%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN036+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 : n009.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 03:38:55 PM UTC 2026
% Result : Theorem 2.16s 1.27s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 143 ( 1 unt; 2 def)
% Number of atoms : 820 ( 0 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 966 ( 352 ~; 517 |; 67 &)
% ( 28 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 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 : 24 ( 23 usr; 20 prp; 0-1 aty)
% Number of functors : 17 ( 17 usr; 15 con; 0-1 aty)
% Number of variables : 312 ( 0 sgn 248 !; 64 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_q(X3) ) )
<=> ( ? [X4] :
! [X5] :
( big_q(X4)
<=> big_q(X5) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_p(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel34) ).
fof(f2,negated_conjecture,
~ ( ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_q(X3) ) )
<=> ( ? [X4] :
! [X5] :
( big_q(X4)
<=> big_q(X5) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_p(X7) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_q(X3) ) )
<~> ( ? [X4] :
! [X5] :
( big_q(X4)
<=> big_q(X5) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_p(X7) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f7,plain,
( ( ~ sP1
| ( ( ! [X4] :
? [X5] :
( ( big_q(X4)
| big_q(X5) )
& ( ~ big_q(X4)
| ~ big_q(X5) ) )
| ( ( ! [X6] : ~ big_p(X6)
| ! [X7] : big_p(X7) )
& ( ? [X7] : ~ big_p(X7)
| ? [X6] : big_p(X6) ) ) )
& ( ( ( ? [X6] : big_p(X6)
| ! [X7] : big_p(X7) )
& ( ! [X6] : ~ big_p(X6)
| ? [X7] : ~ big_p(X7) ) )
| ? [X4] :
! [X5] :
( ( ~ big_q(X4)
| big_q(X5) )
& ( ~ big_q(X5)
| big_q(X4) ) ) ) ) )
& ( ( ( ? [X4] :
! [X5] :
( ( ~ big_q(X4)
| big_q(X5) )
& ( ~ big_q(X5)
| big_q(X4) ) )
| ( ( ! [X6] : ~ big_p(X6)
| ! [X7] : big_p(X7) )
& ( ? [X7] : ~ big_p(X7)
| ? [X6] : big_p(X6) ) ) )
& ( ! [X4] :
? [X5] :
( ( big_q(X4)
| big_q(X5) )
& ( ~ big_q(X4)
| ~ big_q(X5) ) )
| ( ( ? [X6] : big_p(X6)
| ! [X7] : big_p(X7) )
& ( ! [X6] : ~ big_p(X6)
| ? [X7] : ~ big_p(X7) ) ) ) )
| sP1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f8,plain,
( ( ~ sP1
| ( ( ! [X22] :
? [X23] :
( ( big_q(X22)
| big_q(X23) )
& ( ~ big_q(X22)
| ~ big_q(X23) ) )
| ( ( ! [X21] : ~ big_p(X21)
| ! [X20] : big_p(X20) )
& ( ? [X19] : ~ big_p(X19)
| ? [X18] : big_p(X18) ) ) )
& ( ( ( ? [X17] : big_p(X17)
| ! [X16] : big_p(X16) )
& ( ! [X15] : ~ big_p(X15)
| ? [X14] : ~ big_p(X14) ) )
| ? [X12] :
! [X13] :
( ( ~ big_q(X12)
| big_q(X13) )
& ( ~ big_q(X13)
| big_q(X12) ) ) ) ) )
& ( ( ( ? [X10] :
! [X11] :
( ( ~ big_q(X10)
| big_q(X11) )
& ( ~ big_q(X11)
| big_q(X10) ) )
| ( ( ! [X9] : ~ big_p(X9)
| ! [X8] : big_p(X8) )
& ( ? [X7] : ~ big_p(X7)
| ? [X6] : big_p(X6) ) ) )
& ( ! [X4] :
? [X5] :
( ( big_q(X4)
| big_q(X5) )
& ( ~ big_q(X4)
| ~ big_q(X5) ) )
| ( ( ? [X3] : big_p(X3)
| ! [X2] : big_p(X2) )
& ( ! [X1] : ~ big_p(X1)
| ? [X0] : ~ big_p(X0) ) ) ) )
| sP1 ) ),
inference(rectify,[],[f7]) ).
fof(f9,plain,
( ( ~ sP1
| ( ( ! [X22] :
( ( big_q(X22)
| big_q(sK13(X22)) )
& ( ~ big_q(X22)
| ~ big_q(sK13(X22)) ) )
| ( ( ! [X21] : ~ big_p(X21)
| ! [X20] : big_p(X20) )
& ( ~ big_p(sK12)
| big_p(sK11) ) ) )
& ( ( ( big_p(sK10)
| ! [X16] : big_p(X16) )
& ( ! [X15] : ~ big_p(X15)
| ~ big_p(sK9) ) )
| ! [X13] :
( ( ~ big_q(sK8)
| big_q(X13) )
& ( ~ big_q(X13)
| big_q(sK8) ) ) ) ) )
& ( ( ( ! [X11] :
( ( ~ big_q(sK7)
| big_q(X11) )
& ( ~ big_q(X11)
| big_q(sK7) ) )
| ( ( ! [X9] : ~ big_p(X9)
| ! [X8] : big_p(X8) )
& ( ~ big_p(sK6)
| big_p(sK5) ) ) )
& ( ! [X4] :
( ( big_q(X4)
| big_q(sK4(X4)) )
& ( ~ big_q(X4)
| ~ big_q(sK4(X4)) ) )
| ( ( big_p(sK3)
| ! [X2] : big_p(X2) )
& ( ! [X1] : ~ big_p(X1)
| ~ big_p(sK2) ) ) ) )
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK2),skolemize(X3,sK3),skolemize(X5,sK4(X4)),skolemize(X6,sK5),skolemize(X7,sK6),skolemize(X10,sK7),skolemize(X12,sK8),skolemize(X14,sK9),skolemize(X17,sK10),skolemize(X18,sK11),skolemize(X19,sK12),skolemize(X23,sK13(X22))],[f8]) ).
fof(f13,plain,
( ( sP0
| sP1 )
& ( ~ sP0
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X21,X22,X20] :
( ~ sP1
| big_q(X22)
| big_q(sK13(X22))
| ~ big_p(X21)
| big_p(X20) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
! [X21,X22,X20] :
( ~ sP1
| ~ big_q(X22)
| ~ big_q(sK13(X22))
| ~ big_p(X21)
| big_p(X20) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
! [X16,X13] :
( ~ sP1
| big_p(sK10)
| big_p(X16)
| ~ big_q(sK8)
| big_q(X13) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X15,X13] :
( ~ sP1
| ~ big_p(X15)
| ~ big_p(sK9)
| ~ big_q(sK8)
| big_q(X13) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
! [X16,X13] :
( ~ sP1
| big_p(sK10)
| big_p(X16)
| ~ big_q(X13)
| big_q(sK8) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X15,X13] :
( ~ sP1
| ~ big_p(X15)
| ~ big_p(sK9)
| ~ big_q(X13)
| big_q(sK8) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X11,X8,X9] :
( ~ big_q(sK7)
| big_q(X11)
| ~ big_p(X9)
| big_p(X8)
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f23,plain,
! [X11,X8,X9] :
( ~ big_q(X11)
| big_q(sK7)
| ~ big_p(X9)
| big_p(X8)
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f26,plain,
! [X2,X4] :
( big_q(X4)
| big_q(sK4(X4))
| big_p(sK3)
| big_p(X2)
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X2,X4] :
( ~ big_q(X4)
| ~ big_q(sK4(X4))
| big_p(sK3)
| big_p(X2)
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X1,X4] :
( big_q(X4)
| big_q(sK4(X4))
| ~ big_p(X1)
| ~ big_p(sK2)
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f29,plain,
! [X1,X4] :
( ~ big_q(X4)
| ~ big_q(sK4(X4))
| ~ big_p(X1)
| ~ big_p(sK2)
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f46,plain,
( sP0
| sP1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f47,plain,
( ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( sP1
| ~ big_p(sK2)
| ~ big_q(X0)
| ~ big_p(X1)
| ~ big_q(sK4(X0)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( sP1
| big_q(X1)
| big_q(sK4(X1))
| ~ big_p(sK2)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( sP1
| big_p(sK3)
| big_p(X1)
| ~ big_q(X0)
| ~ big_q(sK4(X0)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( sP1
| big_p(sK3)
| big_q(X0)
| big_p(X1)
| big_q(sK4(X0)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1
| big_q(sK7)
| big_p(X2)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1
| big_q(X2)
| big_p(X1)
| ~ big_q(sK7)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( big_q(sK8)
| ~ sP1
| ~ big_p(sK9)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( big_q(sK8)
| big_p(sK10)
| big_p(X1)
| ~ sP1
| ~ big_q(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( big_q(X1)
| ~ sP1
| ~ big_q(sK8)
| ~ big_p(sK9)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( big_p(sK10)
| big_q(X1)
| big_p(X0)
| ~ sP1
| ~ big_q(sK8) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_p(X2)
| ~ sP1
| ~ big_q(X0)
| ~ big_p(X1)
| ~ big_q(sK13(X0)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_q(X1)
| big_p(X2)
| big_q(sK13(X1))
| ~ sP1
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_81,negated_conjecture,
( ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_82,negated_conjecture,
( sP0
| sP1 ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_84,plain,
( sP1
| big_q(sK19)
| big_p(sK19)
| big_p(sK3)
| big_q(sK4(sK19)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_105,plain,
( ~ sP1
| ~ sP0 ),
inference(prop_impl_just,[status(thm)],[c_81]) ).
tcf(c_106,plain,
( ~ sP0
| ~ sP1 ),
inference(renaming,[status(thm)],[c_105]) ).
tcf(c_107,plain,
( sP1
| sP0 ),
inference(prop_impl_just,[status(thm)],[c_82]) ).
tcf(c_108,plain,
( sP0
| sP1 ),
inference(renaming,[status(thm)],[c_107]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] :
( ~ sP0
| ~ big_p(sK2)
| ~ big_q(X0)
| ~ big_p(X1)
| ~ big_q(sK4(X0)) ),
inference(bin_hyper_res,[status(thm)],[c_49,c_106]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] :
( big_q(X1)
| big_q(sK4(X1))
| ~ sP0
| ~ big_p(sK2)
| ~ big_p(X0) ),
inference(bin_hyper_res,[status(thm)],[c_50,c_106]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( big_p(sK3)
| big_p(X1)
| ~ sP0
| ~ big_q(X0)
| ~ big_q(sK4(X0)) ),
inference(bin_hyper_res,[status(thm)],[c_51,c_106]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( big_p(sK3)
| big_q(X0)
| big_p(X1)
| big_q(sK4(X0))
| ~ sP0 ),
inference(bin_hyper_res,[status(thm)],[c_52,c_106]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_q(sK7)
| big_p(X2)
| ~ sP0
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(bin_hyper_res,[status(thm)],[c_55,c_106]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_q(X2)
| big_p(X1)
| ~ sP0
| ~ big_q(sK7)
| ~ big_p(X0) ),
inference(bin_hyper_res,[status(thm)],[c_56,c_106]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( sP0
| big_q(sK8)
| ~ big_p(sK9)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(bin_hyper_res,[status(thm)],[c_57,c_108]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( sP0
| big_q(sK8)
| big_p(sK10)
| big_p(X1)
| ~ big_q(X0) ),
inference(bin_hyper_res,[status(thm)],[c_58,c_108]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( sP0
| big_q(X1)
| ~ big_q(sK8)
| ~ big_p(sK9)
| ~ big_p(X0) ),
inference(bin_hyper_res,[status(thm)],[c_59,c_108]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( sP0
| big_p(sK10)
| big_q(X1)
| big_p(X0)
| ~ big_q(sK8) ),
inference(bin_hyper_res,[status(thm)],[c_60,c_108]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0
| big_p(X2)
| ~ big_q(X0)
| ~ big_p(X1)
| ~ big_q(sK13(X0)) ),
inference(bin_hyper_res,[status(thm)],[c_63,c_108]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0
| big_q(X1)
| big_p(X2)
| big_q(sK13(X1))
| ~ big_p(X0) ),
inference(bin_hyper_res,[status(thm)],[c_64,c_108]) ).
tcf(c_186,plain,
( big_p(sK19)
| big_p(sK3)
| ~ sP0
| ~ big_q(sK19)
| ~ big_q(sK4(sK19)) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_678,plain,
! [X0: $i] :
( ~ iPr_def_10
| big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_176]) ).
tcf(c_679,plain,
! [X0: $i] :
( ~ iPr_def_11
| big_q(sK13(X0))
| big_q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_176]) ).
tcf(c_680,plain,
! [X0: $i] :
( ~ iPr_def_12
| ~ big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_176]) ).
tcf(c_681,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_176]) ).
tcf(c_682,plain,
! [X0: $i] :
( ~ iPr_def_13
| ~ big_q(sK13(X0))
| ~ big_q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_175]) ).
tcf(c_683,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_175]) ).
tcf(c_684,plain,
! [X0: $i] :
( ~ iPr_def_14
| big_q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_172]) ).
tcf(c_685,plain,
( iPr_def_14
| iPr_def_10
| sP0
| big_p(sK10)
| ~ big_q(sK8) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_172]) ).
tcf(c_686,plain,
( iPr_def_14
| iPr_def_12
| sP0
| ~ big_q(sK8)
| ~ big_p(sK9) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_171]) ).
tcf(c_687,plain,
! [X0: $i] :
( ~ iPr_def_15
| ~ big_q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_170]) ).
tcf(c_688,plain,
( iPr_def_15
| iPr_def_10
| sP0
| big_q(sK8)
| big_p(sK10) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_170]) ).
tcf(c_689,plain,
( iPr_def_15
| iPr_def_12
| sP0
| big_q(sK8)
| ~ big_p(sK9) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_169]) ).
tcf(c_690,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ~ sP0
| ~ big_q(sK7) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_168]) ).
tcf(c_691,plain,
( iPr_def_15
| iPr_def_12
| iPr_def_10
| big_q(sK7)
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_167]) ).
tcf(c_692,plain,
! [X0: $i] :
( ~ iPr_def_16
| big_q(sK4(X0))
| big_q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_16])],[c_164]) ).
tcf(c_694,plain,
! [X0: $i] :
( ~ iPr_def_17
| ~ big_q(sK4(X0))
| ~ big_q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_17])],[c_163]) ).
tcf(c_696,plain,
( iPr_def_16
| iPr_def_12
| ~ sP0
| ~ big_p(sK2) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_162]) ).
tcf(c_697,plain,
( iPr_def_17
| iPr_def_12
| ~ sP0
| ~ big_p(sK2) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_161]) ).
tcf(c_714,plain,
( big_p(sK19)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_715,plain,
( big_q(sK19)
| ~ iPr_def_14 ),
inference(instantiation,[status(thm)],[c_684]) ).
tcf(c_716,plain,
( ~ iPr_def_12
| ~ big_p(sK19) ),
inference(instantiation,[status(thm)],[c_680]) ).
tcf(c_717,plain,
( ~ iPr_def_15
| ~ big_q(sK19) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_726,plain,
( big_p(sK9)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_727,plain,
( ~ iPr_def_12
| ~ big_p(sK10) ),
inference(instantiation,[status(thm)],[c_680]) ).
tcf(c_728,plain,
( ~ iPr_def_15
| ~ big_q(sK15) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_729,plain,
! [X0: $i] :
( ~ iPr_def_12
| ~ big_p(sK16(X0)) ),
inference(instantiation,[status(thm)],[c_680]) ).
tcf(c_730,plain,
( ~ iPr_def_12
| ~ big_p(sK16(sK19)) ),
inference(instantiation,[status(thm)],[c_729]) ).
tcf(c_734,plain,
( ~ iPr_def_12
| ~ big_p(sK3) ),
inference(instantiation,[status(thm)],[c_680]) ).
tcf(c_737,plain,
! [X0: $i] :
( ~ iPr_def_15
| ~ big_q(sK4(X0)) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_738,plain,
( ~ iPr_def_15
| ~ big_q(sK4(sK19)) ),
inference(instantiation,[status(thm)],[c_737]) ).
tcf(c_744,plain,
( ~ iPr_def_15
| ~ big_q(sK22) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_745,plain,
! [X0: $i] :
( big_q(sK4(X0))
| ~ iPr_def_14 ),
inference(instantiation,[status(thm)],[c_684]) ).
tcf(c_746,plain,
( big_q(sK4(sK19))
| ~ iPr_def_14 ),
inference(instantiation,[status(thm)],[c_745]) ).
tcf(c_748,plain,
( big_q(sK14)
| ~ iPr_def_14 ),
inference(instantiation,[status(thm)],[c_684]) ).
tcf(c_749,plain,
( big_q(sK21)
| ~ iPr_def_14 ),
inference(instantiation,[status(thm)],[c_684]) ).
tcf(c_757,plain,
! [X0: $i] :
( ~ iPr_def_12
| ~ big_p(sK25(X0)) ),
inference(instantiation,[status(thm)],[c_680]) ).
tcf(c_762,plain,
( big_p(sK2)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_763,plain,
! [X0: $i] :
( big_p(sK16(X0))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_764,plain,
( big_p(sK16(sK19))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_763]) ).
tcf(c_765,plain,
! [X0: $i] :
( big_p(sK25(X0))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_774,plain,
! [X0: $i] :
( ~ iPr_def_15
| ~ big_q(sK13(X0)) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_787,plain,
! [X0: $i] :
( big_q(sK13(X0))
| ~ iPr_def_14 ),
inference(instantiation,[status(thm)],[c_684]) ).
fof(f4,definition,
( sP0
<=> ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_q(X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f5,definition,
( sP1
<=> ( ? [X4] :
! [X5] :
( big_q(X4)
<=> big_q(X5) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_p(X7) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f6,plain,
( sP0
<~> sP1 ),
inference(definition_folding,[],[f3,f5,f4]) ).
fof(f10,plain,
( ( ~ sP0
| ( ( ! [X0] :
? [X1] :
( ( big_p(X0)
| big_p(X1) )
& ( ~ big_p(X0)
| ~ big_p(X1) ) )
| ( ( ! [X2] : ~ big_q(X2)
| ! [X3] : big_q(X3) )
& ( ? [X3] : ~ big_q(X3)
| ? [X2] : big_q(X2) ) ) )
& ( ( ( ? [X2] : big_q(X2)
| ! [X3] : big_q(X3) )
& ( ! [X2] : ~ big_q(X2)
| ? [X3] : ~ big_q(X3) ) )
| ? [X0] :
! [X1] :
( ( ~ big_p(X0)
| big_p(X1) )
& ( ~ big_p(X1)
| big_p(X0) ) ) ) ) )
& ( ( ( ? [X0] :
! [X1] :
( ( ~ big_p(X0)
| big_p(X1) )
& ( ~ big_p(X1)
| big_p(X0) ) )
| ( ( ! [X2] : ~ big_q(X2)
| ! [X3] : big_q(X3) )
& ( ? [X3] : ~ big_q(X3)
| ? [X2] : big_q(X2) ) ) )
& ( ! [X0] :
? [X1] :
( ( big_p(X0)
| big_p(X1) )
& ( ~ big_p(X0)
| ~ big_p(X1) ) )
| ( ( ? [X2] : big_q(X2)
| ! [X3] : big_q(X3) )
& ( ! [X2] : ~ big_q(X2)
| ? [X3] : ~ big_q(X3) ) ) ) )
| sP0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f11,plain,
( ( ~ sP0
| ( ( ! [X22] :
? [X23] :
( ( big_p(X22)
| big_p(X23) )
& ( ~ big_p(X22)
| ~ big_p(X23) ) )
| ( ( ! [X21] : ~ big_q(X21)
| ! [X20] : big_q(X20) )
& ( ? [X19] : ~ big_q(X19)
| ? [X18] : big_q(X18) ) ) )
& ( ( ( ? [X17] : big_q(X17)
| ! [X16] : big_q(X16) )
& ( ! [X15] : ~ big_q(X15)
| ? [X14] : ~ big_q(X14) ) )
| ? [X12] :
! [X13] :
( ( ~ big_p(X12)
| big_p(X13) )
& ( ~ big_p(X13)
| big_p(X12) ) ) ) ) )
& ( ( ( ? [X10] :
! [X11] :
( ( ~ big_p(X10)
| big_p(X11) )
& ( ~ big_p(X11)
| big_p(X10) ) )
| ( ( ! [X9] : ~ big_q(X9)
| ! [X8] : big_q(X8) )
& ( ? [X7] : ~ big_q(X7)
| ? [X6] : big_q(X6) ) ) )
& ( ! [X4] :
? [X5] :
( ( big_p(X4)
| big_p(X5) )
& ( ~ big_p(X4)
| ~ big_p(X5) ) )
| ( ( ? [X3] : big_q(X3)
| ! [X2] : big_q(X2) )
& ( ! [X1] : ~ big_q(X1)
| ? [X0] : ~ big_q(X0) ) ) ) )
| sP0 ) ),
inference(rectify,[],[f10]) ).
fof(f12,plain,
( ( ~ sP0
| ( ( ! [X22] :
( ( big_p(X22)
| big_p(sK25(X22)) )
& ( ~ big_p(X22)
| ~ big_p(sK25(X22)) ) )
| ( ( ! [X21] : ~ big_q(X21)
| ! [X20] : big_q(X20) )
& ( ~ big_q(sK24)
| big_q(sK23) ) ) )
& ( ( ( big_q(sK22)
| ! [X16] : big_q(X16) )
& ( ! [X15] : ~ big_q(X15)
| ~ big_q(sK21) ) )
| ! [X13] :
( ( ~ big_p(sK20)
| big_p(X13) )
& ( ~ big_p(X13)
| big_p(sK20) ) ) ) ) )
& ( ( ( ! [X11] :
( ( ~ big_p(sK19)
| big_p(X11) )
& ( ~ big_p(X11)
| big_p(sK19) ) )
| ( ( ! [X9] : ~ big_q(X9)
| ! [X8] : big_q(X8) )
& ( ~ big_q(sK18)
| big_q(sK17) ) ) )
& ( ! [X4] :
( ( big_p(X4)
| big_p(sK16(X4)) )
& ( ~ big_p(X4)
| ~ big_p(sK16(X4)) ) )
| ( ( big_q(sK15)
| ! [X2] : big_q(X2) )
& ( ! [X1] : ~ big_q(X1)
| ~ big_q(sK14) ) ) ) )
| sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25]),skolemize(X0,sK14),skolemize(X3,sK15),skolemize(X5,sK16(X4)),skolemize(X6,sK17),skolemize(X7,sK18),skolemize(X10,sK19),skolemize(X12,sK20),skolemize(X14,sK21),skolemize(X17,sK22),skolemize(X18,sK23),skolemize(X19,sK24),skolemize(X23,sK25(X22))],[f11]) ).
fof(f30,plain,
! [X21,X22,X20] :
( ~ sP0
| big_p(X22)
| big_p(sK25(X22))
| ~ big_q(X21)
| big_q(X20) ),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X21,X22,X20] :
( ~ sP0
| ~ big_p(X22)
| ~ big_p(sK25(X22))
| ~ big_q(X21)
| big_q(X20) ),
inference(cnf_transformation,[],[f12]) ).
fof(f34,plain,
! [X16,X13] :
( ~ sP0
| big_q(sK22)
| big_q(X16)
| ~ big_p(sK20)
| big_p(X13) ),
inference(cnf_transformation,[],[f12]) ).
fof(f35,plain,
! [X15,X13] :
( ~ sP0
| ~ big_q(X15)
| ~ big_q(sK21)
| ~ big_p(sK20)
| big_p(X13) ),
inference(cnf_transformation,[],[f12]) ).
fof(f36,plain,
! [X16,X13] :
( ~ sP0
| big_q(sK22)
| big_q(X16)
| ~ big_p(X13)
| big_p(sK20) ),
inference(cnf_transformation,[],[f12]) ).
fof(f37,plain,
! [X15,X13] :
( ~ sP0
| ~ big_q(X15)
| ~ big_q(sK21)
| ~ big_p(X13)
| big_p(sK20) ),
inference(cnf_transformation,[],[f12]) ).
fof(f38,plain,
! [X11,X8,X9] :
( ~ big_p(sK19)
| big_p(X11)
| ~ big_q(X9)
| big_q(X8)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f39,plain,
! [X11,X8,X9] :
( ~ big_p(X11)
| big_p(sK19)
| ~ big_q(X9)
| big_q(X8)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f42,plain,
! [X2,X4] :
( big_p(X4)
| big_p(sK16(X4))
| big_q(sK15)
| big_q(X2)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f43,plain,
! [X2,X4] :
( ~ big_p(X4)
| ~ big_p(sK16(X4))
| big_q(sK15)
| big_q(X2)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f44,plain,
! [X1,X4] :
( big_p(X4)
| big_p(sK16(X4))
| ~ big_q(X1)
| ~ big_q(sK14)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f45,plain,
! [X1,X4] :
( ~ big_p(X4)
| ~ big_p(sK16(X4))
| ~ big_q(X1)
| ~ big_q(sK14)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( sP0
| ~ big_q(sK14)
| ~ big_q(X1)
| ~ big_p(X0)
| ~ big_p(sK16(X0)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( sP0
| big_p(X1)
| big_p(sK16(X1))
| ~ big_q(sK14)
| ~ big_q(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( sP0
| big_q(sK15)
| big_q(X1)
| ~ big_p(X0)
| ~ big_p(sK16(X0)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( sP0
| big_q(sK15)
| big_q(X1)
| big_p(X0)
| big_p(sK16(X0)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0
| big_p(sK19)
| big_q(X2)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0
| big_q(X2)
| big_p(X1)
| ~ big_p(sK19)
| ~ big_q(X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( big_p(sK20)
| ~ sP0
| ~ big_q(sK21)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( big_q(sK22)
| big_p(sK20)
| big_q(X1)
| ~ sP0
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( big_p(X1)
| ~ sP0
| ~ big_q(sK21)
| ~ big_p(sK20)
| ~ big_q(X0) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( big_q(sK22)
| big_q(X1)
| big_p(X0)
| ~ sP0
| ~ big_p(sK20) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_q(X2)
| ~ sP0
| ~ big_q(X1)
| ~ big_p(X0)
| ~ big_p(sK25(X0)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_q(X2)
| big_p(X1)
| big_p(sK25(X1))
| ~ sP0
| ~ big_q(X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_92,plain,
( sP0
| big_q(sK19)
| big_q(sK15)
| ~ big_p(sK19)
| ~ big_p(sK16(sK19)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_93,plain,
( sP0
| big_p(sK19)
| big_p(sK16(sK19))
| ~ big_q(sK19)
| ~ big_q(sK14) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_698,plain,
! [X0: $i] :
( ~ iPr_def_18
| big_p(sK25(X0))
| big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_18])],[c_80]) ).
tcf(c_699,plain,
( iPr_def_18
| iPr_def_15
| iPr_def_14
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_80]) ).
tcf(c_700,plain,
! [X0: $i] :
( ~ iPr_def_19
| ~ big_p(sK25(X0))
| ~ big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_19])],[c_79]) ).
tcf(c_701,plain,
( iPr_def_19
| iPr_def_15
| iPr_def_14
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_79]) ).
tcf(c_702,plain,
( iPr_def_14
| iPr_def_10
| big_q(sK22)
| ~ sP0
| ~ big_p(sK20) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_76]) ).
tcf(c_703,plain,
( iPr_def_15
| iPr_def_10
| ~ sP0
| ~ big_q(sK21)
| ~ big_p(sK20) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_75]) ).
tcf(c_704,plain,
( iPr_def_14
| iPr_def_12
| big_q(sK22)
| big_p(sK20)
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_74]) ).
tcf(c_705,plain,
( iPr_def_15
| iPr_def_12
| big_p(sK20)
| ~ sP0
| ~ big_q(sK21) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_73]) ).
tcf(c_706,plain,
( iPr_def_15
| iPr_def_14
| iPr_def_10
| sP0
| ~ big_p(sK19) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_72]) ).
tcf(c_707,plain,
( iPr_def_15
| iPr_def_14
| iPr_def_12
| sP0
| big_p(sK19) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_71]) ).
tcf(c_708,plain,
! [X0: $i] :
( ~ iPr_def_20
| big_p(sK16(X0))
| big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_20])],[c_68]) ).
tcf(c_709,plain,
( iPr_def_20
| iPr_def_14
| sP0
| big_q(sK15) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_68]) ).
tcf(c_710,plain,
! [X0: $i] :
( ~ iPr_def_21
| ~ big_p(sK16(X0))
| ~ big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_21])],[c_67]) ).
tcf(c_712,plain,
( iPr_def_20
| iPr_def_15
| sP0
| ~ big_q(sK14) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_66]) ).
tcf(c_713,plain,
( iPr_def_21
| iPr_def_15
| sP0
| ~ big_q(sK14) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_65]) ).
tcf(c_799,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_787,c_774,c_765,c_764,c_763,c_762,c_757,c_749,c_748,c_746,c_745,c_744,c_738,c_737,c_734,c_730,c_729,c_728,c_727,c_726,c_703,c_710,c_705,c_702,c_700,c_694,c_686,c_682,c_704,c_690,c_689,c_685,c_708,c_706,c_698,c_697,c_696,c_692,c_691,c_688,c_679,c_713,c_712,c_707,c_709,c_701,c_699,c_717,c_687,c_716,c_680,c_715,c_684,c_683,c_681,c_714,c_678,c_186,c_93,c_92,c_84,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN036+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 23:52:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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...
% 2.16/1.27 % SZS status Started for theBenchmark.p
% 2.16/1.27 % SZS status Theorem for theBenchmark.p
% 2.16/1.27
% 2.16/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.16/1.27
% 2.16/1.27 % ------ iProver source info
% 2.16/1.27
% 2.16/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.16/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.16/1.27 % git: non_committed_changes: false
% 2.16/1.27
% 2.16/1.27 % ------ Parsing...
% 2.16/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.16/1.27
% 2.16/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.16/1.27
% 2.16/1.27 % ------ Preprocessing... gs_s sp: 56 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.16/1.27 % ------ Proving...
% 2.16/1.27 % ------ Problem Properties
% 2.16/1.27
% 2.16/1.27 %
% 2.16/1.27 % clauses 36
% 2.16/1.27 % conjectures 0
% 2.16/1.27 % EPR 28
% 2.16/1.27 % Horn 8
% 2.16/1.27 % unary 0
% 2.16/1.27 % binary 4
% 2.16/1.27 % lits 140
% 2.16/1.27 % lits eq 0
% 2.16/1.27 % fd_pure 0
% 2.16/1.27 % fd_pseudo 0
% 2.16/1.27 % fd_cond 0
% 2.16/1.27 % fd_pseudo_cond 0
% 2.16/1.27 % AC symbols 0
% 2.16/1.27
% 2.16/1.27 % ------ Schedule dynamic 5 is on
% 2.16/1.27
% 2.16/1.27 % ------ no conjectures: strip conj schedule
% 2.16/1.27
% 2.16/1.27 % ------ no equalities: superposition off
% 2.16/1.27
% 2.16/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.16/1.27
% 2.16/1.27
% 2.16/1.27 % ------
% 2.16/1.27 % Current options:
% 2.16/1.27 % ------
% 2.16/1.27
% 2.16/1.27
% 2.16/1.27 %
% 2.16/1.27
% 2.16/1.27 % ------ Proving...
% 2.16/1.27 %
% 2.16/1.27
% 2.16/1.27 % SZS status Theorem for theBenchmark.p
% 2.16/1.27
% 2.16/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.16/1.28
% 2.16/1.28
%------------------------------------------------------------------------------