%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV109+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 : n002.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 03:16:26 PM UTC 2026
% Result : Theorem 7.99s 1.71s
% Output : CNFRefutation 7.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 161 ( 50 unt; 4 def)
% Number of atoms : 834 ( 154 equ)
% Maximal formula atoms : 56 ( 5 avg)
% Number of connectives : 980 ( 327 ~; 382 |; 245 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 22 con; 0-3 aty)
% Number of variables : 177 ( 0 sgn 129 !; 48 ?; 24 :)
% 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,
( ( ! [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(pv47,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv47)
& leq(n0,pv5) )
=> ( ! [X18] :
( ( leq(X18,minus(n6,n1))
& leq(n0,X18) )
=> ! [X19] :
( ( leq(X19,minus(n6,n1))
& leq(n0,X19) )
=> a_select3(id_ds1_filter,X18,X19) = a_select3(id_ds1_filter,X19,X18) ) )
& ! [X16,X17] :
( ( leq(X17,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X17)
& leq(n0,X16) )
=> a_select3(pminus_ds1_filter,X16,X17) = a_select3(pminus_ds1_filter,X17,X16) )
& ! [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) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0002) ).
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(pv47,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv47)
& leq(n0,pv5) )
=> ( ! [X18] :
( ( leq(X18,minus(n6,n1))
& leq(n0,X18) )
=> ! [X19] :
( ( leq(X19,minus(n6,n1))
& leq(n0,X19) )
=> a_select3(id_ds1_filter,X18,X19) = a_select3(id_ds1_filter,X19,X18) ) )
& ! [X16,X17] :
( ( leq(X17,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X17)
& leq(n0,X16) )
=> a_select3(pminus_ds1_filter,X16,X17) = a_select3(pminus_ds1_filter,X17,X16) )
& ! [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) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f98,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
fof(f99,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
fof(f100,axiom,
succ(succ(succ(succ(succ(succ(n0)))))) = n6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_6) ).
fof(f101,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f102,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(f103,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
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(pv47,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv47)
& leq(n0,pv5)
& ( ? [X18] :
( leq(X18,minus(n6,n1))
& leq(n0,X18)
& ? [X19] :
( leq(X19,minus(n6,n1))
& leq(n0,X19)
& a_select3(id_ds1_filter,X18,X19) != a_select3(id_ds1_filter,X19,X18) ) )
| ? [X16,X17] :
( leq(X17,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X17)
& leq(n0,X16)
& a_select3(pminus_ds1_filter,X16,X17) != a_select3(pminus_ds1_filter,X17,X16) )
| ? [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) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ) ),
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(pv47,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv47)
& leq(n0,pv5)
& ( ? [X18] :
( leq(X18,minus(n6,n1))
& leq(n0,X18)
& ? [X19] :
( leq(X19,minus(n6,n1))
& leq(n0,X19)
& a_select3(id_ds1_filter,X18,X19) != a_select3(id_ds1_filter,X19,X18) ) )
| ? [X16,X17] :
( leq(X17,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X17)
& leq(n0,X16)
& a_select3(pminus_ds1_filter,X16,X17) != a_select3(pminus_ds1_filter,X17,X16) )
| ? [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) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ) ),
inference(flattening,[],[f104]) ).
fof(f135,plain,
( ~ sP3
| ? [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,[],[f133]) ).
fof(f136,plain,
( ~ sP3
| ? [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,[],[f135]) ).
fof(f137,plain,
( ~ sP3
| ( leq(sK5,minus(n3,n1))
& leq(sK4,minus(n3,n1))
& leq(n0,sK5)
& leq(n0,sK4)
& a_select3(r_ds1_filter,sK4,sK5) != a_select3(r_ds1_filter,sK5,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f136]) ).
fof(f138,plain,
( ~ sP2
| ? [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,[],[f132]) ).
fof(f139,plain,
( ~ sP2
| ? [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,[],[f138]) ).
fof(f140,plain,
( ~ sP2
| ( leq(sK7,minus(n6,n1))
& leq(sK6,minus(n6,n1))
& leq(n0,sK7)
& leq(n0,sK6)
& a_select3(pminus_ds1_filter,sK6,sK7) != a_select3(pminus_ds1_filter,sK7,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f139]) ).
fof(f141,plain,
( ~ sP1
| ? [X16,X17] :
( leq(X17,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X17)
& leq(n0,X16)
& a_select3(pminus_ds1_filter,X16,X17) != a_select3(pminus_ds1_filter,X17,X16) ) ),
inference(nnf_transformation,[],[f131]) ).
fof(f142,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,[],[f141]) ).
fof(f143,plain,
( ~ sP1
| ( leq(sK9,minus(n6,n1))
& leq(sK8,minus(n6,n1))
& leq(n0,sK9)
& leq(n0,sK8)
& a_select3(pminus_ds1_filter,sK8,sK9) != a_select3(pminus_ds1_filter,sK9,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f142]) ).
fof(f147,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(pv47,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv47)
& leq(n0,pv5)
& ( sP0
| sP1
| sP2
| sP3
| ? [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,[],[f134]) ).
fof(f148,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(pv47,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv47)
& leq(n0,pv5)
& ( sP0
| sP1
| sP2
| sP3
| ( leq(sK13,minus(n6,n1))
& leq(sK12,minus(n6,n1))
& leq(n0,sK13)
& leq(n0,sK12)
& a_select3(q_ds1_filter,sK12,sK13) != a_select3(q_ds1_filter,sK13,sK12) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f147]) ).
fof(f152,plain,
( ~ sP3
| leq(sK5,minus(n3,n1)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f153,plain,
( ~ sP3
| leq(sK4,minus(n3,n1)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f154,plain,
( ~ sP3
| leq(n0,sK5) ),
inference(cnf_transformation,[],[f137]) ).
fof(f155,plain,
( ~ sP3
| leq(n0,sK4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f156,plain,
( ~ sP3
| a_select3(r_ds1_filter,sK4,sK5) != a_select3(r_ds1_filter,sK5,sK4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f157,plain,
( ~ sP2
| leq(sK7,minus(n6,n1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f158,plain,
( ~ sP2
| leq(sK6,minus(n6,n1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f159,plain,
( ~ sP2
| leq(n0,sK7) ),
inference(cnf_transformation,[],[f140]) ).
fof(f160,plain,
( ~ sP2
| leq(n0,sK6) ),
inference(cnf_transformation,[],[f140]) ).
fof(f161,plain,
( ~ sP2
| a_select3(pminus_ds1_filter,sK6,sK7) != a_select3(pminus_ds1_filter,sK7,sK6) ),
inference(cnf_transformation,[],[f140]) ).
fof(f162,plain,
( ~ sP1
| leq(sK9,minus(n6,n1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f163,plain,
( ~ sP1
| leq(sK8,minus(n6,n1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f164,plain,
( ~ sP1
| leq(n0,sK9) ),
inference(cnf_transformation,[],[f143]) ).
fof(f165,plain,
( ~ sP1
| leq(n0,sK8) ),
inference(cnf_transformation,[],[f143]) ).
fof(f166,plain,
( ~ sP1
| a_select3(pminus_ds1_filter,sK8,sK9) != a_select3(pminus_ds1_filter,sK9,sK8) ),
inference(cnf_transformation,[],[f143]) ).
fof(f172,plain,
! [X10,X11] :
( ~ leq(X10,minus(n6,n1))
| ~ leq(n0,X10)
| ~ leq(X11,minus(n6,n1))
| ~ leq(n0,X11)
| a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ),
inference(cnf_transformation,[],[f148]) ).
fof(f173,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,[],[f148]) ).
fof(f175,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,[],[f148]) ).
fof(f176,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,[],[f148]) ).
fof(f177,plain,
leq(pv47,minus(n6,n1)),
inference(cnf_transformation,[],[f148]) ).
fof(f178,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f148]) ).
fof(f179,plain,
leq(n0,pv47),
inference(cnf_transformation,[],[f148]) ).
fof(f180,plain,
leq(n0,pv5),
inference(cnf_transformation,[],[f148]) ).
fof(f181,plain,
( sP0
| sP1
| sP2
| sP3
| leq(sK13,minus(n6,n1))
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f148]) ).
fof(f182,plain,
( sP0
| sP1
| sP2
| sP3
| leq(sK12,minus(n6,n1))
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f148]) ).
fof(f183,plain,
( sP0
| sP1
| sP2
| sP3
| leq(n0,sK13)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f148]) ).
fof(f184,plain,
( sP0
| sP1
| sP2
| sP3
| leq(n0,sK12)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f148]) ).
fof(f185,plain,
( sP0
| sP1
| sP2
| sP3
| a_select3(q_ds1_filter,sK12,sK13) != a_select3(q_ds1_filter,sK13,sK12)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f148]) ).
fof(f198,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f101]) ).
fof(f209,plain,
n3 = succ(succ(succ(n0))),
inference(cnf_transformation,[],[f103]) ).
fof(f218,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f227,plain,
n6 = succ(succ(succ(succ(succ(succ(n0)))))),
inference(cnf_transformation,[],[f100]) ).
fof(f236,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f102]) ).
fof(f242,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f98]) ).
fof(f248,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(cnf_transformation,[],[f99]) ).
fof(f257,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f264,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f272,plain,
n1 = plus(n1,n0),
inference(definition_unfolding,[],[f198,f264]) ).
fof(f273,plain,
n3 = plus(n1,plus(n1,plus(n1,n0))),
inference(definition_unfolding,[],[f209,f264,f264,f264]) ).
fof(f274,plain,
n6 = plus(n1,plus(n1,plus(n1,plus(n1,plus(n1,plus(n1,n0)))))),
inference(definition_unfolding,[],[f227,f264,f264,f264,f264,f264,f264]) ).
fof(f275,plain,
n2 = plus(n1,plus(n1,n0)),
inference(definition_unfolding,[],[f236,f264,f264]) ).
fof(f277,plain,
n4 = plus(n1,plus(n1,plus(n1,plus(n1,n0)))),
inference(definition_unfolding,[],[f242,f264,f264,f264,f264]) ).
fof(f280,plain,
n5 = plus(n1,plus(n1,plus(n1,plus(n1,plus(n1,n0))))),
inference(definition_unfolding,[],[f248,f264,f264,f264,f264,f264]) ).
fof(f285,plain,
! [X0] : minus(plus(n1,X0),n1) = X0,
inference(definition_unfolding,[],[f257,f218,f264]) ).
tcf(c_49,plain,
( ~ sP3
| ( a_select3(r_ds1_filter,sK4,sK5) != a_select3(r_ds1_filter,sK5,sK4) ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_50,plain,
( leq(n0,sK4)
| ~ sP3 ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_51,plain,
( leq(n0,sK5)
| ~ sP3 ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_52,plain,
( leq(sK4,minus(n3,n1))
| ~ sP3 ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_53,plain,
( leq(sK5,minus(n3,n1))
| ~ sP3 ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_54,plain,
( ~ sP2
| ( a_select3(pminus_ds1_filter,sK6,sK7) != a_select3(pminus_ds1_filter,sK7,sK6) ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_55,plain,
( leq(n0,sK6)
| ~ sP2 ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_56,plain,
( leq(n0,sK7)
| ~ sP2 ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_57,plain,
( leq(sK6,minus(n6,n1))
| ~ sP2 ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_58,plain,
( leq(sK7,minus(n6,n1))
| ~ sP2 ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_59,plain,
( ~ sP1
| ( a_select3(pminus_ds1_filter,sK8,sK9) != a_select3(pminus_ds1_filter,sK9,sK8) ) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_60,plain,
( leq(n0,sK8)
| ~ sP1 ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_61,plain,
( leq(n0,sK9)
| ~ sP1 ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_62,plain,
( leq(sK8,minus(n6,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_63,plain,
( leq(sK9,minus(n6,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_69,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ( a_select3(q_ds1_filter,sK12,sK13) != a_select3(q_ds1_filter,sK13,sK12) ) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_70,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| leq(n0,sK12)
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1)) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_71,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| leq(n0,sK13)
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_72,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| leq(sK12,minus(n6,n1))
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_73,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| leq(sK13,minus(n6,n1))
| ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_74,negated_conjecture,
leq(n0,pv5),
inference(cnf_transformation,[],[f180]) ).
tcf(c_75,negated_conjecture,
leq(n0,pv47),
inference(cnf_transformation,[],[f179]) ).
tcf(c_76,negated_conjecture,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f178]) ).
tcf(c_77,negated_conjecture,
leq(pv47,minus(n6,n1)),
inference(cnf_transformation,[],[f177]) ).
tcf(c_78,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,[],[f176]) ).
tcf(c_79,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,[],[f175]) ).
tcf(c_81,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,[],[f173]) ).
tcf(c_82,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(n6,n1)) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_95,plain,
plus(n1,n0) = n1,
inference(cnf_transformation,[],[f272]) ).
tcf(c_106,plain,
plus(n1,plus(n1,plus(n1,n0))) = n3,
inference(cnf_transformation,[],[f273]) ).
tcf(c_123,plain,
plus(n1,plus(n1,plus(n1,plus(n1,plus(n1,plus(n1,n0)))))) = n6,
inference(cnf_transformation,[],[f274]) ).
tcf(c_132,plain,
plus(n1,plus(n1,n0)) = n2,
inference(cnf_transformation,[],[f275]) ).
tcf(c_138,plain,
plus(n1,plus(n1,plus(n1,plus(n1,n0)))) = n4,
inference(cnf_transformation,[],[f277]) ).
tcf(c_144,plain,
plus(n1,plus(n1,plus(n1,plus(n1,plus(n1,n0))))) = n5,
inference(cnf_transformation,[],[f280]) ).
tcf(c_153,plain,
! [X0: $i] : minus(plus(n1,X0),n1) = X0,
inference(cnf_transformation,[],[f285]) ).
tcf(c_192,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| leq(n0,sK13) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_74,c_76,c_71]) ).
tcf(c_194,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| leq(n0,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_70,c_74,c_76,c_70]) ).
tcf(c_196,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| leq(sK13,minus(n6,n1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_74,c_76,c_73]) ).
tcf(c_198,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| leq(sK12,minus(n6,n1)) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_74,c_76,c_72]) ).
tcf(c_200,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| ( a_select3(q_ds1_filter,sK12,sK13) != a_select3(q_ds1_filter,sK13,sK12) ) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_74,c_76,c_69]) ).
tcf(c_985,plain,
plus(n1,n1) = n2,
inference(light_normalisation,[status(thm)],[c_132,c_95]) ).
tcf(c_1034,plain,
plus(n1,n2) = n3,
inference(light_normalisation,[status(thm)],[c_106,c_95,c_985]) ).
tcf(c_1069,plain,
plus(n1,n3) = n4,
inference(light_normalisation,[status(thm)],[c_138,c_95,c_985,c_1034]) ).
tcf(c_1092,plain,
plus(n1,n4) = n5,
inference(light_normalisation,[status(thm)],[c_144,c_95,c_985,c_1034,c_1069]) ).
tcf(c_1107,plain,
plus(n1,n5) = n6,
inference(light_normalisation,[status(thm)],[c_123,c_95,c_985,c_1034,c_1069,c_1092]) ).
tcf(c_8035,plain,
! [X0: $i] :
( sP0
| sP1
| sP2
| sP3
| ( a_select3(q_ds1_filter,X0,sK12) = a_select3(q_ds1_filter,sK12,X0) )
| ~ leq(n0,sK12)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(superposition,[status(thm)],[c_198,c_78]) ).
tcf(c_8311,plain,
! [X0: $i] :
( sP0
| sP1
| sP2
| sP3
| ( a_select3(q_ds1_filter,X0,sK12) = a_select3(q_ds1_filter,sK12,X0) )
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_8035,c_194,c_8035]) ).
tcf(c_8312,plain,
! [X0: $i] :
( sP0
| sP1
| sP2
| sP3
| ( a_select3(q_ds1_filter,X0,sK12) = a_select3(q_ds1_filter,sK12,X0) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(renaming,[status(thm)],[c_8311]) ).
tcf(c_8329,plain,
( sP0
| sP1
| sP2
| sP3
| ( a_select3(q_ds1_filter,sK12,sK13) = a_select3(q_ds1_filter,sK13,sK12) )
| ~ leq(n0,sK13) ),
inference(superposition,[status(thm)],[c_196,c_8312]) ).
tcf(c_8344,plain,
( sP0
| sP1
| sP2
| sP3 ),
inference(global_subsumption_just,[status(thm)],[c_8329,c_192,c_200,c_8329]) ).
tcf(c_8473,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK4) = a_select3(r_ds1_filter,sK4,X0) )
| ~ sP3
| ~ leq(n0,sK4)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(superposition,[status(thm)],[c_52,c_79]) ).
tcf(c_8489,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK5) = a_select3(r_ds1_filter,sK5,X0) )
| ~ sP3
| ~ leq(n0,sK5)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(superposition,[status(thm)],[c_53,c_79]) ).
tcf(c_8511,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK6) = a_select3(pminus_ds1_filter,sK6,X0) )
| ~ sP2
| ~ leq(n0,sK6)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(superposition,[status(thm)],[c_57,c_81]) ).
tcf(c_8615,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK8) = a_select3(pminus_ds1_filter,sK8,X0) )
| ~ sP1
| ~ leq(n0,sK8)
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(superposition,[status(thm)],[c_62,c_81]) ).
tcf(c_8812,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK4) = a_select3(r_ds1_filter,sK4,X0) )
| ~ sP3
| ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_8473,c_50,c_8473]) ).
tcf(c_8813,plain,
! [X0: $i] :
( ( a_select3(r_ds1_filter,X0,sK4) = a_select3(r_ds1_filter,sK4,X0) )
| ~ sP3
| ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1)) ),
inference(renaming,[status(thm)],[c_8812]) ).
tcf(c_8824,plain,
( ( a_select3(r_ds1_filter,sK4,sK5) = a_select3(r_ds1_filter,sK5,sK4) )
| ~ sP3
| ~ leq(n0,sK5) ),
inference(superposition,[status(thm)],[c_53,c_8813]) ).
tcf(c_8832,plain,
~ sP3,
inference(global_subsumption_just,[status(thm)],[c_8489,c_51,c_49,c_8824]) ).
tcf(c_8886,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK6) = a_select3(pminus_ds1_filter,sK6,X0) )
| ~ sP2
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_8511,c_55,c_8511]) ).
tcf(c_8887,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK6) = a_select3(pminus_ds1_filter,sK6,X0) )
| ~ sP2
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(renaming,[status(thm)],[c_8886]) ).
tcf(c_8898,plain,
( ( a_select3(pminus_ds1_filter,sK6,sK7) = a_select3(pminus_ds1_filter,sK7,sK6) )
| ~ sP2
| ~ leq(n0,sK7) ),
inference(superposition,[status(thm)],[c_58,c_8887]) ).
tcf(c_8903,plain,
( ( a_select3(pminus_ds1_filter,sK6,pv47) = a_select3(pminus_ds1_filter,pv47,sK6) )
| ~ sP2
| ~ leq(n0,pv47) ),
inference(superposition,[status(thm)],[c_77,c_8887]) ).
tcf(c_8905,plain,
( ( a_select3(pminus_ds1_filter,sK6,pv47) = a_select3(pminus_ds1_filter,pv47,sK6) )
| ~ sP2 ),
inference(forward_subsumption_resolution,[status(thm)],[c_8903,c_75]) ).
tcf(c_8938,plain,
~ sP2,
inference(global_subsumption_just,[status(thm)],[c_8905,c_56,c_54,c_8898]) ).
tcf(c_9015,plain,
! [X0: $i] :
( ( a_select3(id_ds1_filter,sK10,X0) = a_select3(id_ds1_filter,X0,sK10) )
| ~ leq(n0,sK10)
| ~ leq(n0,X0)
| ~ leq(sK10,minus(n6,n1))
| ~ leq(X0,minus(n6,n1)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_9040,plain,
minus(n6,n1) = n5,
inference(superposition,[status(thm)],[c_1107,c_153]) ).
tcf(c_9057,plain,
( leq(sK9,n5)
| ~ sP1 ),
inference(demodulation,[status(thm)],[c_63,c_9040]) ).
tcf(c_9230,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK8) = a_select3(pminus_ds1_filter,sK8,X0) )
| ~ sP1
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_8615,c_60,c_8615]) ).
tcf(c_9231,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK8) = a_select3(pminus_ds1_filter,sK8,X0) )
| ~ sP1
| ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1)) ),
inference(renaming,[status(thm)],[c_9230]) ).
tcf(c_9233,plain,
! [X0: $i] :
( ( a_select3(pminus_ds1_filter,X0,sK8) = a_select3(pminus_ds1_filter,sK8,X0) )
| ~ sP1
| ~ leq(n0,X0)
| ~ leq(X0,n5) ),
inference(light_normalisation,[status(thm)],[c_9231,c_9040]) ).
tcf(c_9247,plain,
( ( a_select3(pminus_ds1_filter,sK8,sK9) = a_select3(pminus_ds1_filter,sK9,sK8) )
| ~ sP1
| ~ leq(sK9,n5) ),
inference(superposition,[status(thm)],[c_61,c_9233]) ).
tcf(c_9250,plain,
( ( a_select3(pminus_ds1_filter,sK8,pv5) = a_select3(pminus_ds1_filter,pv5,sK8) )
| ~ sP1
| ~ leq(pv5,n5) ),
inference(superposition,[status(thm)],[c_74,c_9233]) ).
tcf(c_9308,plain,
~ sP1,
inference(global_subsumption_just,[status(thm)],[c_9250,c_59,c_9057,c_9247]) ).
tcf(c_10708,plain,
( ( a_select3(id_ds1_filter,sK10,sK11) = a_select3(id_ds1_filter,sK11,sK10) )
| ~ leq(n0,sK11)
| ~ leq(n0,sK10)
| ~ leq(sK11,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1)) ),
inference(instantiation,[status(thm)],[c_9015]) ).
fof(f130,definition,
( ~ sP0
| ? [X18] :
( leq(X18,minus(n6,n1))
& leq(n0,X18)
& ? [X19] :
( leq(X19,minus(n6,n1))
& leq(n0,X19)
& a_select3(id_ds1_filter,X18,X19) != a_select3(id_ds1_filter,X19,X18) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f131,definition,
( ~ sP1
| ? [X16,X17] :
( leq(X17,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X17)
& leq(n0,X16)
& a_select3(pminus_ds1_filter,X16,X17) != a_select3(pminus_ds1_filter,X17,X16) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f132,definition,
( ~ sP2
| ? [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,[sP2])],[predicate_definition_introduction]) ).
fof(f133,definition,
( ~ sP3
| ? [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,[sP3])],[predicate_definition_introduction]) ).
fof(f134,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(pv47,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv47)
& leq(n0,pv5)
& ( sP0
| sP1
| sP2
| sP3
| ? [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) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ) ),
inference(definition_folding,[],[f105,f133,f132,f131,f130]) ).
fof(f144,plain,
( ~ sP0
| ? [X18] :
( leq(X18,minus(n6,n1))
& leq(n0,X18)
& ? [X19] :
( leq(X19,minus(n6,n1))
& leq(n0,X19)
& a_select3(id_ds1_filter,X18,X19) != a_select3(id_ds1_filter,X19,X18) ) ) ),
inference(nnf_transformation,[],[f130]) ).
fof(f145,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,[],[f144]) ).
fof(f146,plain,
( ~ sP0
| ( leq(sK10,minus(n6,n1))
& leq(n0,sK10)
& leq(sK11,minus(n6,n1))
& leq(n0,sK11)
& a_select3(id_ds1_filter,sK10,sK11) != a_select3(id_ds1_filter,sK11,sK10) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f145]) ).
fof(f167,plain,
( ~ sP0
| leq(sK10,minus(n6,n1)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f168,plain,
( ~ sP0
| leq(n0,sK10) ),
inference(cnf_transformation,[],[f146]) ).
fof(f169,plain,
( ~ sP0
| leq(sK11,minus(n6,n1)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f170,plain,
( ~ sP0
| leq(n0,sK11) ),
inference(cnf_transformation,[],[f146]) ).
fof(f171,plain,
( ~ sP0
| a_select3(id_ds1_filter,sK10,sK11) != a_select3(id_ds1_filter,sK11,sK10) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_64,plain,
( ~ sP0
| ( a_select3(id_ds1_filter,sK10,sK11) != a_select3(id_ds1_filter,sK11,sK10) ) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_65,plain,
( leq(n0,sK11)
| ~ sP0 ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_66,plain,
( leq(sK11,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_67,plain,
( leq(n0,sK10)
| ~ sP0 ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_68,plain,
( leq(sK10,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_10709,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10708,c_9308,c_8938,c_8832,c_8344,c_64,c_66,c_68,c_65,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV109+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.06/0.34 % Computer : n002.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Thu Sep 24 18:34:49 UTC 2026
% 0.06/0.35 % CPUTime :
% 0.06/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.40 % Proving...
% 7.99/1.71 % SZS status Started for theBenchmark.p
% 7.99/1.71 % SZS status Theorem for theBenchmark.p
% 7.99/1.71
% 7.99/1.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.99/1.71
% 7.99/1.71 % ------ iProver source info
% 7.99/1.71
% 7.99/1.71 % git: date: 2026-07-19 20:42:38 +0200
% 7.99/1.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.99/1.71 % git: non_committed_changes: false
% 7.99/1.71
% 7.99/1.71 % ------ Parsing...
% 7.99/1.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.99/1.71
% 7.99/1.71 % ------ 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 %
% 7.99/1.71
% 7.99/1.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.99/1.71
% 7.99/1.71 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.99/1.71 % ------ Proving...
% 7.99/1.71 % ------ Problem Properties
% 7.99/1.71
% 7.99/1.71 %
% 7.99/1.71 % clauses 111
% 7.99/1.71 % conjectures 13
% 7.99/1.71 % EPR 62
% 7.99/1.71 % Horn 98
% 7.99/1.71 % unary 61
% 7.99/1.71 % binary 30
% 7.99/1.71 % lits 220
% 7.99/1.71 % lits eq 57
% 7.99/1.71 % fd_pure 0
% 7.99/1.71 % fd_pseudo 0
% 7.99/1.71 % fd_cond 7
% 7.99/1.71 % fd_pseudo_cond 2
% 7.99/1.71 % AC symbols 0
% 7.99/1.71
% 7.99/1.71 % ------ Schedule dynamic 5 is on
% 7.99/1.71
% 7.99/1.71 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.99/1.71
% 7.99/1.71
% 7.99/1.71 % ------
% 7.99/1.71 % Current options:
% 7.99/1.71 % ------
% 7.99/1.71
% 7.99/1.71
% 7.99/1.71 %
% 7.99/1.71
% 7.99/1.71 % ------ Proving...
% 7.99/1.71 %
% 7.99/1.71
% 7.99/1.71 % SZS status Theorem for theBenchmark.p
% 7.99/1.71
% 7.99/1.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.99/1.71
% 7.99/1.71
%------------------------------------------------------------------------------