(f54,negated_conjecture,
~ ( ( ! [X8] :
( ( leq(X8,minus(n6,n1))
& leq(n0,X8) )
=> ! [X9] :
( ( leq(X9,minus(n6,n1))
& leq(n0,X9) )
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X6,X7] :
( ( leq(X7,minus(n6,n1))
& leq(X6,minus(n6,n1))
& leq(n0,X7)
& leq(n0,X6) )
=> a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ( leq(X5,minus(n6,n1))
& leq(X4,minus(n6,n1))
& leq(n0,X5)
& leq(n0,X4) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ( leq(X3,minus(n3,n1))
& leq(X2,minus(n3,n1))
& leq(n0,X3)
& leq(n0,X2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ( leq(X1,minus(n6,n1))
& leq(X0,minus(n6,n1))
& leq(n0,X1)
& leq(n0,X0) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [X14,X15] :
( ( leq(X15,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X15)
& leq(n0,X14) )
=> a_select3(pminus_ds1_filter,X14,X15) = a_select3(pminus_ds1_filter,X15,X14) )
& ! [X12,X13] :
( ( leq(X13,minus(n3,n1))
& leq(X12,minus(n3,n1))
& leq(n0,X13)
& leq(n0,X12) )
=> a_select3(r_ds1_filter,X12,X13) = a_select3(r_ds1_filter,X13,X12) )
& ! [X10,X11] :
( ( leq(X11,minus(n6,n1))
& leq(X10,minus(n6,n1))
& leq(n0,X11)
& leq(n0,X10) )
=> a_select3(q_ds1_filter,X10,X11) = a_select3(q_ds1_filter,X11,X10) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f104,plain,
( ! [X8] :
( ~ leq(X8,minus(n6,n1))
| ~ leq(n0,X8)
| ! [X9] :
( ~ leq(X9,minus(n6,n1))
| ~ leq(n0,X9)
| a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X6,X7] :
( ~ leq(X7,minus(n6,n1))
| ~ leq(X6,minus(n6,n1))
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,minus(n6,n1))
| ~ leq(X4,minus(n6,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,minus(n3,n1))
| ~ leq(X2,minus(n3,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5)
& ( ? [X14,X15] :
( leq(X15,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X15)
& leq(n0,X14)
& a_select3(pminus_ds1_filter,X14,X15) != a_select3(pminus_ds1_filter,X15,X14) )
| ? [X12,X13] :
( leq(X13,minus(n3,n1))
& leq(X12,minus(n3,n1))
& leq(n0,X13)
& leq(n0,X12)
& a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12) )
| ? [X10,X11] :
( leq(X11,minus(n6,n1))
& leq(X10,minus(n6,n1))
& leq(n0,X11)
& leq(n0,X10)
& a_select3(q_ds1_filter,X10,X11) != a_select3(q_ds1_filter,X11,X10) ) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f105,plain,
( ! [X8] :
( ~ leq(X8,minus(n6,n1))
| ~ leq(n0,X8)
| ! [X9] :
( ~ leq(X9,minus(n6,n1))
| ~ leq(n0,X9)
| a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X6,X7] :
( ~ leq(X7,minus(n6,n1))
| ~ leq(X6,minus(n6,n1))
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,minus(n6,n1))
| ~ leq(X4,minus(n6,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,minus(n3,n1))
| ~ leq(X2,minus(n3,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5)
& ( ? [X14,X15] :
( leq(X15,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X15)
& leq(n0,X14)
& a_select3(pminus_ds1_filter,X14,X15) != a_select3(pminus_ds1_filter,X15,X14) )
| ? [X12,X13] :
( leq(X13,minus(n3,n1))
& leq(X12,minus(n3,n1))
& leq(n0,X13)
& leq(n0,X12)
& a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12) )
| ? [X10,X11] :
( leq(X11,minus(n6,n1))
& leq(X10,minus(n6,n1))
& leq(n0,X11)
& leq(n0,X10)
& a_select3(q_ds1_filter,X10,X11) != a_select3(q_ds1_filter,X11,X10) ) ) ),
inference(flattening,[],[f104]) ).
fof(f133,plain,
( ~ sP1
| ? [X12,X13] :
( leq(X13,minus(n3,n1))
& leq(X12,minus(n3,n1))
& leq(n0,X13)
& leq(n0,X12)
& a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12) ) ),
inference(nnf_transformation,[],[f131]) ).
fof(f134,plain,
( ~ sP1
| ? [X0,X1] :
( leq(X1,minus(n3,n1))
& leq(X0,minus(n3,n1))
& leq(n0,X1)
& leq(n0,X0)
& a_select3(r_ds1_filter,X0,X1) != a_select3(r_ds1_filter,X1,X0) ) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
( ~ sP1
| ( leq(sK3,minus(n3,n1))
& leq(sK2,minus(n3,n1))
& leq(n0,sK3)
& leq(n0,sK2)
& a_select3(r_ds1_filter,sK2,sK3) != a_select3(r_ds1_filter,sK3,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f134]) ).
fof(f139,plain,
( ! [X10] :
( ~ leq(X10,minus(n6,n1))
| ~ leq(n0,X10)
| ! [X11] :
( ~ leq(X11,minus(n6,n1))
| ~ leq(n0,X11)
| a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) )
& ! [X8,X9] :
( ~ leq(X9,minus(n6,n1))
| ~ leq(X8,minus(n6,n1))
| ~ leq(n0,X9)
| ~ leq(n0,X8)
| a_select3(pminus_ds1_filter,X8,X9) = a_select3(pminus_ds1_filter,X9,X8) )
& ! [X6,X7] :
( ~ leq(X7,minus(n6,n1))
| ~ leq(X6,minus(n6,n1))
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,minus(n3,n1))
| ~ leq(X4,minus(n3,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,minus(n6,n1))
| ~ leq(X2,minus(n6,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5)
& ( sP0
| sP1
| ? [X0,X1] :
( leq(X1,minus(n6,n1))
& leq(X0,minus(n6,n1))
& leq(n0,X1)
& leq(n0,X0)
& a_select3(q_ds1_filter,X0,X1) != a_select3(q_ds1_filter,X1,X0) ) ) ),
inference(rectify,[],[f132]) ).
fof(f140,plain,
( ! [X10] :
( ~ leq(X10,minus(n6,n1))
| ~ leq(n0,X10)
| ! [X11] :
( ~ leq(X11,minus(n6,n1))
| ~ leq(n0,X11)
| a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) )
& ! [X8,X9] :
( ~ leq(X9,minus(n6,n1))
| ~ leq(X8,minus(n6,n1))
| ~ leq(n0,X9)
| ~ leq(n0,X8)
| a_select3(pminus_ds1_filter,X8,X9) = a_select3(pminus_ds1_filter,X9,X8) )
& ! [X6,X7] :
( ~ leq(X7,minus(n6,n1))
| ~ leq(X6,minus(n6,n1))
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,minus(n3,n1))
| ~ leq(X4,minus(n3,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,minus(n6,n1))
| ~ leq(X2,minus(n6,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5)
& ( sP0
| sP1
| ( leq(sK7,minus(n6,n1))
& leq(sK6,minus(n6,n1))
& leq(n0,sK7)
& leq(n0,sK6)
& a_select3(q_ds1_filter,sK6,sK7) != a_select3(q_ds1_filter,sK7,sK6) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f139]) ).
fof(f144,plain,
( ~ sP1
| leq(sK3,minus(n3,n1)) ),
inference(cnf_transformation,[],[f135]) ).
fof(f145,plain,
( ~ sP1
| leq(sK2,minus(n3,n1)) ),
inference(cnf_transformation,[],[f135]) ).
fof(f146,plain,
( ~ sP1
| leq(n0,sK3) ),
inference(cnf_transformation,[],[f135]) ).
fof(f147,plain,
( ~ sP1
| leq(n0,sK2) ),
inference(cnf_transformation,[],[f135]) ).
fof(f148,plain,
( ~ sP1
| a_select3(r_ds1_filter,sK2,sK3) != a_select3(r_ds1_filter,sK3,sK2) ),
inference(cnf_transformation,[],[f135]) ).
fof(f155,plain,
! [X8,X9] :
( ~ leq(X9,minus(n6,n1))
| ~ leq(X8,minus(n6,n1))
| ~ leq(n0,X9)
| ~ leq(n0,X8)
| a_select3(pminus_ds1_filter,X8,X9) = a_select3(pminus_ds1_filter,X9,X8) ),
inference(cnf_transformation,[],[f140]) ).
fof(f157,plain,
! [X4,X5] :
( ~ leq(X5,minus(n3,n1))
| ~ leq(X4,minus(n3,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4) ),
inference(cnf_transformation,[],[f140]) ).
fof(f158,plain,
! [X2,X3] :
( ~ leq(X3,minus(n6,n1))
| ~ leq(X2,minus(n6,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2) ),
inference(cnf_transformation,[],[f140]) ).
fof(f161,plain,
( sP0
| sP1
| leq(sK7,minus(n6,n1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f162,plain,
( sP0
| sP1
| leq(sK6,minus(n6,n1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f163,plain,
( sP0
| sP1
| leq(n0,sK7) ),
inference(cnf_transformation,[],[f140]) ).
fof(f164,plain,
( sP0
| sP1
| leq(n0,sK6) ),
inference(cnf_transformation,[],[f140]) ).
fof(f165,plain,
( sP0
| sP1
| a_select3(q_ds1_filter,sK6,sK7) != a_select3(q_ds1_filter,sK7,sK6) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_49,plain,
( ~ sP1
| ( a_select3(r_ds1_filter,sK2,sK3) != a_select3(r_ds1_filter,sK3,sK2) ) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_50,plain,
( leq(n0,sK2)
| ~ sP1 ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_51,plain,
( leq(n0,sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_52,plain,
( leq(sK2,minus(n3,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_53,plain,
( leq(sK3,minus(n3,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_59,negated_conjecture,
( sP0
| sP1
| ( a_select3(q_ds1_filter,sK6,sK7) != a_select3(q_ds1_filter,sK7,sK6) ) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_60,negated_conjecture,
( sP0
| sP1
| leq(n0,sK6) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_61,negated_conjecture,
( sP0
| sP1
| leq(n0,sK7) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_62,negated_conjecture,
( sP0
| sP1
| leq(sK6,minus(n6,n1)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_63,negated_conjecture,
( sP0
| sP1
| leq(sK7,minus(n6,n1)) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i] :
( ( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_67,negated_conjecture,
! [X0: $i,X1: $i] :
( ( a_select3(r_ds1_filter,X0,X1) = a_select3(r_ds1_filter,X1,X0) )
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| ~ leq(X1,minus(n3,n1))
| ~ leq(X0,minus(n3,n1)) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_69,negated_conjecture,
! [X0: $i,X1: $i] :
( ( a_select3(pminus_ds1_filter,X0,X1) = a_select3(pminus_ds1_filter,X1,X0) )
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_4493,plain,
! [X0: $i] :
( sP0
| sP1
| ( a_select3(q_ds1_filter,X0,sK6) = a_select3(q_ds1_filter,sK6,X0) )
| ~ leq(n0,sK6)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(superposition,[status(thm)],[c_62,c_66]) ).
tcf(c_4595,plain,
! [X0: $i] :
( sP0
| sP1
| ( a_select3(q_ds1_filter,X0,sK6) = a_select3(q_ds1_filter,sK6,X0) )
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4493,c_60,c_4493]) ).
tcf(c_4596,plain,
! [X0: $i] :
( sP0
| sP1
| ( a_select3(q_ds1_filter,X0,sK6) = a_select3(q_ds1_filter,sK6,X0) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(renaming,[status(thm)],[c_4595]) ).
tcf(c_4609,plain,
( sP0
| sP1
| ( a_select3(q_ds1_filter,sK6,sK7) = a_select3(q_ds1_filter,sK7,sK6) )
| ~ leq(n0,sK7) ),
inference(superposition,[status(thm)],[c_63,c_4596]) ).
tcf(c_4619,plain,
( sP0
| sP1 ),
inference(global_subsumption_just,[status(thm)],[c_4609,c_61,c_59,c_4609]) ).
tcf(c_4704,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK2) = a_select3(r_ds1_filter,sK2,X0) )
| ~ sP1
| ~ leq(n0,sK2)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(superposition,[status(thm)],[c_52,c_67]) ).
tcf(c_4726,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK3) = a_select3(r_ds1_filter,sK3,X0) )
| ~ sP1
| ~ leq(n0,sK3)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(superposition,[status(thm)],[c_53,c_67]) ).
tcf(c_4859,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK2) = a_select3(r_ds1_filter,sK2,X0) )
| ~ sP1
| ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4704,c_50,c_4704]) ).
tcf(c_4860,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK2) = a_select3(r_ds1_filter,sK2,X0) )
| ~ sP1
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(renaming,[status(thm)],[c_4859]) ).
tcf(c_4871,plain,
( ( a_select3(r_ds1_filter,sK2,sK3) = a_select3(r_ds1_filter,sK3,sK2) )
| ~ sP1
| ~ leq(n0,sK3) ),
inference(superposition,[status(thm)],[c_53,c_4860]) ).
tcf(c_4879,plain,
~ sP1,
inference(global_subsumption_just,[status(thm)],[c_4726,c_51,c_49,c_4871]) ).
tcf(c_5059,plain,
( ( a_select3(pminus_ds1_filter,sK4,sK5) = a_select3(pminus_ds1_filter,sK5,sK4) )
| ~ leq(n0,sK5)
| ~ leq(n0,sK4)
| ~ leq(sK5,minus(n6,n1))
| ~ leq(sK4,minus(n6,n1)) ),
inference(instantiation,[status(thm)],[c_69]) ).
fof(f130,definition,
( ~ sP0
| ? [X14,X15] :
( leq(X15,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X15)
& leq(n0,X14)
& a_select3(pminus_ds1_filter,X14,X15) != a_select3(pminus_ds1_filter,X15,X14) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f131,definition,
( ~ sP1
| ? [X12,X13] :
( leq(X13,minus(n3,n1))
& leq(X12,minus(n3,n1))
& leq(n0,X13)
& leq(n0,X12)
& a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f132,plain,
( ! [X8] :
( ~ leq(X8,minus(n6,n1))
| ~ leq(n0,X8)
| ! [X9] :
( ~ leq(X9,minus(n6,n1))
| ~ leq(n0,X9)
| a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X6,X7] :
( ~ leq(X7,minus(n6,n1))
| ~ leq(X6,minus(n6,n1))
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,minus(n6,n1))
| ~ leq(X4,minus(n6,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,minus(n3,n1))
| ~ leq(X2,minus(n3,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5)
& ( sP0
| sP1
| ? [X10,X11] :
( leq(X11,minus(n6,n1))
& leq(X10,minus(n6,n1))
& leq(n0,X11)
& leq(n0,X10)
& a_select3(q_ds1_filter,X10,X11) != a_select3(q_ds1_filter,X11,X10) ) ) ),
inference(definition_folding,[],[f105,f131,f130]) ).
fof(f136,plain,
( ~ sP0
| ? [X14,X15] :
( leq(X15,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X15)
& leq(n0,X14)
& a_select3(pminus_ds1_filter,X14,X15) != a_select3(pminus_ds1_filter,X15,X14) ) ),
inference(nnf_transformation,[],[f130]) ).
fof(f137,plain,
( ~ sP0
| ? [X0,X1] :
( leq(X1,minus(n6,n1))
& leq(X0,minus(n6,n1))
& leq(n0,X1)
& leq(n0,X0)
& a_select3(pminus_ds1_filter,X0,X1) != a_select3(pminus_ds1_filter,X1,X0) ) ),
inference(rectify,[],[f136]) ).
fof(f138,plain,
( ~ sP0
| ( leq(sK5,minus(n6,n1))
& leq(sK4,minus(n6,n1))
& leq(n0,sK5)
& leq(n0,sK4)
& a_select3(pminus_ds1_filter,sK4,sK5) != a_select3(pminus_ds1_filter,sK5,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f137]) ).
fof(f149,plain,
( ~ sP0
| leq(sK5,minus(n6,n1)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f150,plain,
( ~ sP0
| leq(sK4,minus(n6,n1)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f151,plain,
( ~ sP0
| leq(n0,sK5) ),
inference(cnf_transformation,[],[f138]) ).
fof(f152,plain,
( ~ sP0
| leq(n0,sK4) ),
inference(cnf_transformation,[],[f138]) ).
fof(f153,plain,
( ~ sP0
| a_select3(pminus_ds1_filter,sK4,sK5) != a_select3(pminus_ds1_filter,sK5,sK4) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_54,plain,
( ~ sP0
| ( a_select3(pminus_ds1_filter,sK4,sK5) != a_select3(pminus_ds1_filter,sK5,sK4) ) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_55,plain,
( leq(n0,sK4)
| ~ sP0 ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_56,plain,
( leq(n0,sK5)
| ~ sP0 ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_57,plain,
( leq(sK4,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_58,plain,
( leq(sK5,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_5060,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5059,c_4879,c_4619,c_54,c_57,c_58,c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV116+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.34 % Computer : n019.cluster.edu
% 0.09/5.34 % Model : x86_64 x86_64
% 0.09/5.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.34 % Memory : 8046.5625MB
% 0.09/5.34 % OS : Linux 6.8.0-71-generic
% 0.09/5.34 % CPULimit : 300
% 0.09/5.34 % WCLimit : 300
% 0.09/5.34 % DateTime : Thu Sep 24 18:33:13 UTC 2026
% 0.09/5.34 % CPUTime :
% 0.09/5.34 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 Running first-order theorem proving
% 0.09/5.39 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
% 0.09/5.39
% 0.09/5.39 % ======== iProver multi-core TPTP/SMT =========
% 0.09/5.39
% 0.09/5.40 % Detected problem language: tptp
% 0.13/5.41 % Proving...
% 0.85/6.28 % SZS status Started for theBenchmark.p
% 0.85/6.28 % SZS status Theorem for theBenchmark.p
% 0.85/6.28
% 0.85/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.85/6.28
% 0.85/6.28 % ------ iProver source info
% 0.85/6.28
% 0.85/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.85/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.85/6.28 % git: non_committed_changes: false
% 0.85/6.28
% 0.85/6.28 % ------ Parsing...
% 0.85/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.85/6.28
% 0.85/6.28 % ------ Preprocessing... sup_sim: 11 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.85/6.28
% 0.85/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.85/6.28
% 0.85/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.85/6.28 % ------ Proving...
% 0.85/6.28 % ------ Problem Properties
% 0.85/6.28
% 0.85/6.28 %
% 0.85/6.28 % clauses 99
% 0.85/6.28 % conjectures 11
% 0.85/6.28 % EPR 57
% 0.85/6.28 % Horn 86
% 0.85/6.28 % unary 59
% 0.85/6.28 % binary 20
% 0.85/6.28 % lits 188
% 0.85/6.28 % lits eq 55
% 0.85/6.28 % fd_pure 0
% 0.85/6.28 % fd_pseudo 0
% 0.85/6.28 % fd_cond 7
% 0.85/6.28 % fd_pseudo_cond 2
% 0.85/6.28 % AC symbols 0
% 0.85/6.28
% 0.85/6.28 % ------ Schedule dynamic 5 is on
% 0.85/6.28
% 0.85/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.85/6.28
% 0.85/6.28
% 0.85/6.28 % ------
% 0.85/6.28 % Current options:
% 0.85/6.28 % ------
% 0.85/6.28
% 0.85/6.28
% 0.85/6.28 %
% 0.85/6.28
% 0.85/6.28 % ------ Proving...
% 0.85/6.28 %
% 0.85/6.28
% 0.85/6.28 % SZS status Theorem for theBenchmark.p
% 0.85/6.28
% 0.85/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.85/6.28
% 0.85/6.28
%------------------------------------------------------------------------------