TSTP Solution File: SYN067+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SYN067+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 : Fri May 3 03:28:56 EDT 2024
% Result : Theorem 2.39s 1.11s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 137 ( 9 unt; 0 def)
% Number of atoms : 663 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 843 ( 317 ~; 362 |; 143 &)
% ( 5 <=>; 13 =>; 0 <=; 3 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-1 aty)
% Number of variables : 246 ( 2 sgn 97 !; 77 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ( ( big_p(X0)
=> ? [X1] :
( big_r(X0,X1)
& big_p(X1) ) )
& big_p(a) )
=> ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) ) )
<=> ! [X4] :
( ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| ~ ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
| ~ big_p(a) )
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| big_p(X4)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( ( big_p(X0)
=> ? [X1] :
( big_r(X0,X1)
& big_p(X1) ) )
& big_p(a) )
=> ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) ) )
<=> ! [X4] :
( ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| ~ ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
| ~ big_p(a) )
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f3,plain,
~ ( ! [X0] :
( ( ( big_p(X0)
=> ? [X1] :
( big_r(X0,X1)
& big_p(X1) ) )
& big_p(a) )
=> ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) ) )
<=> ! [X4] :
( ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ~ ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
| ~ big_p(a) )
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) )
| ( ! [X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1) )
& big_p(X0) )
| ~ big_p(a) )
<~> ! [X4] :
( ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a) )
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X0] :
( ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) )
| ( ! [X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1) )
& big_p(X0) )
| ~ big_p(a) )
<~> ! [X4] :
( ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a) )
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X4] :
( sP0(X4)
<=> ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f7,plain,
( sP1
<=> ! [X0] :
( ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) )
| ( ! [X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1) )
& big_p(X0) )
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f8,plain,
( sP1
<~> ! [X4] :
( sP0(X4)
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(definition_folding,[],[f5,f7,f6]) ).
fof(f9,plain,
( ( sP1
| ? [X0] :
( ! [X2,X3] :
( ~ big_r(X3,X2)
| ~ big_r(X0,X3)
| ~ big_p(X2) )
& ( ? [X1] :
( big_r(X0,X1)
& big_p(X1) )
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X0] :
( ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) )
| ( ! [X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1) )
& big_p(X0) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f10,plain,
( ( sP1
| ? [X0] :
( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ( ? [X3] :
( big_r(X0,X3)
& big_p(X3) )
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X4] :
( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ( ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
& big_p(X4) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(rectify,[],[f9]) ).
fof(f11,plain,
( ? [X0] :
( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ( ? [X3] :
( big_r(X0,X3)
& big_p(X3) )
| ~ big_p(X0) )
& big_p(a) )
=> ( ! [X2,X1] :
( ~ big_r(X2,X1)
| ~ big_r(sK2,X2)
| ~ big_p(X1) )
& ( ? [X3] :
( big_r(sK2,X3)
& big_p(X3) )
| ~ big_p(sK2) )
& big_p(a) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
( ? [X3] :
( big_r(sK2,X3)
& big_p(X3) )
=> ( big_r(sK2,sK3)
& big_p(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
! [X4] :
( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
=> ( big_r(sK5(X4),sK4(X4))
& big_r(X4,sK5(X4))
& big_p(sK4(X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ( sP1
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(sK2,X2)
| ~ big_p(X1) )
& ( ( big_r(sK2,sK3)
& big_p(sK3) )
| ~ big_p(sK2) )
& big_p(a) ) )
& ( ! [X4] :
( ( big_r(sK5(X4),sK4(X4))
& big_r(X4,sK5(X4))
& big_p(sK4(X4)) )
| ( ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
& big_p(X4) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f10,f13,f12,f11]) ).
fof(f15,plain,
! [X4] :
( ( sP0(X4)
| ( ! [X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(X4,X6)
| ~ big_p(X5) )
& ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
& big_p(a) ) )
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a)
| ~ sP0(X4) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f16,plain,
! [X4] :
( ( sP0(X4)
| ( ! [X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(X4,X6)
| ~ big_p(X5) )
& ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
& big_p(a) ) )
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a)
| ~ sP0(X4) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ? [X3] :
( big_r(X0,X3)
& big_p(X3) )
& big_p(a) ) )
& ( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X0,X5)
& big_p(X4) )
| ! [X6] :
( ~ big_r(X0,X6)
| ~ big_p(X6) )
| ~ big_p(a)
| ~ sP0(X0) ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ? [X3] :
( big_r(X0,X3)
& big_p(X3) )
=> ( big_r(X0,sK6(X0))
& big_p(sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0] :
( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X0,X5)
& big_p(X4) )
=> ( big_r(sK8(X0),sK7(X0))
& big_r(X0,sK8(X0))
& big_p(sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& big_r(X0,sK6(X0))
& big_p(sK6(X0))
& big_p(a) ) )
& ( ( big_r(sK8(X0),sK7(X0))
& big_r(X0,sK8(X0))
& big_p(sK7(X0)) )
| ! [X6] :
( ~ big_r(X0,X6)
| ~ big_p(X6) )
| ~ big_p(a)
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f17,f19,f18]) ).
fof(f21,plain,
( ( ? [X4] :
( ~ sP0(X4)
| ( ! [X8,X9] :
( ~ big_r(X9,X8)
| ~ big_r(X4,X9)
| ~ big_p(X8) )
& ~ big_p(X4)
& big_p(a) ) )
| ~ sP1 )
& ( ! [X4] :
( sP0(X4)
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) )
| sP1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f22,plain,
( ( ? [X0] :
( ~ sP0(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ~ big_p(X0)
& big_p(a) ) )
| ~ sP1 )
& ( ! [X3] :
( sP0(X3)
& ( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X3,X5)
& big_p(X4) )
| big_p(X3)
| ~ big_p(a) ) )
| sP1 ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
( ? [X0] :
( ~ sP0(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ~ big_p(X0)
& big_p(a) ) )
=> ( ~ sP0(sK9)
| ( ! [X2,X1] :
( ~ big_r(X2,X1)
| ~ big_r(sK9,X2)
| ~ big_p(X1) )
& ~ big_p(sK9)
& big_p(a) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X3] :
( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X3,X5)
& big_p(X4) )
=> ( big_r(sK11(X3),sK10(X3))
& big_r(X3,sK11(X3))
& big_p(sK10(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
( ( ~ sP0(sK9)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(sK9,X2)
| ~ big_p(X1) )
& ~ big_p(sK9)
& big_p(a) )
| ~ sP1 )
& ( ! [X3] :
( sP0(X3)
& ( ( big_r(sK11(X3),sK10(X3))
& big_r(X3,sK11(X3))
& big_p(sK10(X3)) )
| big_p(X3)
| ~ big_p(a) ) )
| sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f22,f24,f23]) ).
fof(f26,plain,
! [X4] :
( big_p(sK4(X4))
| big_p(X4)
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X7,X4] :
( big_p(sK4(X4))
| ~ big_r(X4,X7)
| ~ big_p(X7)
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X4] :
( big_r(X4,sK5(X4))
| big_p(X4)
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X7,X4] :
( big_r(X4,sK5(X4))
| ~ big_r(X4,X7)
| ~ big_p(X7)
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X4] :
( big_r(sK5(X4),sK4(X4))
| big_p(X4)
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X7,X4] :
( big_r(sK5(X4),sK4(X4))
| ~ big_r(X4,X7)
| ~ big_p(X7)
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
( sP1
| big_p(a) ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
( sP1
| big_p(sK3)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
( sP1
| big_r(sK2,sK3)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f35,plain,
! [X2,X1] :
( sP1
| ~ big_r(X2,X1)
| ~ big_r(sK2,X2)
| ~ big_p(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f36,plain,
! [X0,X6] :
( big_p(sK7(X0))
| ~ big_r(X0,X6)
| ~ big_p(X6)
| ~ big_p(a)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0,X6] :
( big_r(X0,sK8(X0))
| ~ big_r(X0,X6)
| ~ big_p(X6)
| ~ big_p(a)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X6] :
( big_r(sK8(X0),sK7(X0))
| ~ big_r(X0,X6)
| ~ big_p(X6)
| ~ big_p(a)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0] :
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X0] :
( sP0(X0)
| big_p(sK6(X0)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f41,plain,
! [X0] :
( sP0(X0)
| big_r(X0,sK6(X0)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f42,plain,
! [X2,X0,X1] :
( sP0(X0)
| ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X3] :
( big_p(sK10(X3))
| big_p(X3)
| ~ big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
! [X3] :
( big_r(X3,sK11(X3))
| big_p(X3)
| ~ big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X3] :
( big_r(sK11(X3),sK10(X3))
| big_p(X3)
| ~ big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X3] :
( sP0(X3)
| sP1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
( ~ sP0(sK9)
| big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
( ~ sP0(sK9)
| ~ big_p(sK9)
| ~ sP1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f49,plain,
! [X2,X1] :
( ~ sP0(sK9)
| ~ big_r(X2,X1)
| ~ big_r(sK9,X2)
| ~ big_p(X1)
| ~ sP1 ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_49,plain,
( ~ big_r(X0,X1)
| ~ big_r(sK2,X0)
| ~ big_p(X1)
| sP1 ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_50,plain,
( ~ big_p(sK2)
| big_r(sK2,sK3)
| sP1 ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_51,plain,
( ~ big_p(sK2)
| big_p(sK3)
| sP1 ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_52,plain,
( big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_53,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ big_p(a)
| ~ sP1
| big_r(sK5(X0),sK4(X0)) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_54,plain,
( ~ big_p(a)
| ~ sP1
| big_r(sK5(X0),sK4(X0))
| big_p(X0) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_55,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ big_p(a)
| ~ sP1
| big_r(X0,sK5(X0)) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_56,plain,
( ~ big_p(a)
| ~ sP1
| big_r(X0,sK5(X0))
| big_p(X0) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_57,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ big_p(a)
| ~ sP1
| big_p(sK4(X0)) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_58,plain,
( ~ big_p(a)
| ~ sP1
| big_p(sK4(X0))
| big_p(X0) ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_59,plain,
( ~ big_r(X0,X1)
| ~ big_r(X2,X0)
| ~ big_p(X1)
| sP0(X2) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_60,plain,
( big_r(X0,sK6(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_61,plain,
( big_p(sK6(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_62,plain,
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_63,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP0(X0)
| ~ big_p(a)
| big_r(sK8(X0),sK7(X0)) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_64,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP0(X0)
| ~ big_p(a)
| big_r(X0,sK8(X0)) ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_65,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP0(X0)
| ~ big_p(a)
| big_p(sK7(X0)) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_66,negated_conjecture,
( ~ big_r(X0,X1)
| ~ big_r(sK9,X0)
| ~ big_p(X1)
| ~ sP0(sK9)
| ~ sP1 ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_67,negated_conjecture,
( ~ big_p(sK9)
| ~ sP0(sK9)
| ~ sP1 ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_68,negated_conjecture,
( ~ sP0(sK9)
| ~ sP1
| big_p(a) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_69,negated_conjecture,
( sP0(X0)
| sP1 ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_70,negated_conjecture,
( ~ big_p(a)
| big_r(sK11(X0),sK10(X0))
| big_p(X0)
| sP1 ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_71,negated_conjecture,
( ~ big_p(a)
| big_r(X0,sK11(X0))
| big_p(X0)
| sP1 ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_72,negated_conjecture,
( ~ big_p(a)
| big_p(sK10(X0))
| big_p(X0)
| sP1 ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_86,negated_conjecture,
( ~ sP0(sK9)
| big_p(a) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_52,c_68]) ).
cnf(c_88,negated_conjecture,
( big_p(sK10(X0))
| big_p(X0)
| sP1 ),
inference(global_subsumption_just,[status(thm)],[c_72,c_52,c_72]) ).
cnf(c_90,negated_conjecture,
( big_r(X0,sK11(X0))
| big_p(X0)
| sP1 ),
inference(global_subsumption_just,[status(thm)],[c_71,c_52,c_71]) ).
cnf(c_92,negated_conjecture,
( big_r(sK11(X0),sK10(X0))
| big_p(X0)
| sP1 ),
inference(global_subsumption_just,[status(thm)],[c_70,c_52,c_70]) ).
cnf(c_105,plain,
big_p(a),
inference(backward_subsumption_resolution,[status(thm)],[c_86,c_62]) ).
cnf(c_109,plain,
( ~ sP1
| big_p(sK4(X0))
| big_p(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_105]) ).
cnf(c_110,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP1
| big_p(sK4(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_105]) ).
cnf(c_111,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP0(X0)
| big_p(sK7(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_105]) ).
cnf(c_112,plain,
( ~ sP1
| big_r(X0,sK5(X0))
| big_p(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_105]) ).
cnf(c_113,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP1
| big_r(X0,sK5(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_105]) ).
cnf(c_114,plain,
( ~ sP1
| big_r(sK5(X0),sK4(X0))
| big_p(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_105]) ).
cnf(c_115,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP1
| big_r(sK5(X0),sK4(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_53,c_105]) ).
cnf(c_116,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP0(X0)
| big_r(X0,sK8(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_105]) ).
cnf(c_117,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP0(X0)
| big_r(sK8(X0),sK7(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_105]) ).
cnf(c_204,plain,
( ~ big_r(X0,X1)
| ~ big_r(sK9,X0)
| ~ big_p(X1)
| ~ sP1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_66,c_59]) ).
cnf(c_3068,negated_conjecture,
( big_r(sK11(X0),sK10(X0))
| big_p(X0)
| sP1 ),
inference(demodulation,[status(thm)],[c_92]) ).
cnf(c_3069,negated_conjecture,
( big_r(X0,sK11(X0))
| big_p(X0)
| sP1 ),
inference(demodulation,[status(thm)],[c_90]) ).
cnf(c_3070,negated_conjecture,
( big_p(sK10(X0))
| big_p(X0)
| sP1 ),
inference(demodulation,[status(thm)],[c_88]) ).
cnf(c_3072,negated_conjecture,
( ~ big_p(sK9)
| ~ sP0(sK9)
| ~ sP1 ),
inference(demodulation,[status(thm)],[c_67]) ).
cnf(c_3073,plain,
( ~ sP1
| big_p(sK4(sK9))
| big_p(sK9) ),
inference(instantiation,[status(thm)],[c_109]) ).
cnf(c_3074,plain,
( ~ sP1
| big_r(sK9,sK5(sK9))
| big_p(sK9) ),
inference(instantiation,[status(thm)],[c_112]) ).
cnf(c_3075,plain,
( ~ sP1
| big_r(sK5(sK9),sK4(sK9))
| big_p(sK9) ),
inference(instantiation,[status(thm)],[c_114]) ).
cnf(c_3082,plain,
( ~ big_r(sK5(sK9),X0)
| ~ big_r(sK9,sK5(sK9))
| ~ big_p(X0)
| ~ sP1 ),
inference(instantiation,[status(thm)],[c_204]) ).
cnf(c_3112,plain,
( big_r(sK9,sK6(sK9))
| sP0(sK9) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_3113,plain,
( big_p(sK6(sK9))
| sP0(sK9) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_3134,plain,
( ~ big_r(sK9,sK6(sK9))
| ~ big_p(sK6(sK9))
| ~ sP1
| big_r(sK5(sK9),sK4(sK9)) ),
inference(instantiation,[status(thm)],[c_115]) ).
cnf(c_3135,plain,
( ~ big_r(sK9,sK6(sK9))
| ~ big_p(sK6(sK9))
| ~ sP1
| big_r(sK9,sK5(sK9)) ),
inference(instantiation,[status(thm)],[c_113]) ).
cnf(c_3137,plain,
( ~ big_r(sK9,sK6(sK9))
| ~ big_p(sK6(sK9))
| ~ sP1
| big_p(sK4(sK9)) ),
inference(instantiation,[status(thm)],[c_110]) ).
cnf(c_3212,plain,
( ~ big_r(sK5(sK9),sK4(sK9))
| ~ big_r(sK9,sK5(sK9))
| ~ big_p(sK4(sK9))
| ~ sP1 ),
inference(instantiation,[status(thm)],[c_3082]) ).
cnf(c_3242,plain,
( big_r(sK2,sK11(sK2))
| big_p(sK2)
| sP1 ),
inference(instantiation,[status(thm)],[c_3069]) ).
cnf(c_3243,plain,
( big_r(sK11(sK2),sK10(sK2))
| big_p(sK2)
| sP1 ),
inference(instantiation,[status(thm)],[c_3068]) ).
cnf(c_3244,plain,
( big_p(sK10(sK2))
| big_p(sK2)
| sP1 ),
inference(instantiation,[status(thm)],[c_3070]) ).
cnf(c_3300,negated_conjecture,
( ~ sP0(sK9)
| ~ sP1 ),
inference(global_subsumption_just,[status(thm)],[c_3072,c_67,c_3073,c_3074,c_3075,c_3212]) ).
cnf(c_3302,negated_conjecture,
~ sP1,
inference(global_subsumption_just,[status(thm)],[c_3300,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3300]) ).
cnf(c_3305,plain,
( big_r(X0,sK11(X0))
| big_p(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3069,c_3302]) ).
cnf(c_3333,plain,
( big_p(sK3)
| ~ big_p(sK2) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_51,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3300]) ).
cnf(c_3334,plain,
( ~ big_p(sK2)
| big_p(sK3) ),
inference(renaming,[status(thm)],[c_3333]) ).
cnf(c_3359,plain,
( big_r(sK2,sK3)
| ~ big_p(sK2) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_50,c_3302]) ).
cnf(c_3360,plain,
( ~ big_p(sK2)
| big_r(sK2,sK3) ),
inference(renaming,[status(thm)],[c_3359]) ).
cnf(c_3383,plain,
( ~ big_p(X1)
| ~ big_r(X0,X1)
| big_p(sK7(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_111,c_69,c_111,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3300]) ).
cnf(c_3384,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| big_p(sK7(X0)) ),
inference(renaming,[status(thm)],[c_3383]) ).
cnf(c_3391,plain,
( ~ big_p(sK2)
| ~ big_p(sK3)
| big_p(sK7(sK2)) ),
inference(superposition,[status(thm)],[c_3360,c_3384]) ).
cnf(c_3468,plain,
( ~ big_p(X1)
| ~ big_r(X0,X1)
| big_r(X0,sK8(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_116,c_69,c_116,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3300]) ).
cnf(c_3469,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| big_r(X0,sK8(X0)) ),
inference(renaming,[status(thm)],[c_3468]) ).
cnf(c_3476,plain,
( ~ big_p(sK2)
| ~ big_p(sK3)
| big_r(sK2,sK8(sK2)) ),
inference(superposition,[status(thm)],[c_3360,c_3469]) ).
cnf(c_3524,plain,
( ~ big_r(sK11(sK2),X0)
| ~ big_r(sK2,sK11(sK2))
| ~ big_p(X0)
| sP1 ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_3551,plain,
( ~ big_p(X1)
| ~ big_r(X0,X1)
| big_r(sK8(X0),sK7(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_117,c_69,c_117,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3300]) ).
cnf(c_3552,plain,
( ~ big_r(X0,X1)
| ~ big_p(X1)
| big_r(sK8(X0),sK7(X0)) ),
inference(renaming,[status(thm)],[c_3551]) ).
cnf(c_3661,plain,
( ~ big_p(X1)
| ~ big_r(sK2,X0)
| ~ big_r(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_49,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3300]) ).
cnf(c_3662,plain,
( ~ big_r(X0,X1)
| ~ big_r(sK2,X0)
| ~ big_p(X1) ),
inference(renaming,[status(thm)],[c_3661]) ).
cnf(c_3672,plain,
( ~ big_r(sK2,X0)
| ~ big_p(sK11(X0))
| big_p(X0) ),
inference(superposition,[status(thm)],[c_3305,c_3662]) ).
cnf(c_3767,plain,
( ~ big_p(sK11(sK11(sK2)))
| big_p(sK11(sK2))
| big_p(sK2) ),
inference(superposition,[status(thm)],[c_3305,c_3672]) ).
cnf(c_3799,plain,
( ~ big_r(sK11(sK2),sK10(sK2))
| ~ big_r(sK2,sK11(sK2))
| ~ big_p(sK10(sK2))
| sP1 ),
inference(instantiation,[status(thm)],[c_3524]) ).
cnf(c_3824,plain,
( ~ big_p(sK3)
| big_p(sK7(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_3391,c_51,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3244,c_3243,c_3242,c_3300,c_3391,c_3799]) ).
cnf(c_3826,plain,
big_p(sK7(sK2)),
inference(global_subsumption_just,[status(thm)],[c_3824,c_51,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3244,c_3243,c_3242,c_3300,c_3391,c_3799]) ).
cnf(c_3836,plain,
( ~ big_p(sK3)
| big_r(sK2,sK8(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_3476,c_51,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3244,c_3243,c_3242,c_3300,c_3476,c_3799]) ).
cnf(c_3838,plain,
big_r(sK2,sK8(sK2)),
inference(global_subsumption_just,[status(thm)],[c_3836,c_51,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3244,c_3243,c_3242,c_3300,c_3476,c_3799]) ).
cnf(c_3922,plain,
big_p(sK2),
inference(global_subsumption_just,[status(thm)],[c_3767,c_3113,c_3112,c_3137,c_3135,c_3134,c_3212,c_3244,c_3243,c_3242,c_3300,c_3799]) ).
cnf(c_3924,plain,
big_r(sK2,sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_3360,c_3922]) ).
cnf(c_3925,plain,
big_p(sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_3334,c_3922]) ).
cnf(c_4169,plain,
( ~ big_p(sK3)
| big_r(sK8(sK2),sK7(sK2)) ),
inference(superposition,[status(thm)],[c_3924,c_3552]) ).
cnf(c_4174,plain,
big_r(sK8(sK2),sK7(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_4169,c_3925]) ).
cnf(c_4186,plain,
( ~ big_r(sK2,sK8(sK2))
| ~ big_p(sK7(sK2)) ),
inference(superposition,[status(thm)],[c_4174,c_3662]) ).
cnf(c_4191,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4186,c_3826,c_3838]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SYN067+1 : TPTP v8.1.2. Released v2.0.0.
% 0.02/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n004.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu May 2 20:37:48 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.39/1.11 % SZS status Started for theBenchmark.p
% 2.39/1.11 % SZS status Theorem for theBenchmark.p
% 2.39/1.11
% 2.39/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.39/1.11
% 2.39/1.11 ------ iProver source info
% 2.39/1.11
% 2.39/1.11 git: date: 2024-05-02 19:28:25 +0000
% 2.39/1.11 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.39/1.11 git: non_committed_changes: false
% 2.39/1.11
% 2.39/1.11 ------ Parsing...
% 2.39/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.39/1.11
% 2.39/1.11 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 2.39/1.11
% 2.39/1.11 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.39/1.11 ------ Proving...
% 2.39/1.11 ------ Problem Properties
% 2.39/1.11
% 2.39/1.11
% 2.39/1.11 clauses 22
% 2.39/1.11 conjectures 5
% 2.39/1.11 EPR 8
% 2.39/1.11 Horn 11
% 2.39/1.11 unary 1
% 2.39/1.11 binary 3
% 2.39/1.11 lits 70
% 2.39/1.11 lits eq 0
% 2.39/1.11 fd_pure 0
% 2.39/1.11 fd_pseudo 0
% 2.39/1.11 fd_cond 0
% 2.39/1.11 fd_pseudo_cond 0
% 2.39/1.11 AC symbols 0
% 2.39/1.11
% 2.39/1.11 ------ Schedule dynamic 5 is on
% 2.39/1.11
% 2.39/1.11 ------ no equalities: superposition off
% 2.39/1.11
% 2.39/1.11 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.39/1.11
% 2.39/1.11
% 2.39/1.11 ------
% 2.39/1.11 Current options:
% 2.39/1.11 ------
% 2.39/1.11
% 2.39/1.11
% 2.39/1.11
% 2.39/1.11
% 2.39/1.11 ------ Proving...
% 2.39/1.11
% 2.39/1.11
% 2.39/1.11 % SZS status Theorem for theBenchmark.p
% 2.39/1.11
% 2.39/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.39/1.11
% 2.39/1.11
%------------------------------------------------------------------------------