%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 03:39:04 PM UTC 2026
% Result : Theorem 2.52s 1.17s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 115 ( 2 unt; 2 def)
% Number of atoms : 603 ( 0 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 756 ( 290 ~; 348 |; 107 &)
% ( 4 <=>; 4 =>; 0 <=; 3 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-1 aty)
% Number of variables : 213 ( 0 sgn 156 !; 57 ?; 73 :)
% 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,[status(cth)],[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] :
( ( ? [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(ennf_transformation,[],[f2]) ).
fof(f4,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] :
( ( ? [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(flattening,[],[f3]) ).
fof(f8,plain,
( ( ~ sP1
| ! [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) ) ) )
& ( ? [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) ) )
| sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( ~ sP1
| ! [X4] :
( ( big_p(X4)
& ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) ) )
| ~ big_p(a)
| ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) ) ) )
& ( ? [X0] :
( ( ~ big_p(X0)
| ? [X3] :
( big_r(X0,X3)
& big_p(X3) ) )
& big_p(a)
& ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) ) )
| sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( ~ sP1
| ! [X4] :
( ( big_p(X4)
& ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) ) )
| ~ big_p(a)
| ( big_r(sK5(X4),sK4(X4))
& big_r(X4,sK5(X4))
& big_p(sK4(X4)) ) ) )
& ( ( ( ~ big_p(sK2)
| ( big_r(sK2,sK3)
& big_p(sK3) ) )
& big_p(a)
& ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(sK2,X2)
| ~ big_p(X1) ) )
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X3,sK3),skolemize(X5,sK4(X4)),skolemize(X6,sK5(X4))],[f9]) ).
fof(f15,plain,
( ( sP1
| ! [X4] :
( sP0(X4)
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| big_p(X4)
| ~ big_p(a) ) ) )
& ( ~ sP1
| ? [X4] :
( ~ sP0(X4)
| ( ! [X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(X4,X6)
| ~ big_p(X5) )
& ~ big_p(X4)
& big_p(a) ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f16,plain,
( ( sP1
| ! [X3] :
( sP0(X3)
& ( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X3,X5)
& big_p(X4) )
| big_p(X3)
| ~ big_p(a) ) ) )
& ( ~ sP1
| ? [X0] :
( ~ sP0(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ~ big_p(X0)
& big_p(a) ) ) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
( ( 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
| ~ sP0(sK9)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(sK9,X2)
| ~ big_p(X1) )
& ~ big_p(sK9)
& big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X4,sK10(X3)),skolemize(X5,sK11(X3))],[f16]) ).
fof(f18,plain,
! [X4] :
( ~ sP1
| big_p(X4)
| ~ big_p(a)
| big_r(sK5(X4),sK4(X4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
! [X7,X4] :
( ~ sP1
| ~ big_r(X4,X7)
| ~ big_p(X7)
| ~ big_p(a)
| big_r(sK5(X4),sK4(X4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X4] :
( ~ sP1
| big_p(X4)
| ~ big_p(a)
| big_r(X4,sK5(X4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X7,X4] :
( ~ sP1
| ~ big_r(X4,X7)
| ~ big_p(X7)
| ~ big_p(a)
| big_r(X4,sK5(X4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X4] :
( ~ sP1
| big_p(X4)
| ~ big_p(a)
| big_p(sK4(X4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X7,X4] :
( ~ sP1
| ~ big_r(X4,X7)
| ~ big_p(X7)
| ~ big_p(a)
| big_p(sK4(X4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
( ~ big_p(sK2)
| big_r(sK2,sK3)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
( ~ big_p(sK2)
| big_p(sK3)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f26,plain,
( big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f27,plain,
! [X2,X1] :
( ~ big_r(X2,X1)
| ~ big_r(sK2,X2)
| ~ big_p(X1)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f35,plain,
! [X3] :
( sP1
| sP0(X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X3] :
( sP1
| big_r(sK11(X3),sK10(X3))
| big_p(X3)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X3] :
( sP1
| big_r(X3,sK11(X3))
| big_p(X3)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X3] :
( sP1
| big_p(sK10(X3))
| big_p(X3)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f17]) ).
fof(f39,plain,
! [X2,X1] :
( ~ sP1
| ~ sP0(sK9)
| ~ big_r(X2,X1)
| ~ big_r(sK9,X2)
| ~ big_p(X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
( ~ sP1
| ~ sP0(sK9)
| ~ big_p(sK9) ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
( ~ sP1
| ~ sP0(sK9)
| big_p(a) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( sP1
| ~ big_p(X1)
| ~ big_r(sK2,X0)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
( sP1
| big_p(a) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
( sP1
| big_p(sK3)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,plain,
( sP1
| big_r(sK2,sK3)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( big_p(sK4(X0))
| ~ sP1
| ~ big_p(a)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,plain,
! [X0: $i] :
( big_p(X0)
| big_p(sK4(X0))
| ~ sP1
| ~ big_p(a) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( big_r(X0,sK5(X0))
| ~ sP1
| ~ big_p(a)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_56,plain,
! [X0: $i] :
( big_p(X0)
| big_r(X0,sK5(X0))
| ~ sP1
| ~ big_p(a) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( big_r(sK5(X0),sK4(X0))
| ~ sP1
| ~ big_p(a)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_58,plain,
! [X0: $i] :
( big_p(X0)
| big_r(sK5(X0),sK4(X0))
| ~ sP1
| ~ big_p(a) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_66,negated_conjecture,
( big_p(a)
| ~ sP1
| ~ sP0(sK9) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_67,negated_conjecture,
( ~ sP1
| ~ sP0(sK9)
| ~ big_p(sK9) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_68,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ sP1
| ~ sP0(sK9)
| ~ big_p(X1)
| ~ big_r(sK9,X0)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_69,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_p(sK10(X0))
| ~ big_p(a) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_r(X0,sK11(X0))
| ~ big_p(a) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_71,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_r(sK11(X0),sK10(X0))
| ~ big_p(a) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_72,negated_conjecture,
! [X0: $i] :
( sP1
| sP0(X0) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_86,negated_conjecture,
( big_p(a)
| ~ sP0(sK9) ),
inference(global_subsumption_just,[status(thm)],[c_66,c_50,c_66]) ).
tcf(c_88,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_p(sK10(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_50,c_69]) ).
tcf(c_90,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_r(X0,sK11(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_70,c_50,c_70]) ).
tcf(c_92,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_r(sK11(X0),sK10(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_50,c_71]) ).
tcf(c_3079,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_r(sK11(X0),sK10(X0)) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_3080,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_r(X0,sK11(X0)) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_3082,negated_conjecture,
! [X0: $i] :
( sP1
| sP0(X0) ),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_3377,plain,
( sP1
| sP0(sK2) ),
inference(instantiation,[status(thm)],[c_3082]) ).
tcf(c_3600,plain,
! [X0: $i] :
( sP1
| big_p(X0)
| ~ big_p(sK10(X0))
| ~ big_r(sK2,sK11(X0)) ),
inference(superposition,[status(thm)],[c_3079,c_49]) ).
tcf(c_3754,plain,
! [X0: $i] :
( sP1
| big_p(X0)
| ~ big_r(sK2,sK11(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_3600,c_88,c_3600]) ).
tcf(c_3762,plain,
( sP1
| big_p(sK2) ),
inference(superposition,[status(thm)],[c_3080,c_3754]) ).
tcf(c_3786,plain,
( sP1
| big_p(sK3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_3762]) ).
tcf(c_3788,plain,
( sP1
| big_r(sK2,sK3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_3762]) ).
tcf(c_3924,plain,
! [X0: $i] :
( sP1
| ~ big_p(X0)
| ~ big_r(sK2,sK8(sK2))
| ~ big_r(sK8(sK2),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_4269,plain,
( sP1
| ~ big_p(sK7(sK2))
| ~ big_r(sK2,sK8(sK2))
| ~ big_r(sK8(sK2),sK7(sK2)) ),
inference(instantiation,[status(thm)],[c_3924]) ).
fof(f5,definition,
! [X4] :
( sP0(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) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,definition,
( sP1
<=> ! [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) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f7,plain,
( sP1
<~> ! [X4] :
( sP0(X4)
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f11,plain,
! [X4] :
( ( ~ sP0(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) )
& ( ( ! [X8,X9] :
( ~ big_r(X9,X8)
| ~ big_r(X4,X9)
| ~ big_p(X8) )
& ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
& big_p(a) )
| sP0(X4) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f12,plain,
! [X4] :
( ( ~ sP0(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) )
& ( ( ! [X8,X9] :
( ~ big_r(X9,X8)
| ~ big_r(X4,X9)
| ~ big_p(X8) )
& ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
& big_p(a) )
| sP0(X4) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ( ~ sP0(X0)
| ? [X5,X6] :
( big_r(X6,X5)
& big_r(X0,X6)
& big_p(X5) )
| ! [X4] :
( ~ big_r(X0,X4)
| ~ big_p(X4) )
| ~ big_p(a) )
& ( ( ! [X2,X3] :
( ~ big_r(X3,X2)
| ~ big_r(X0,X3)
| ~ big_p(X2) )
& ? [X1] :
( big_r(X0,X1)
& big_p(X1) )
& big_p(a) )
| sP0(X0) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0] :
( ( ~ sP0(X0)
| ( big_r(sK8(X0),sK7(X0))
& big_r(X0,sK8(X0))
& big_p(sK7(X0)) )
| ! [X4] :
( ~ big_r(X0,X4)
| ~ big_p(X4) )
| ~ big_p(a) )
& ( ( ! [X2,X3] :
( ~ big_r(X3,X2)
| ~ big_r(X0,X3)
| ~ big_p(X2) )
& big_r(X0,sK6(X0))
& big_p(sK6(X0))
& big_p(a) )
| sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X1,sK6(X0)),skolemize(X5,sK7(X0)),skolemize(X6,sK8(X0))],[f13]) ).
fof(f28,plain,
! [X0,X4] :
( ~ sP0(X0)
| big_r(sK8(X0),sK7(X0))
| ~ big_r(X0,X4)
| ~ big_p(X4)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0,X4] :
( ~ sP0(X0)
| big_r(X0,sK8(X0))
| ~ big_r(X0,X4)
| ~ big_p(X4)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X0,X4] :
( ~ sP0(X0)
| big_p(sK7(X0))
| ~ big_r(X0,X4)
| ~ big_p(X4)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X2,X3,X0] :
( ~ big_r(X3,X2)
| ~ big_r(X0,X3)
| ~ big_p(X2)
| sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
! [X0] :
( big_r(X0,sK6(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0] :
( big_p(sK6(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0] :
( big_p(a)
| sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_59,plain,
! [X0: $i] :
( big_p(a)
| sP0(X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,plain,
! [X0: $i] :
( sP0(X0)
| big_p(sK6(X0)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_61,plain,
! [X0: $i] :
( sP0(X0)
| big_r(X0,sK6(X0)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0)
| ~ big_p(X2)
| ~ big_r(X1,X2)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( big_p(sK7(X0))
| ~ big_p(a)
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( big_r(X0,sK8(X0))
| ~ big_p(a)
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( big_r(sK8(X0),sK7(X0))
| ~ big_p(a)
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_105,plain,
big_p(a),
inference(backward_subsumption_resolution,[status(thm)],[c_86,c_59]) ).
tcf(c_109,plain,
! [X0: $i] :
( big_p(X0)
| big_p(sK4(X0))
| ~ sP1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_105]) ).
tcf(c_110,plain,
! [X0: $i] :
( big_p(X0)
| big_r(sK5(X0),sK4(X0))
| ~ sP1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_105]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( big_r(sK5(X0),sK4(X0))
| ~ sP1
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_105]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( big_p(sK4(X0))
| ~ sP1
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_53,c_105]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( big_p(sK7(X0))
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_105]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( big_r(sK8(X0),sK7(X0))
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_105]) ).
tcf(c_115,plain,
! [X0: $i] :
( big_p(X0)
| big_r(X0,sK5(X0))
| ~ sP1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_105]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( big_r(X0,sK5(X0))
| ~ sP1
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_105]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( big_r(X0,sK8(X0))
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_105]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i] :
( ~ sP1
| ~ big_p(X1)
| ~ big_r(sK9,X0)
| ~ big_r(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_62]) ).
tcf(c_3068,plain,
! [X0: $i,X1: $i] :
( ~ sP1
| ~ big_p(X1)
| ~ big_r(sK9,X0)
| ~ big_r(X0,X1) ),
inference(demodulation,[status(thm)],[c_204]) ).
tcf(c_3069,plain,
! [X0: $i,X1: $i] :
( big_r(X0,sK8(X0))
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_3070,plain,
! [X0: $i,X1: $i] :
( big_r(X0,sK5(X0))
| ~ sP1
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_3071,plain,
! [X0: $i] :
( big_p(X0)
| big_r(X0,sK5(X0))
| ~ sP1 ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_3072,plain,
! [X0: $i,X1: $i] :
( big_r(sK8(X0),sK7(X0))
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_3073,plain,
! [X0: $i,X1: $i] :
( big_p(sK7(X0))
| ~ sP0(X0)
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_3074,plain,
! [X0: $i,X1: $i] :
( big_p(sK4(X0))
| ~ sP1
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_3075,plain,
! [X0: $i,X1: $i] :
( big_r(sK5(X0),sK4(X0))
| ~ sP1
| ~ big_p(X1)
| ~ big_r(X0,X1) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_3076,plain,
! [X0: $i] :
( big_p(X0)
| big_r(sK5(X0),sK4(X0))
| ~ sP1 ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_3077,plain,
! [X0: $i] :
( big_p(X0)
| big_p(sK4(X0))
| ~ sP1 ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_3084,plain,
( big_p(sK9)
| big_p(sK4(sK9))
| ~ sP1 ),
inference(instantiation,[status(thm)],[c_3077]) ).
tcf(c_3085,plain,
( big_p(sK9)
| big_r(sK9,sK5(sK9))
| ~ sP1 ),
inference(instantiation,[status(thm)],[c_3071]) ).
tcf(c_3086,plain,
( big_p(sK9)
| big_r(sK5(sK9),sK4(sK9))
| ~ sP1 ),
inference(instantiation,[status(thm)],[c_3076]) ).
tcf(c_3093,plain,
! [X0: $i] :
( ~ sP1
| ~ big_p(X0)
| ~ big_r(sK9,sK5(sK9))
| ~ big_r(sK5(sK9),X0) ),
inference(instantiation,[status(thm)],[c_3068]) ).
tcf(c_3122,plain,
( sP0(sK9)
| big_r(sK9,sK6(sK9)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_3123,plain,
( sP0(sK9)
| big_p(sK6(sK9)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_3145,plain,
( big_r(sK5(sK9),sK4(sK9))
| ~ sP1
| ~ big_p(sK6(sK9))
| ~ big_r(sK9,sK6(sK9)) ),
inference(instantiation,[status(thm)],[c_3075]) ).
tcf(c_3147,plain,
( big_r(sK9,sK5(sK9))
| ~ sP1
| ~ big_p(sK6(sK9))
| ~ big_r(sK9,sK6(sK9)) ),
inference(instantiation,[status(thm)],[c_3070]) ).
tcf(c_3148,plain,
( big_p(sK4(sK9))
| ~ sP1
| ~ big_p(sK6(sK9))
| ~ big_r(sK9,sK6(sK9)) ),
inference(instantiation,[status(thm)],[c_3074]) ).
tcf(c_3225,plain,
( big_r(sK8(sK2),sK7(sK2))
| ~ sP0(sK2)
| ~ big_p(sK3)
| ~ big_r(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_3072]) ).
tcf(c_3893,plain,
( sP1
| big_r(sK2,sK8(sK2))
| ~ sP0(sK2)
| ~ big_p(sK3) ),
inference(superposition,[status(thm)],[c_3788,c_3069]) ).
tcf(c_4308,plain,
( sP1
| big_p(sK7(sK2))
| ~ sP0(sK2)
| ~ big_p(sK3) ),
inference(superposition,[status(thm)],[c_3788,c_3073]) ).
tcf(c_4579,plain,
( ~ sP1
| ~ big_p(sK4(sK9))
| ~ big_r(sK9,sK5(sK9))
| ~ big_r(sK5(sK9),sK4(sK9)) ),
inference(instantiation,[status(thm)],[c_3093]) ).
tcf(c_4809,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4579,c_4308,c_4269,c_3893,c_3788,c_3786,c_3377,c_3225,c_3145,c_3147,c_3148,c_3122,c_3123,c_3086,c_3085,c_3084,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 00:06:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.52/1.17 % SZS status Started for theBenchmark.p
% 2.52/1.17 % SZS status Theorem for theBenchmark.p
% 2.52/1.17
% 2.52/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.52/1.17
% 2.52/1.17 % ------ iProver source info
% 2.52/1.17
% 2.52/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.52/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.52/1.17 % git: non_committed_changes: false
% 2.52/1.17
% 2.52/1.17 % ------ Parsing...
% 2.52/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.52/1.17
% 2.52/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.52/1.17
% 2.52/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.52/1.17 % ------ Proving...
% 2.52/1.17 % ------ Problem Properties
% 2.52/1.17
% 2.52/1.17 %
% 2.52/1.17 % clauses 22
% 2.52/1.17 % conjectures 5
% 2.52/1.17 % EPR 8
% 2.52/1.17 % Horn 11
% 2.52/1.17 % unary 1
% 2.52/1.17 % binary 3
% 2.52/1.17 % lits 70
% 2.52/1.17 % lits eq 0
% 2.52/1.17 % fd_pure 0
% 2.52/1.17 % fd_pseudo 0
% 2.52/1.17 % fd_cond 0
% 2.52/1.17 % fd_pseudo_cond 0
% 2.52/1.17 % AC symbols 0
% 2.52/1.17
% 2.52/1.17 % ------ Schedule dynamic 5 is on
% 2.52/1.17
% 2.52/1.17 % ------ no equalities: superposition off
% 2.52/1.17
% 2.52/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.52/1.17
% 2.52/1.17
% 2.52/1.17 % ------
% 2.52/1.17 % Current options:
% 2.52/1.17 % ------
% 2.52/1.17
% 2.52/1.17
% 2.52/1.17 %
% 2.52/1.17
% 2.52/1.17 % ------ Proving...
% 2.52/1.17 %
% 2.52/1.17
% 2.52/1.17 % SZS status Theorem for theBenchmark.p
% 2.52/1.17
% 2.52/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.52/1.17
% 2.52/1.17
%------------------------------------------------------------------------------