TSTP Solution File: SWV114+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWV114+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 22:31:11 EDT 2023
% Result : Theorem 3.74s 1.13s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 112 ( 15 unt; 0 def)
% Number of atoms : 632 ( 98 equ)
% Maximal formula atoms : 39 ( 5 avg)
% Number of connectives : 776 ( 256 ~; 244 |; 242 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 18 con; 0-3 aty)
% Number of variables : 175 ( 0 sgn; 102 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f53,conjecture,
( ( ! [X20,X21] :
( ( leq(X21,minus(n6,n1))
& leq(X20,minus(n6,n1))
& leq(n0,X21)
& leq(n0,X20) )
=> a_select3(pminus_ds1_filter,X20,X21) = a_select3(pminus_ds1_filter,X21,X20) )
& ! [X3,X19] :
( ( leq(X19,minus(n3,n1))
& leq(X3,minus(n3,n1))
& leq(n0,X19)
& leq(n0,X3) )
=> a_select3(r_ds1_filter,X3,X19) = a_select3(r_ds1_filter,X19,X3) )
& ! [X13,X17] :
( ( leq(X17,minus(n6,n1))
& leq(X13,minus(n6,n1))
& leq(n0,X17)
& leq(n0,X13) )
=> a_select3(q_ds1_filter,X13,X17) = a_select3(q_ds1_filter,X17,X13) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [X18] :
( ( leq(X18,minus(n0,n1))
& leq(n0,X18) )
=> ! [X14] :
( ( leq(X14,minus(n6,n1))
& leq(n0,X14) )
=> a_select3(id_ds1_filter,X18,X14) = a_select3(id_ds1_filter,X14,X18) ) )
& ! [X15,X5] :
( ( leq(X5,minus(n6,n1))
& leq(X15,minus(n6,n1))
& leq(n0,X5)
& leq(n0,X15) )
=> a_select3(pminus_ds1_filter,X15,X5) = a_select3(pminus_ds1_filter,X5,X15) )
& ! [X4,X10] :
( ( leq(X10,minus(n3,n1))
& leq(X4,minus(n3,n1))
& leq(n0,X10)
& leq(n0,X4) )
=> a_select3(r_ds1_filter,X4,X10) = a_select3(r_ds1_filter,X10,X4) )
& ! [X27,X28] :
( ( leq(X28,minus(n6,n1))
& leq(X27,minus(n6,n1))
& leq(n0,X28)
& leq(n0,X27) )
=> a_select3(q_ds1_filter,X27,X28) = a_select3(q_ds1_filter,X28,X27) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0007) ).
fof(f54,negated_conjecture,
~ ( ( ! [X20,X21] :
( ( leq(X21,minus(n6,n1))
& leq(X20,minus(n6,n1))
& leq(n0,X21)
& leq(n0,X20) )
=> a_select3(pminus_ds1_filter,X20,X21) = a_select3(pminus_ds1_filter,X21,X20) )
& ! [X3,X19] :
( ( leq(X19,minus(n3,n1))
& leq(X3,minus(n3,n1))
& leq(n0,X19)
& leq(n0,X3) )
=> a_select3(r_ds1_filter,X3,X19) = a_select3(r_ds1_filter,X19,X3) )
& ! [X13,X17] :
( ( leq(X17,minus(n6,n1))
& leq(X13,minus(n6,n1))
& leq(n0,X17)
& leq(n0,X13) )
=> a_select3(q_ds1_filter,X13,X17) = a_select3(q_ds1_filter,X17,X13) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [X18] :
( ( leq(X18,minus(n0,n1))
& leq(n0,X18) )
=> ! [X14] :
( ( leq(X14,minus(n6,n1))
& leq(n0,X14) )
=> a_select3(id_ds1_filter,X18,X14) = a_select3(id_ds1_filter,X14,X18) ) )
& ! [X15,X5] :
( ( leq(X5,minus(n6,n1))
& leq(X15,minus(n6,n1))
& leq(n0,X5)
& leq(n0,X15) )
=> a_select3(pminus_ds1_filter,X15,X5) = a_select3(pminus_ds1_filter,X5,X15) )
& ! [X4,X10] :
( ( leq(X10,minus(n3,n1))
& leq(X4,minus(n3,n1))
& leq(n0,X10)
& leq(n0,X4) )
=> a_select3(r_ds1_filter,X4,X10) = a_select3(r_ds1_filter,X10,X4) )
& ! [X27,X28] :
( ( leq(X28,minus(n6,n1))
& leq(X27,minus(n6,n1))
& leq(n0,X28)
& leq(n0,X27) )
=> a_select3(q_ds1_filter,X27,X28) = a_select3(q_ds1_filter,X28,X27) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f124,plain,
~ ( ( ! [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) )
& ! [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) )
& ! [X4,X5] :
( ( leq(X5,minus(n6,n1))
& leq(X4,minus(n6,n1))
& leq(n0,X5)
& leq(n0,X4) )
=> a_select3(q_ds1_filter,X4,X5) = a_select3(q_ds1_filter,X5,X4) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [X6] :
( ( leq(X6,minus(n0,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) ) )
& ! [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) )
& ! [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) )
& ! [X12,X13] :
( ( leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12) )
=> a_select3(q_ds1_filter,X12,X13) = a_select3(q_ds1_filter,X13,X12) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
inference(rectify,[],[f54]) ).
fof(f128,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f129,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(flattening,[],[f128]) ).
fof(f166,plain,
( ( ? [X6] :
( ? [X7] :
( a_select3(id_ds1_filter,X6,X7) != a_select3(id_ds1_filter,X7,X6)
& leq(X7,minus(n6,n1))
& leq(n0,X7) )
& leq(X6,minus(n0,n1))
& leq(n0,X6) )
| ? [X8,X9] :
( a_select3(pminus_ds1_filter,X8,X9) != a_select3(pminus_ds1_filter,X9,X8)
& leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8) )
| ? [X10,X11] :
( a_select3(r_ds1_filter,X10,X11) != a_select3(r_ds1_filter,X11,X10)
& leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10) )
| ? [X12,X13] :
( a_select3(q_ds1_filter,X12,X13) != a_select3(q_ds1_filter,X13,X12)
& leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) = a_select3(pminus_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(X3,minus(n3,n1))
| ~ leq(X2,minus(n3,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2) )
& ! [X4,X5] :
( a_select3(q_ds1_filter,X4,X5) = a_select3(q_ds1_filter,X5,X4)
| ~ leq(X5,minus(n6,n1))
| ~ leq(X4,minus(n6,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ),
inference(ennf_transformation,[],[f124]) ).
fof(f167,plain,
( ( ? [X6] :
( ? [X7] :
( a_select3(id_ds1_filter,X6,X7) != a_select3(id_ds1_filter,X7,X6)
& leq(X7,minus(n6,n1))
& leq(n0,X7) )
& leq(X6,minus(n0,n1))
& leq(n0,X6) )
| ? [X8,X9] :
( a_select3(pminus_ds1_filter,X8,X9) != a_select3(pminus_ds1_filter,X9,X8)
& leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8) )
| ? [X10,X11] :
( a_select3(r_ds1_filter,X10,X11) != a_select3(r_ds1_filter,X11,X10)
& leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10) )
| ? [X12,X13] :
( a_select3(q_ds1_filter,X12,X13) != a_select3(q_ds1_filter,X13,X12)
& leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) = a_select3(pminus_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(X3,minus(n3,n1))
| ~ leq(X2,minus(n3,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2) )
& ! [X4,X5] :
( a_select3(q_ds1_filter,X4,X5) = a_select3(q_ds1_filter,X5,X4)
| ~ leq(X5,minus(n6,n1))
| ~ leq(X4,minus(n6,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ),
inference(flattening,[],[f166]) ).
fof(f189,plain,
( ? [X12,X13] :
( a_select3(q_ds1_filter,X12,X13) != a_select3(q_ds1_filter,X13,X12)
& leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12) )
| ~ sP4 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f190,plain,
( ? [X10,X11] :
( a_select3(r_ds1_filter,X10,X11) != a_select3(r_ds1_filter,X11,X10)
& leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10) )
| ~ sP5 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f191,plain,
( ? [X8,X9] :
( a_select3(pminus_ds1_filter,X8,X9) != a_select3(pminus_ds1_filter,X9,X8)
& leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8) )
| ~ sP6 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f192,plain,
( ( ? [X6] :
( ? [X7] :
( a_select3(id_ds1_filter,X6,X7) != a_select3(id_ds1_filter,X7,X6)
& leq(X7,minus(n6,n1))
& leq(n0,X7) )
& leq(X6,minus(n0,n1))
& leq(n0,X6) )
| sP6
| sP5
| sP4
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) = a_select3(pminus_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(X3,minus(n3,n1))
| ~ leq(X2,minus(n3,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2) )
& ! [X4,X5] :
( a_select3(q_ds1_filter,X4,X5) = a_select3(q_ds1_filter,X5,X4)
| ~ leq(X5,minus(n6,n1))
| ~ leq(X4,minus(n6,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ),
inference(definition_folding,[],[f167,f191,f190,f189]) ).
fof(f193,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f240,plain,
( ? [X8,X9] :
( a_select3(pminus_ds1_filter,X8,X9) != a_select3(pminus_ds1_filter,X9,X8)
& leq(X9,minus(n6,n1))
& leq(X8,minus(n6,n1))
& leq(n0,X9)
& leq(n0,X8) )
| ~ sP6 ),
inference(nnf_transformation,[],[f191]) ).
fof(f241,plain,
( ? [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) != a_select3(pminus_ds1_filter,X1,X0)
& leq(X1,minus(n6,n1))
& leq(X0,minus(n6,n1))
& leq(n0,X1)
& leq(n0,X0) )
| ~ sP6 ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
( ? [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) != a_select3(pminus_ds1_filter,X1,X0)
& leq(X1,minus(n6,n1))
& leq(X0,minus(n6,n1))
& leq(n0,X1)
& leq(n0,X0) )
=> ( a_select3(pminus_ds1_filter,sK34,sK35) != a_select3(pminus_ds1_filter,sK35,sK34)
& leq(sK35,minus(n6,n1))
& leq(sK34,minus(n6,n1))
& leq(n0,sK35)
& leq(n0,sK34) ) ),
introduced(choice_axiom,[]) ).
fof(f243,plain,
( ( a_select3(pminus_ds1_filter,sK34,sK35) != a_select3(pminus_ds1_filter,sK35,sK34)
& leq(sK35,minus(n6,n1))
& leq(sK34,minus(n6,n1))
& leq(n0,sK35)
& leq(n0,sK34) )
| ~ sP6 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35])],[f241,f242]) ).
fof(f244,plain,
( ? [X10,X11] :
( a_select3(r_ds1_filter,X10,X11) != a_select3(r_ds1_filter,X11,X10)
& leq(X11,minus(n3,n1))
& leq(X10,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X10) )
| ~ sP5 ),
inference(nnf_transformation,[],[f190]) ).
fof(f245,plain,
( ? [X0,X1] :
( a_select3(r_ds1_filter,X0,X1) != a_select3(r_ds1_filter,X1,X0)
& leq(X1,minus(n3,n1))
& leq(X0,minus(n3,n1))
& leq(n0,X1)
& leq(n0,X0) )
| ~ sP5 ),
inference(rectify,[],[f244]) ).
fof(f246,plain,
( ? [X0,X1] :
( a_select3(r_ds1_filter,X0,X1) != a_select3(r_ds1_filter,X1,X0)
& leq(X1,minus(n3,n1))
& leq(X0,minus(n3,n1))
& leq(n0,X1)
& leq(n0,X0) )
=> ( a_select3(r_ds1_filter,sK36,sK37) != a_select3(r_ds1_filter,sK37,sK36)
& leq(sK37,minus(n3,n1))
& leq(sK36,minus(n3,n1))
& leq(n0,sK37)
& leq(n0,sK36) ) ),
introduced(choice_axiom,[]) ).
fof(f247,plain,
( ( a_select3(r_ds1_filter,sK36,sK37) != a_select3(r_ds1_filter,sK37,sK36)
& leq(sK37,minus(n3,n1))
& leq(sK36,minus(n3,n1))
& leq(n0,sK37)
& leq(n0,sK36) )
| ~ sP5 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f245,f246]) ).
fof(f248,plain,
( ? [X12,X13] :
( a_select3(q_ds1_filter,X12,X13) != a_select3(q_ds1_filter,X13,X12)
& leq(X13,minus(n6,n1))
& leq(X12,minus(n6,n1))
& leq(n0,X13)
& leq(n0,X12) )
| ~ sP4 ),
inference(nnf_transformation,[],[f189]) ).
fof(f249,plain,
( ? [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) != a_select3(q_ds1_filter,X1,X0)
& leq(X1,minus(n6,n1))
& leq(X0,minus(n6,n1))
& leq(n0,X1)
& leq(n0,X0) )
| ~ sP4 ),
inference(rectify,[],[f248]) ).
fof(f250,plain,
( ? [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) != a_select3(q_ds1_filter,X1,X0)
& leq(X1,minus(n6,n1))
& leq(X0,minus(n6,n1))
& leq(n0,X1)
& leq(n0,X0) )
=> ( a_select3(q_ds1_filter,sK38,sK39) != a_select3(q_ds1_filter,sK39,sK38)
& leq(sK39,minus(n6,n1))
& leq(sK38,minus(n6,n1))
& leq(n0,sK39)
& leq(n0,sK38) ) ),
introduced(choice_axiom,[]) ).
fof(f251,plain,
( ( a_select3(q_ds1_filter,sK38,sK39) != a_select3(q_ds1_filter,sK39,sK38)
& leq(sK39,minus(n6,n1))
& leq(sK38,minus(n6,n1))
& leq(n0,sK39)
& leq(n0,sK38) )
| ~ sP4 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f249,f250]) ).
fof(f252,plain,
( ( ? [X0] :
( ? [X1] :
( a_select3(id_ds1_filter,X0,X1) != a_select3(id_ds1_filter,X1,X0)
& leq(X1,minus(n6,n1))
& leq(n0,X1) )
& leq(X0,minus(n0,n1))
& leq(n0,X0) )
| sP6
| sP5
| sP4
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [X2,X3] :
( a_select3(pminus_ds1_filter,X2,X3) = a_select3(pminus_ds1_filter,X3,X2)
| ~ leq(X3,minus(n6,n1))
| ~ leq(X2,minus(n6,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(X5,minus(n3,n1))
| ~ leq(X4,minus(n3,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4) )
& ! [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) = a_select3(q_ds1_filter,X7,X6)
| ~ leq(X7,minus(n6,n1))
| ~ leq(X6,minus(n6,n1))
| ~ leq(n0,X7)
| ~ leq(n0,X6) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ),
inference(rectify,[],[f192]) ).
fof(f253,plain,
( ? [X0] :
( ? [X1] :
( a_select3(id_ds1_filter,X0,X1) != a_select3(id_ds1_filter,X1,X0)
& leq(X1,minus(n6,n1))
& leq(n0,X1) )
& leq(X0,minus(n0,n1))
& leq(n0,X0) )
=> ( ? [X1] :
( a_select3(id_ds1_filter,sK40,X1) != a_select3(id_ds1_filter,X1,sK40)
& leq(X1,minus(n6,n1))
& leq(n0,X1) )
& leq(sK40,minus(n0,n1))
& leq(n0,sK40) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
( ? [X1] :
( a_select3(id_ds1_filter,sK40,X1) != a_select3(id_ds1_filter,X1,sK40)
& leq(X1,minus(n6,n1))
& leq(n0,X1) )
=> ( a_select3(id_ds1_filter,sK40,sK41) != a_select3(id_ds1_filter,sK41,sK40)
& leq(sK41,minus(n6,n1))
& leq(n0,sK41) ) ),
introduced(choice_axiom,[]) ).
fof(f255,plain,
( ( ( a_select3(id_ds1_filter,sK40,sK41) != a_select3(id_ds1_filter,sK41,sK40)
& leq(sK41,minus(n6,n1))
& leq(n0,sK41)
& leq(sK40,minus(n0,n1))
& leq(n0,sK40) )
| sP6
| sP5
| sP4
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [X2,X3] :
( a_select3(pminus_ds1_filter,X2,X3) = a_select3(pminus_ds1_filter,X3,X2)
| ~ leq(X3,minus(n6,n1))
| ~ leq(X2,minus(n6,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(X5,minus(n3,n1))
| ~ leq(X4,minus(n3,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4) )
& ! [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) = a_select3(q_ds1_filter,X7,X6)
| ~ leq(X7,minus(n6,n1))
| ~ leq(X6,minus(n6,n1))
| ~ leq(n0,X7)
| ~ leq(n0,X6) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f252,f254,f253]) ).
fof(f258,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f260,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f263,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f193]) ).
fof(f346,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f366,plain,
( leq(n0,sK34)
| ~ sP6 ),
inference(cnf_transformation,[],[f243]) ).
fof(f367,plain,
( leq(n0,sK35)
| ~ sP6 ),
inference(cnf_transformation,[],[f243]) ).
fof(f368,plain,
( leq(sK34,minus(n6,n1))
| ~ sP6 ),
inference(cnf_transformation,[],[f243]) ).
fof(f369,plain,
( leq(sK35,minus(n6,n1))
| ~ sP6 ),
inference(cnf_transformation,[],[f243]) ).
fof(f370,plain,
( a_select3(pminus_ds1_filter,sK34,sK35) != a_select3(pminus_ds1_filter,sK35,sK34)
| ~ sP6 ),
inference(cnf_transformation,[],[f243]) ).
fof(f371,plain,
( leq(n0,sK36)
| ~ sP5 ),
inference(cnf_transformation,[],[f247]) ).
fof(f372,plain,
( leq(n0,sK37)
| ~ sP5 ),
inference(cnf_transformation,[],[f247]) ).
fof(f373,plain,
( leq(sK36,minus(n3,n1))
| ~ sP5 ),
inference(cnf_transformation,[],[f247]) ).
fof(f374,plain,
( leq(sK37,minus(n3,n1))
| ~ sP5 ),
inference(cnf_transformation,[],[f247]) ).
fof(f375,plain,
( a_select3(r_ds1_filter,sK36,sK37) != a_select3(r_ds1_filter,sK37,sK36)
| ~ sP5 ),
inference(cnf_transformation,[],[f247]) ).
fof(f376,plain,
( leq(n0,sK38)
| ~ sP4 ),
inference(cnf_transformation,[],[f251]) ).
fof(f377,plain,
( leq(n0,sK39)
| ~ sP4 ),
inference(cnf_transformation,[],[f251]) ).
fof(f378,plain,
( leq(sK38,minus(n6,n1))
| ~ sP4 ),
inference(cnf_transformation,[],[f251]) ).
fof(f379,plain,
( leq(sK39,minus(n6,n1))
| ~ sP4 ),
inference(cnf_transformation,[],[f251]) ).
fof(f380,plain,
( a_select3(q_ds1_filter,sK38,sK39) != a_select3(q_ds1_filter,sK39,sK38)
| ~ sP4 ),
inference(cnf_transformation,[],[f251]) ).
fof(f381,plain,
leq(n0,pv5),
inference(cnf_transformation,[],[f255]) ).
fof(f382,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f255]) ).
fof(f383,plain,
! [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) = a_select3(q_ds1_filter,X7,X6)
| ~ leq(X7,minus(n6,n1))
| ~ leq(X6,minus(n6,n1))
| ~ leq(n0,X7)
| ~ leq(n0,X6) ),
inference(cnf_transformation,[],[f255]) ).
fof(f384,plain,
! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(X5,minus(n3,n1))
| ~ leq(X4,minus(n3,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4) ),
inference(cnf_transformation,[],[f255]) ).
fof(f385,plain,
! [X2,X3] :
( a_select3(pminus_ds1_filter,X2,X3) = a_select3(pminus_ds1_filter,X3,X2)
| ~ leq(X3,minus(n6,n1))
| ~ leq(X2,minus(n6,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f386,plain,
( leq(n0,sK40)
| sP6
| sP5
| sP4
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f255]) ).
fof(f387,plain,
( leq(sK40,minus(n0,n1))
| sP6
| sP5
| sP4
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[],[f255]) ).
fof(f441,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f263,f346]) ).
cnf(c_51,plain,
~ gt(X0,X0),
inference(cnf_transformation,[],[f258]) ).
cnf(c_53,plain,
( ~ leq(X0,X1)
| ~ leq(X1,X2)
| leq(X0,X2) ),
inference(cnf_transformation,[],[f260]) ).
cnf(c_57,plain,
( ~ leq(X0,minus(X1,n1))
| gt(X1,X0) ),
inference(cnf_transformation,[],[f441]) ).
cnf(c_157,plain,
( a_select3(pminus_ds1_filter,sK34,sK35) != a_select3(pminus_ds1_filter,sK35,sK34)
| ~ sP6 ),
inference(cnf_transformation,[],[f370]) ).
cnf(c_158,plain,
( ~ sP6
| leq(sK35,minus(n6,n1)) ),
inference(cnf_transformation,[],[f369]) ).
cnf(c_159,plain,
( ~ sP6
| leq(sK34,minus(n6,n1)) ),
inference(cnf_transformation,[],[f368]) ).
cnf(c_160,plain,
( ~ sP6
| leq(n0,sK35) ),
inference(cnf_transformation,[],[f367]) ).
cnf(c_161,plain,
( ~ sP6
| leq(n0,sK34) ),
inference(cnf_transformation,[],[f366]) ).
cnf(c_162,plain,
( a_select3(r_ds1_filter,sK36,sK37) != a_select3(r_ds1_filter,sK37,sK36)
| ~ sP5 ),
inference(cnf_transformation,[],[f375]) ).
cnf(c_163,plain,
( ~ sP5
| leq(sK37,minus(n3,n1)) ),
inference(cnf_transformation,[],[f374]) ).
cnf(c_164,plain,
( ~ sP5
| leq(sK36,minus(n3,n1)) ),
inference(cnf_transformation,[],[f373]) ).
cnf(c_165,plain,
( ~ sP5
| leq(n0,sK37) ),
inference(cnf_transformation,[],[f372]) ).
cnf(c_166,plain,
( ~ sP5
| leq(n0,sK36) ),
inference(cnf_transformation,[],[f371]) ).
cnf(c_167,plain,
( a_select3(q_ds1_filter,sK38,sK39) != a_select3(q_ds1_filter,sK39,sK38)
| ~ sP4 ),
inference(cnf_transformation,[],[f380]) ).
cnf(c_168,plain,
( ~ sP4
| leq(sK39,minus(n6,n1)) ),
inference(cnf_transformation,[],[f379]) ).
cnf(c_169,plain,
( ~ sP4
| leq(sK38,minus(n6,n1)) ),
inference(cnf_transformation,[],[f378]) ).
cnf(c_170,plain,
( ~ sP4
| leq(n0,sK39) ),
inference(cnf_transformation,[],[f377]) ).
cnf(c_171,plain,
( ~ sP4
| leq(n0,sK38) ),
inference(cnf_transformation,[],[f376]) ).
cnf(c_175,negated_conjecture,
( ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5)
| leq(sK40,minus(n0,n1))
| sP6
| sP5
| sP4 ),
inference(cnf_transformation,[],[f387]) ).
cnf(c_176,negated_conjecture,
( ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5)
| leq(n0,sK40)
| sP6
| sP5
| sP4 ),
inference(cnf_transformation,[],[f386]) ).
cnf(c_177,negated_conjecture,
( ~ leq(X0,minus(n6,n1))
| ~ leq(X1,minus(n6,n1))
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| a_select3(pminus_ds1_filter,X0,X1) = a_select3(pminus_ds1_filter,X1,X0) ),
inference(cnf_transformation,[],[f385]) ).
cnf(c_178,negated_conjecture,
( ~ leq(X0,minus(n3,n1))
| ~ leq(X1,minus(n3,n1))
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| a_select3(r_ds1_filter,X0,X1) = a_select3(r_ds1_filter,X1,X0) ),
inference(cnf_transformation,[],[f384]) ).
cnf(c_179,negated_conjecture,
( ~ leq(X0,minus(n6,n1))
| ~ leq(X1,minus(n6,n1))
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) ),
inference(cnf_transformation,[],[f383]) ).
cnf(c_180,negated_conjecture,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f382]) ).
cnf(c_181,negated_conjecture,
leq(n0,pv5),
inference(cnf_transformation,[],[f381]) ).
cnf(c_232,plain,
~ gt(n0,n0),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_260,plain,
( ~ leq(n0,minus(n0,n1))
| gt(n0,n0) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_324,negated_conjecture,
( leq(n0,sK40)
| sP6
| sP5
| sP4 ),
inference(global_subsumption_just,[status(thm)],[c_176,c_181,c_180,c_176]) ).
cnf(c_328,negated_conjecture,
( leq(sK40,minus(n0,n1))
| sP6
| sP5
| sP4 ),
inference(global_subsumption_just,[status(thm)],[c_175,c_181,c_180,c_175]) ).
cnf(c_11253,plain,
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| ~ leq(n0,sK35)
| ~ sP6
| a_select3(pminus_ds1_filter,X0,sK35) = a_select3(pminus_ds1_filter,sK35,X0) ),
inference(superposition,[status(thm)],[c_158,c_177]) ).
cnf(c_11282,plain,
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| ~ leq(n0,sK34)
| ~ sP6
| a_select3(q_ds1_filter,X0,sK34) = a_select3(q_ds1_filter,sK34,X0) ),
inference(superposition,[status(thm)],[c_159,c_179]) ).
cnf(c_11309,plain,
( ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X0)
| ~ leq(n0,sK37)
| ~ sP5
| a_select3(r_ds1_filter,X0,sK37) = a_select3(r_ds1_filter,sK37,X0) ),
inference(superposition,[status(thm)],[c_163,c_178]) ).
cnf(c_11341,plain,
( ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1))
| ~ sP6
| a_select3(pminus_ds1_filter,X0,sK35) = a_select3(pminus_ds1_filter,sK35,X0) ),
inference(global_subsumption_just,[status(thm)],[c_11253,c_160,c_11253]) ).
cnf(c_11342,plain,
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| ~ sP6
| a_select3(pminus_ds1_filter,X0,sK35) = a_select3(pminus_ds1_filter,sK35,X0) ),
inference(renaming,[status(thm)],[c_11341]) ).
cnf(c_11354,plain,
( ~ leq(n0,sK34)
| ~ sP6
| a_select3(pminus_ds1_filter,sK34,sK35) = a_select3(pminus_ds1_filter,sK35,sK34) ),
inference(superposition,[status(thm)],[c_159,c_11342]) ).
cnf(c_11362,plain,
~ sP6,
inference(global_subsumption_just,[status(thm)],[c_11282,c_161,c_157,c_11354]) ).
cnf(c_11370,plain,
( leq(sK40,minus(n0,n1))
| sP5
| sP4 ),
inference(backward_subsumption_resolution,[status(thm)],[c_328,c_11362]) ).
cnf(c_11475,plain,
( ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X0)
| ~ leq(n0,sK36)
| ~ sP5
| a_select3(r_ds1_filter,X0,sK36) = a_select3(r_ds1_filter,sK36,X0) ),
inference(superposition,[status(thm)],[c_164,c_178]) ).
cnf(c_11492,plain,
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| ~ leq(n0,sK39)
| ~ sP4
| a_select3(q_ds1_filter,X0,sK39) = a_select3(q_ds1_filter,sK39,X0) ),
inference(superposition,[status(thm)],[c_168,c_179]) ).
cnf(c_11493,plain,
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| ~ leq(n0,sK39)
| ~ sP4
| a_select3(pminus_ds1_filter,X0,sK39) = a_select3(pminus_ds1_filter,sK39,X0) ),
inference(superposition,[status(thm)],[c_168,c_177]) ).
cnf(c_11550,plain,
( ~ leq(n0,X0)
| ~ leq(X0,minus(n3,n1))
| ~ sP5
| a_select3(r_ds1_filter,X0,sK37) = a_select3(r_ds1_filter,sK37,X0) ),
inference(global_subsumption_just,[status(thm)],[c_11309,c_165,c_11309]) ).
cnf(c_11551,plain,
( ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X0)
| ~ sP5
| a_select3(r_ds1_filter,X0,sK37) = a_select3(r_ds1_filter,sK37,X0) ),
inference(renaming,[status(thm)],[c_11550]) ).
cnf(c_11563,plain,
( ~ leq(n0,sK36)
| ~ sP5
| a_select3(r_ds1_filter,sK36,sK37) = a_select3(r_ds1_filter,sK37,sK36) ),
inference(superposition,[status(thm)],[c_164,c_11551]) ).
cnf(c_11606,plain,
~ sP5,
inference(global_subsumption_just,[status(thm)],[c_11475,c_166,c_162,c_11563]) ).
cnf(c_11610,plain,
( leq(sK40,minus(n0,n1))
| sP4 ),
inference(backward_subsumption_resolution,[status(thm)],[c_11370,c_11606]) ).
cnf(c_11623,plain,
( ~ leq(n0,X0)
| ~ leq(X0,minus(n6,n1))
| ~ sP4
| a_select3(q_ds1_filter,X0,sK39) = a_select3(q_ds1_filter,sK39,X0) ),
inference(global_subsumption_just,[status(thm)],[c_11492,c_170,c_11492]) ).
cnf(c_11624,plain,
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| ~ sP4
| a_select3(q_ds1_filter,X0,sK39) = a_select3(q_ds1_filter,sK39,X0) ),
inference(renaming,[status(thm)],[c_11623]) ).
cnf(c_11636,plain,
( ~ leq(n0,sK38)
| ~ sP4
| a_select3(q_ds1_filter,sK38,sK39) = a_select3(q_ds1_filter,sK39,sK38) ),
inference(superposition,[status(thm)],[c_169,c_11624]) ).
cnf(c_11643,plain,
~ sP4,
inference(global_subsumption_just,[status(thm)],[c_11493,c_171,c_167,c_11636]) ).
cnf(c_11756,plain,
leq(sK40,minus(n0,n1)),
inference(global_subsumption_just,[status(thm)],[c_11610,c_328,c_11362,c_11606,c_11643]) ).
cnf(c_15128,plain,
( ~ leq(X0,sK40)
| leq(X0,minus(n0,n1)) ),
inference(superposition,[status(thm)],[c_11756,c_53]) ).
cnf(c_15312,plain,
( ~ leq(n0,sK40)
| leq(n0,minus(n0,n1)) ),
inference(instantiation,[status(thm)],[c_15128]) ).
cnf(c_15313,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15312,c_11643,c_11606,c_11362,c_324,c_260,c_232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV114+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 08:14:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.74/1.13 % SZS status Started for theBenchmark.p
% 3.74/1.13 % SZS status Theorem for theBenchmark.p
% 3.74/1.13
% 3.74/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.74/1.13
% 3.74/1.13 ------ iProver source info
% 3.74/1.13
% 3.74/1.13 git: date: 2023-05-31 18:12:56 +0000
% 3.74/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.74/1.13 git: non_committed_changes: false
% 3.74/1.13 git: last_make_outside_of_git: false
% 3.74/1.13
% 3.74/1.13 ------ Parsing...
% 3.74/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.74/1.13
% 3.74/1.13 ------ Preprocessing... sup_sim: 17 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.74/1.13
% 3.74/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.74/1.13
% 3.74/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.74/1.13 ------ Proving...
% 3.74/1.13 ------ Problem Properties
% 3.74/1.13
% 3.74/1.13
% 3.74/1.13 clauses 182
% 3.74/1.13 conjectures 10
% 3.74/1.13 EPR 61
% 3.74/1.13 Horn 126
% 3.74/1.13 unary 64
% 3.74/1.13 binary 49
% 3.74/1.13 lits 571
% 3.74/1.13 lits eq 128
% 3.74/1.13 fd_pure 0
% 3.74/1.13 fd_pseudo 0
% 3.74/1.13 fd_cond 7
% 3.74/1.13 fd_pseudo_cond 4
% 3.74/1.13 AC symbols 0
% 3.74/1.13
% 3.74/1.13 ------ Schedule dynamic 5 is on
% 3.74/1.13
% 3.74/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.74/1.13
% 3.74/1.13
% 3.74/1.13 ------
% 3.74/1.13 Current options:
% 3.74/1.13 ------
% 3.74/1.13
% 3.74/1.13
% 3.74/1.13
% 3.74/1.13
% 3.74/1.13 ------ Proving...
% 3.74/1.13
% 3.74/1.13
% 3.74/1.13 % SZS status Theorem for theBenchmark.p
% 3.74/1.13
% 3.74/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.74/1.13
% 3.74/1.13
%------------------------------------------------------------------------------