%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV117+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 4.43s 11.53s
% Output : CNFRefutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 104 ( 15 unt; 3 def)
% Number of atoms : 634 ( 100 equ)
% Maximal formula atoms : 44 ( 6 avg)
% Number of connectives : 781 ( 267 ~; 306 |; 186 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 16 con; 0-3 aty)
% Number of variables : 147 ( 0 sgn 109 !; 38 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [X0] : plus(n1,X0) = succ(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_l) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
fof(f53,conjecture,
( ( ! [X6] :
( ( leq(X6,minus(plus(n1,minus(n6,n1)),n1))
& leq(n0,X6) )
=> ! [X7] :
( ( leq(X7,minus(n6,n1))
& leq(n0,X7) )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_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] :
( ( leq(X14,minus(n6,n1))
& leq(n0,X14) )
=> ! [X15] :
( ( leq(X15,minus(n6,n1))
& leq(n0,X15) )
=> a_select3(id_ds1_filter,X14,X15) = a_select3(id_ds1_filter,X15,X14) ) )
& ! [X12,X13] :
( ( leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12) )
=> a_select3(pminus_ds1_filter,X12,X13) = a_select3(pminus_ds1_filter,X13,X12) )
& ! [X10,X11] :
( ( leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10) )
=> a_select3(r_ds1_filter,X10,X11) = a_select3(r_ds1_filter,X11,X10) )
& ! [X8,X9] :
( ( leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8) )
=> a_select3(q_ds1_filter,X8,X9) = a_select3(q_ds1_filter,X9,X8) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0010) ).
fof(f54,negated_conjecture,
~ ( ( ! [X6] :
( ( leq(X6,minus(plus(n1,minus(n6,n1)),n1))
& leq(n0,X6) )
=> ! [X7] :
( ( leq(X7,minus(n6,n1))
& leq(n0,X7) )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_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] :
( ( leq(X14,minus(n6,n1))
& leq(n0,X14) )
=> ! [X15] :
( ( leq(X15,minus(n6,n1))
& leq(n0,X15) )
=> a_select3(id_ds1_filter,X14,X15) = a_select3(id_ds1_filter,X15,X14) ) )
& ! [X12,X13] :
( ( leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12) )
=> a_select3(pminus_ds1_filter,X12,X13) = a_select3(pminus_ds1_filter,X13,X12) )
& ! [X10,X11] :
( ( leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10) )
=> a_select3(r_ds1_filter,X10,X11) = a_select3(r_ds1_filter,X11,X10) )
& ! [X8,X9] :
( ( leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8) )
=> a_select3(q_ds1_filter,X8,X9) = a_select3(q_ds1_filter,X9,X8) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f104,plain,
( ! [X6] :
( ~ leq(X6,minus(plus(n1,minus(n6,n1)),n1))
| ~ leq(n0,X6)
| ! [X7] :
( ~ leq(X7,minus(n6,n1))
| ~ leq(n0,X7)
| a_select3(id_ds1_filter,X6,X7) = a_select3(id_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] :
( leq(X14,minus(n6,n1))
& leq(n0,X14)
& ? [X15] :
( leq(X15,minus(n6,n1))
& leq(n0,X15)
& a_select3(id_ds1_filter,X14,X15) != a_select3(id_ds1_filter,X15,X14) ) )
| ? [X12,X13] :
( leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12)
& a_select3(pminus_ds1_filter,X12,X13) != a_select3(pminus_ds1_filter,X13,X12) )
| ? [X10,X11] :
( leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10)
& a_select3(r_ds1_filter,X10,X11) != a_select3(r_ds1_filter,X11,X10) )
| ? [X8,X9] :
( leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8)
& a_select3(q_ds1_filter,X8,X9) != a_select3(q_ds1_filter,X9,X8) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f105,plain,
( ! [X6] :
( ~ leq(X6,minus(plus(n1,minus(n6,n1)),n1))
| ~ leq(n0,X6)
| ! [X7] :
( ~ leq(X7,minus(n6,n1))
| ~ leq(n0,X7)
| a_select3(id_ds1_filter,X6,X7) = a_select3(id_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] :
( leq(X14,minus(n6,n1))
& leq(n0,X14)
& ? [X15] :
( leq(X15,minus(n6,n1))
& leq(n0,X15)
& a_select3(id_ds1_filter,X14,X15) != a_select3(id_ds1_filter,X15,X14) ) )
| ? [X12,X13] :
( leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12)
& a_select3(pminus_ds1_filter,X12,X13) != a_select3(pminus_ds1_filter,X13,X12) )
| ? [X10,X11] :
( leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10)
& a_select3(r_ds1_filter,X10,X11) != a_select3(r_ds1_filter,X11,X10) )
| ? [X8,X9] :
( leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8)
& a_select3(q_ds1_filter,X8,X9) != a_select3(q_ds1_filter,X9,X8) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ) ),
inference(flattening,[],[f104]) ).
fof(f134,plain,
( ~ sP2
| ? [X10,X11] :
( leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10)
& a_select3(r_ds1_filter,X10,X11) != a_select3(r_ds1_filter,X11,X10) ) ),
inference(nnf_transformation,[],[f132]) ).
fof(f135,plain,
( ~ sP2
| ? [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,[],[f134]) ).
fof(f136,plain,
( ~ sP2
| ( leq(sK4,minus(n3,n1))
& leq(sK3,minus(n3,n1))
& leq(n0,sK4)
& leq(n0,sK3)
& a_select3(r_ds1_filter,sK3,sK4) != a_select3(r_ds1_filter,sK4,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f135]) ).
fof(f137,plain,
( ~ sP1
| ? [X12,X13] :
( leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12)
& a_select3(pminus_ds1_filter,X12,X13) != a_select3(pminus_ds1_filter,X13,X12) ) ),
inference(nnf_transformation,[],[f131]) ).
fof(f138,plain,
( ~ sP1
| ? [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,[],[f137]) ).
fof(f139,plain,
( ~ sP1
| ( leq(sK6,minus(n6,n1))
& leq(sK5,minus(n6,n1))
& leq(n0,sK6)
& leq(n0,sK5)
& a_select3(pminus_ds1_filter,sK5,sK6) != a_select3(pminus_ds1_filter,sK6,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f138]) ).
fof(f143,plain,
( ! [X8] :
( ~ leq(X8,minus(plus(n1,minus(n6,n1)),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(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
| sP2
| ? [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) ) ),
inference(rectify,[],[f133]) ).
fof(f144,plain,
( ! [X8] :
( ~ leq(X8,minus(plus(n1,minus(n6,n1)),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(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
| sP2
| ( leq(sK10,minus(n6,n1))
& leq(sK9,minus(n6,n1))
& leq(n0,sK10)
& leq(n0,sK9)
& a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f143]) ).
fof(f148,plain,
( ~ sP2
| leq(sK4,minus(n3,n1)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f149,plain,
( ~ sP2
| leq(sK3,minus(n3,n1)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f150,plain,
( ~ sP2
| leq(n0,sK4) ),
inference(cnf_transformation,[],[f136]) ).
fof(f151,plain,
( ~ sP2
| leq(n0,sK3) ),
inference(cnf_transformation,[],[f136]) ).
fof(f152,plain,
( ~ sP2
| a_select3(r_ds1_filter,sK3,sK4) != a_select3(r_ds1_filter,sK4,sK3) ),
inference(cnf_transformation,[],[f136]) ).
fof(f153,plain,
( ~ sP1
| leq(sK6,minus(n6,n1)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f154,plain,
( ~ sP1
| leq(sK5,minus(n6,n1)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f155,plain,
( ~ sP1
| leq(n0,sK6) ),
inference(cnf_transformation,[],[f139]) ).
fof(f156,plain,
( ~ sP1
| leq(n0,sK5) ),
inference(cnf_transformation,[],[f139]) ).
fof(f157,plain,
( ~ sP1
| a_select3(pminus_ds1_filter,sK5,sK6) != a_select3(pminus_ds1_filter,sK6,sK5) ),
inference(cnf_transformation,[],[f139]) ).
fof(f163,plain,
! [X8,X9] :
( ~ leq(X8,minus(plus(n1,minus(n6,n1)),n1))
| ~ leq(n0,X8)
| ~ leq(X9,minus(n6,n1))
| ~ leq(n0,X9)
| a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ),
inference(cnf_transformation,[],[f144]) ).
fof(f164,plain,
! [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) ),
inference(cnf_transformation,[],[f144]) ).
fof(f165,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,[],[f144]) ).
fof(f166,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,[],[f144]) ).
fof(f167,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f144]) ).
fof(f168,plain,
leq(n0,pv5),
inference(cnf_transformation,[],[f144]) ).
fof(f169,plain,
( sP0
| sP1
| sP2
| leq(sK10,minus(n6,n1))
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f144]) ).
fof(f170,plain,
( sP0
| sP1
| sP2
| leq(sK9,minus(n6,n1))
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f144]) ).
fof(f171,plain,
( sP0
| sP1
| sP2
| leq(n0,sK10)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f144]) ).
fof(f172,plain,
( sP0
| sP1
| sP2
| leq(n0,sK9)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f144]) ).
fof(f173,plain,
( sP0
| sP1
| sP2
| a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f144]) ).
fof(f205,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f216,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f251,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f278,plain,
! [X0] : minus(plus(n1,X0),n1) = X0,
inference(definition_unfolding,[],[f251,f216,f205]) ).
tcf(c_49,plain,
( ~ sP2
| ( a_select3(r_ds1_filter,sK3,sK4) != a_select3(r_ds1_filter,sK4,sK3) ) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_50,plain,
( leq(n0,sK3)
| ~ sP2 ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_51,plain,
( leq(n0,sK4)
| ~ sP2 ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_52,plain,
( leq(sK3,minus(n3,n1))
| ~ sP2 ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_53,plain,
( leq(sK4,minus(n3,n1))
| ~ sP2 ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_54,plain,
( ~ sP1
| ( a_select3(pminus_ds1_filter,sK5,sK6) != a_select3(pminus_ds1_filter,sK6,sK5) ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_55,plain,
( leq(n0,sK5)
| ~ sP1 ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_56,plain,
( leq(n0,sK6)
| ~ sP1 ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_57,plain,
( leq(sK5,minus(n6,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_58,plain,
( leq(sK6,minus(n6,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_64,negated_conjecture,
( sP0
| sP1
| sP2
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ( a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9) ) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_65,negated_conjecture,
( sP0
| sP1
| sP2
| leq(n0,sK9)
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1)) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_66,negated_conjecture,
( sP0
| sP1
| sP2
| leq(n0,sK10)
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_67,negated_conjecture,
( sP0
| sP1
| sP2
| leq(sK9,minus(n6,n1))
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_68,negated_conjecture,
( sP0
| sP1
| sP2
| leq(sK10,minus(n6,n1))
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1)) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_69,negated_conjecture,
leq(n0,pv5),
inference(cnf_transformation,[],[f168]) ).
tcf(c_70,negated_conjecture,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f167]) ).
tcf(c_71,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,[],[f166]) ).
tcf(c_72,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,[],[f165]) ).
tcf(c_73,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,[],[f164]) ).
tcf(c_74,negated_conjecture,
! [X0: $i,X1: $i] :
( ( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0) )
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(plus(n1,minus(n6,n1)),n1)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_150,plain,
! [X0: $i] : minus(plus(n1,X0),n1) = X0,
inference(cnf_transformation,[],[f278]) ).
tcf(c_184,negated_conjecture,
( sP0
| sP1
| sP2
| leq(n0,sK10) ),
inference(global_subsumption_just,[status(thm)],[c_66,c_69,c_70,c_66]) ).
tcf(c_186,negated_conjecture,
( sP0
| sP1
| sP2
| leq(n0,sK9) ),
inference(global_subsumption_just,[status(thm)],[c_65,c_69,c_70,c_65]) ).
tcf(c_188,negated_conjecture,
( sP0
| sP1
| sP2
| leq(sK10,minus(n6,n1)) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_69,c_70,c_68]) ).
tcf(c_190,negated_conjecture,
( sP0
| sP1
| sP2
| leq(sK9,minus(n6,n1)) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_69,c_70,c_67]) ).
tcf(c_192,negated_conjecture,
( sP0
| sP1
| sP2
| ( a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9) ) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_69,c_70,c_64]) ).
tcf(c_1098,plain,
! [X0: $i,X1: $i] :
( ( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0) )
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1)) ),
inference(demodulation,[status(thm)],[c_74,c_150]) ).
tcf(c_3861,plain,
! [X0: $i] :
( sP0
| sP1
| sP2
| ( a_select3(q_ds1_filter,X0,sK9) = a_select3(q_ds1_filter,sK9,X0) )
| ~ leq(n0,sK9)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(superposition,[status(thm)],[c_190,c_71]) ).
tcf(c_3935,plain,
! [X0: $i] :
( sP0
| sP1
| sP2
| ( a_select3(q_ds1_filter,X0,sK9) = a_select3(q_ds1_filter,sK9,X0) )
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3861,c_186,c_3861]) ).
tcf(c_3936,plain,
! [X0: $i] :
( sP0
| sP1
| sP2
| ( a_select3(q_ds1_filter,X0,sK9) = a_select3(q_ds1_filter,sK9,X0) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(renaming,[status(thm)],[c_3935]) ).
tcf(c_3951,plain,
( sP0
| sP1
| sP2
| ( a_select3(q_ds1_filter,sK9,sK10) = a_select3(q_ds1_filter,sK10,sK9) )
| ~ leq(n0,sK10) ),
inference(superposition,[status(thm)],[c_188,c_3936]) ).
tcf(c_3963,plain,
( sP0
| sP1
| sP2 ),
inference(global_subsumption_just,[status(thm)],[c_3951,c_184,c_192,c_3951]) ).
tcf(c_4069,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK3) = a_select3(r_ds1_filter,sK3,X0) )
| ~ sP2
| ~ leq(n0,sK3)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(superposition,[status(thm)],[c_52,c_72]) ).
tcf(c_4080,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK3) = a_select3(r_ds1_filter,sK3,X0) )
| ~ sP2
| ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4069,c_50,c_4069]) ).
tcf(c_4081,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK3) = a_select3(r_ds1_filter,sK3,X0) )
| ~ sP2
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(renaming,[status(thm)],[c_4080]) ).
tcf(c_4101,plain,
( ( a_select3(r_ds1_filter,sK3,sK4) = a_select3(r_ds1_filter,sK4,sK3) )
| ~ sP2
| ~ leq(n0,sK4) ),
inference(superposition,[status(thm)],[c_53,c_4081]) ).
tcf(c_4103,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK4) = a_select3(r_ds1_filter,sK4,X0) )
| ~ sP2
| ~ leq(n0,sK4)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(superposition,[status(thm)],[c_53,c_72]) ).
tcf(c_4125,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK5) = a_select3(pminus_ds1_filter,sK5,X0) )
| ~ sP1
| ~ leq(n0,sK5)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(superposition,[status(thm)],[c_57,c_73]) ).
tcf(c_4126,plain,
! [X0: $i] :
( ( a_select3(q_ds1_filter,X0,sK5) = a_select3(q_ds1_filter,sK5,X0) )
| ~ sP1
| ~ leq(n0,sK5)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(superposition,[status(thm)],[c_57,c_71]) ).
tcf(c_4319,plain,
~ sP2,
inference(global_subsumption_just,[status(thm)],[c_4103,c_51,c_49,c_4101]) ).
tcf(c_4324,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK5) = a_select3(pminus_ds1_filter,sK5,X0) )
| ~ sP1
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4125,c_55,c_4125]) ).
tcf(c_4325,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK5) = a_select3(pminus_ds1_filter,sK5,X0) )
| ~ sP1
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(renaming,[status(thm)],[c_4324]) ).
tcf(c_4336,plain,
( ( a_select3(pminus_ds1_filter,sK5,sK6) = a_select3(pminus_ds1_filter,sK6,sK5) )
| ~ sP1
| ~ leq(n0,sK6) ),
inference(superposition,[status(thm)],[c_58,c_4325]) ).
tcf(c_4354,plain,
~ sP1,
inference(global_subsumption_just,[status(thm)],[c_4126,c_56,c_54,c_4336]) ).
tcf(c_4507,plain,
( ( a_select3(id_ds1_filter,sK7,sK8) = a_select3(id_ds1_filter,sK8,sK7) )
| ~ leq(n0,sK8)
| ~ leq(n0,sK7)
| ~ leq(sK8,minus(n6,n1))
| ~ leq(sK7,minus(n6,n1)) ),
inference(instantiation,[status(thm)],[c_1098]) ).
fof(f130,definition,
( ~ sP0
| ? [X14] :
( leq(X14,minus(n6,n1))
& leq(n0,X14)
& ? [X15] :
( leq(X15,minus(n6,n1))
& leq(n0,X15)
& a_select3(id_ds1_filter,X14,X15) != a_select3(id_ds1_filter,X15,X14) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f131,definition,
( ~ sP1
| ? [X12,X13] :
( leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12)
& a_select3(pminus_ds1_filter,X12,X13) != a_select3(pminus_ds1_filter,X13,X12) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f132,definition,
( ~ sP2
| ? [X10,X11] :
( leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10)
& a_select3(r_ds1_filter,X10,X11) != a_select3(r_ds1_filter,X11,X10) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f133,plain,
( ! [X6] :
( ~ leq(X6,minus(plus(n1,minus(n6,n1)),n1))
| ~ leq(n0,X6)
| ! [X7] :
( ~ leq(X7,minus(n6,n1))
| ~ leq(n0,X7)
| a_select3(id_ds1_filter,X6,X7) = a_select3(id_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
| sP2
| ? [X8,X9] :
( leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8)
& a_select3(q_ds1_filter,X8,X9) != a_select3(q_ds1_filter,X9,X8) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ) ),
inference(definition_folding,[],[f105,f132,f131,f130]) ).
fof(f140,plain,
( ~ sP0
| ? [X14] :
( leq(X14,minus(n6,n1))
& leq(n0,X14)
& ? [X15] :
( leq(X15,minus(n6,n1))
& leq(n0,X15)
& a_select3(id_ds1_filter,X14,X15) != a_select3(id_ds1_filter,X15,X14) ) ) ),
inference(nnf_transformation,[],[f130]) ).
fof(f141,plain,
( ~ sP0
| ? [X0] :
( leq(X0,minus(n6,n1))
& leq(n0,X0)
& ? [X1] :
( leq(X1,minus(n6,n1))
& leq(n0,X1)
& a_select3(id_ds1_filter,X0,X1) != a_select3(id_ds1_filter,X1,X0) ) ) ),
inference(rectify,[],[f140]) ).
fof(f142,plain,
( ~ sP0
| ( leq(sK7,minus(n6,n1))
& leq(n0,sK7)
& leq(sK8,minus(n6,n1))
& leq(n0,sK8)
& a_select3(id_ds1_filter,sK7,sK8) != a_select3(id_ds1_filter,sK8,sK7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f141]) ).
fof(f158,plain,
( ~ sP0
| leq(sK7,minus(n6,n1)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f159,plain,
( ~ sP0
| leq(n0,sK7) ),
inference(cnf_transformation,[],[f142]) ).
fof(f160,plain,
( ~ sP0
| leq(sK8,minus(n6,n1)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f161,plain,
( ~ sP0
| leq(n0,sK8) ),
inference(cnf_transformation,[],[f142]) ).
fof(f162,plain,
( ~ sP0
| a_select3(id_ds1_filter,sK7,sK8) != a_select3(id_ds1_filter,sK8,sK7) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_59,plain,
( ~ sP0
| ( a_select3(id_ds1_filter,sK7,sK8) != a_select3(id_ds1_filter,sK8,sK7) ) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_60,plain,
( leq(n0,sK8)
| ~ sP0 ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_61,plain,
( leq(sK8,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_62,plain,
( leq(n0,sK7)
| ~ sP0 ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_63,plain,
( leq(sK7,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_4508,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4507,c_4354,c_4319,c_3963,c_59,c_61,c_63,c_60,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV117+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/10.60 % Computer : n015.cluster.edu
% 0.11/10.60 % Model : x86_64 x86_64
% 0.11/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.60 % Memory : 8046.5625MB
% 0.11/10.60 % OS : Linux 6.8.0-71-generic
% 0.11/10.60 % CPULimit : 300
% 0.11/10.60 % WCLimit : 300
% 0.11/10.60 % DateTime : Thu Sep 24 18:36:37 UTC 2026
% 0.11/10.61 % CPUTime :
% 0.11/10.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/10.64 Running first-order theorem proving
% 0.11/10.64 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
% 0.11/10.66
% 0.11/10.66 % ======== iProver multi-core TPTP/SMT =========
% 0.11/10.66
% 0.11/10.66 % Detected problem language: tptp
% 0.11/10.67 % Proving...
% 4.43/11.53 % SZS status Started for theBenchmark.p
% 4.43/11.53 % SZS status Theorem for theBenchmark.p
% 4.43/11.53
% 4.43/11.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.43/11.53
% 4.43/11.53 % ------ iProver source info
% 4.43/11.53
% 4.43/11.53 % git: date: 2026-07-19 20:42:38 +0200
% 4.43/11.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.43/11.53 % git: non_committed_changes: false
% 4.43/11.53
% 4.43/11.53 % ------ Parsing...
% 4.43/11.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.43/11.53
% 4.43/11.53 % ------ Preprocessing... sup_sim: 12 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.43/11.53
% 4.43/11.53 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.43/11.53
% 4.43/11.53 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.43/11.53 % ------ Proving...
% 4.43/11.53 % ------ Problem Properties
% 4.43/11.53
% 4.43/11.53 %
% 4.43/11.53 % clauses 104
% 4.43/11.53 % conjectures 10
% 4.43/11.53 % EPR 59
% 4.43/11.53 % Horn 91
% 4.43/11.53 % unary 59
% 4.43/11.53 % binary 25
% 4.43/11.53 % lits 203
% 4.43/11.53 % lits eq 56
% 4.43/11.53 % fd_pure 0
% 4.43/11.53 % fd_pseudo 0
% 4.43/11.53 % fd_cond 7
% 4.43/11.53 % fd_pseudo_cond 2
% 4.43/11.53 % AC symbols 0
% 4.43/11.53
% 4.43/11.53 % ------ Schedule dynamic 5 is on
% 4.43/11.53
% 4.43/11.53 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.43/11.53
% 4.43/11.53
% 4.43/11.53 % ------
% 4.43/11.53 % Current options:
% 4.43/11.53 % ------
% 4.43/11.53
% 4.43/11.53
% 4.43/11.53 %
% 4.43/11.53
% 4.43/11.53 % ------ Proving...
% 4.43/11.53 %
% 4.43/11.53
% 4.43/11.53 % SZS status Theorem for theBenchmark.p
% 4.43/11.53
% 4.43/11.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.43/11.53
% 4.43/11.53
%------------------------------------------------------------------------------