%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYO604+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 03:51:32 PM UTC 2026
% Result : Theorem 6.02s 1.65s
% Output : CNFRefutation 6.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 317 ( 2 unt; 4 def)
% Number of atoms : 1532 ( 0 equ)
% Maximal formula atoms : 59 ( 4 avg)
% Number of connectives : 1770 ( 619 ~; 913 |; 235 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-1 aty)
% Number of variables : 571 ( 0 sgn 471 !; 100 ?; 282 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ~ ? [X0] :
! [X1] :
( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& g_false_only(X1,X0) )
| ( ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) )
& g_true_only(X1,X0) ) )
& ? [X0] :
( ~ ? [X1] :
( ( ( ( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_false_only(X1,X0) )
| ( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_both(X1,X0) )
| ( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
| ( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) ) )
& g_true_only(X1,X0) ) )
& ? [X1] :
( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) )
& g_both(X1,X0) ) ) )
| ! [X0] :
? [X1] :
( ( ( ( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_false_only(X1,X0) )
| ( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_both(X1,X0) )
| ( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
| ( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) ) )
& g_true_only(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc3) ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [X0] :
! [X1] :
( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& g_false_only(X1,X0) )
| ( ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) )
& g_true_only(X1,X0) ) )
& ? [X0] :
( ~ ? [X1] :
( ( ( ( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_false_only(X1,X0) )
| ( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_both(X1,X0) )
| ( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
| ( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) ) )
& g_true_only(X1,X0) ) )
& ? [X1] :
( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) )
& g_both(X1,X0) ) ) )
| ! [X0] :
? [X1] :
( ( ( ( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_false_only(X1,X0) )
| ( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_both(X1,X0) )
| ( ( ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
| ( ~ ? [X2] :
( g_true_only(X2,X1)
& g_true_only(X1,X2) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) ) )
& g_true_only(X1,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X0,X1] :
( g_true_only(X0,X1)
<=> ( ~ g_false(X0,X1)
& g_true(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_only_g) ).
fof(f4,axiom,
! [X0,X1] :
( g_both(X0,X1)
<=> ( g_false(X0,X1)
& g_true(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both_g) ).
fof(f5,axiom,
! [X0,X1] :
( g_false_only(X0,X1)
<=> ( ~ g_true(X0,X1)
& g_false(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_only_g) ).
fof(f6,axiom,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exhaustion_g) ).
fof(f7,plain,
~ ( ( ~ ? [X23] :
! [X24] :
( ( ? [X26] :
( g_true_only(X26,X24)
& g_true_only(X24,X26) )
& g_false_only(X24,X23) )
| ( ! [X25] :
( g_false_only(X25,X24)
| g_false_only(X24,X25) )
& g_true_only(X24,X23) ) )
& ? [X10] :
( ~ ? [X14] :
( ( ( ( ~ ? [X22] :
( g_true_only(X22,X14)
& g_true_only(X14,X22) )
& ? [X21] :
( ~ g_false_only(X21,X14)
& ~ g_false_only(X14,X21)
& ( g_both(X21,X14)
| g_both(X14,X21) ) ) )
| ! [X20] :
( g_false_only(X20,X14)
| g_false_only(X14,X20) ) )
& g_false_only(X14,X10) )
| ( ( ? [X19] :
( g_true_only(X19,X14)
& g_true_only(X14,X19) )
| ! [X18] :
( g_false_only(X18,X14)
| g_false_only(X14,X18) ) )
& g_both(X14,X10) )
| ( ( ? [X17] :
( g_true_only(X17,X14)
& g_true_only(X14,X17) )
| ( ~ ? [X16] :
( g_true_only(X16,X14)
& g_true_only(X14,X16) )
& ? [X15] :
( ~ g_false_only(X15,X14)
& ~ g_false_only(X14,X15)
& ( g_both(X15,X14)
| g_both(X14,X15) ) ) ) )
& g_true_only(X14,X10) ) )
& ? [X11] :
( ~ ? [X13] :
( g_true_only(X13,X11)
& g_true_only(X11,X13) )
& ? [X12] :
( ~ g_false_only(X12,X11)
& ~ g_false_only(X11,X12)
& ( g_both(X12,X11)
| g_both(X11,X12) ) )
& g_both(X11,X10) ) ) )
| ! [X0] :
? [X1] :
( ( ( ( ~ ? [X9] :
( g_true_only(X9,X1)
& g_true_only(X1,X9) )
& ? [X8] :
( ~ g_false_only(X8,X1)
& ~ g_false_only(X1,X8)
& ( g_both(X8,X1)
| g_both(X1,X8) ) ) )
| ! [X7] :
( g_false_only(X7,X1)
| g_false_only(X1,X7) ) )
& g_false_only(X1,X0) )
| ( ( ? [X6] :
( g_true_only(X6,X1)
& g_true_only(X1,X6) )
| ! [X5] :
( g_false_only(X5,X1)
| g_false_only(X1,X5) ) )
& g_both(X1,X0) )
| ( ( ? [X4] :
( g_true_only(X4,X1)
& g_true_only(X1,X4) )
| ( ~ ? [X3] :
( g_true_only(X3,X1)
& g_true_only(X1,X3) )
& ? [X2] :
( ~ g_false_only(X2,X1)
& ~ g_false_only(X1,X2)
& ( g_both(X2,X1)
| g_both(X1,X2) ) ) ) )
& g_true_only(X1,X0) ) ) ),
inference(rectify,[],[f2]) ).
fof(f8,plain,
( ( ? [X23] :
! [X24] :
( ( ? [X26] :
( g_true_only(X26,X24)
& g_true_only(X24,X26) )
& g_false_only(X24,X23) )
| ( ! [X25] :
( g_false_only(X25,X24)
| g_false_only(X24,X25) )
& g_true_only(X24,X23) ) )
| ! [X10] :
( ? [X14] :
( ( ( ( ! [X22] :
( ~ g_true_only(X22,X14)
| ~ g_true_only(X14,X22) )
& ? [X21] :
( ~ g_false_only(X21,X14)
& ~ g_false_only(X14,X21)
& ( g_both(X21,X14)
| g_both(X14,X21) ) ) )
| ! [X20] :
( g_false_only(X20,X14)
| g_false_only(X14,X20) ) )
& g_false_only(X14,X10) )
| ( ( ? [X19] :
( g_true_only(X19,X14)
& g_true_only(X14,X19) )
| ! [X18] :
( g_false_only(X18,X14)
| g_false_only(X14,X18) ) )
& g_both(X14,X10) )
| ( ( ? [X17] :
( g_true_only(X17,X14)
& g_true_only(X14,X17) )
| ( ! [X16] :
( ~ g_true_only(X16,X14)
| ~ g_true_only(X14,X16) )
& ? [X15] :
( ~ g_false_only(X15,X14)
& ~ g_false_only(X14,X15)
& ( g_both(X15,X14)
| g_both(X14,X15) ) ) ) )
& g_true_only(X14,X10) ) )
| ! [X11] :
( ? [X13] :
( g_true_only(X13,X11)
& g_true_only(X11,X13) )
| ! [X12] :
( g_false_only(X12,X11)
| g_false_only(X11,X12)
| ( ~ g_both(X12,X11)
& ~ g_both(X11,X12) ) )
| ~ g_both(X11,X10) ) ) )
& ? [X0] :
! [X1] :
( ( ( ( ? [X9] :
( g_true_only(X9,X1)
& g_true_only(X1,X9) )
| ! [X8] :
( g_false_only(X8,X1)
| g_false_only(X1,X8)
| ( ~ g_both(X8,X1)
& ~ g_both(X1,X8) ) ) )
& ? [X7] :
( ~ g_false_only(X7,X1)
& ~ g_false_only(X1,X7) ) )
| ~ g_false_only(X1,X0) )
& ( ( ! [X6] :
( ~ g_true_only(X6,X1)
| ~ g_true_only(X1,X6) )
& ? [X5] :
( ~ g_false_only(X5,X1)
& ~ g_false_only(X1,X5) ) )
| ~ g_both(X1,X0) )
& ( ( ! [X4] :
( ~ g_true_only(X4,X1)
| ~ g_true_only(X1,X4) )
& ( ? [X3] :
( g_true_only(X3,X1)
& g_true_only(X1,X3) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2)
| ( ~ g_both(X2,X1)
& ~ g_both(X1,X2) ) ) ) )
| ~ g_true_only(X1,X0) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f14,plain,
( ~ sP3
| ? [X23] :
! [X24] :
( ( ? [X26] :
( g_true_only(X26,X24)
& g_true_only(X24,X26) )
& g_false_only(X24,X23) )
| ( ! [X25] :
( g_false_only(X25,X24)
| g_false_only(X24,X25) )
& g_true_only(X24,X23) ) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f15,plain,
( ~ sP3
| ? [X0] :
! [X1] :
( ( ? [X3] :
( g_true_only(X3,X1)
& g_true_only(X1,X3) )
& g_false_only(X1,X0) )
| ( ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) )
& g_true_only(X1,X0) ) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
( ~ sP3
| ! [X1] :
( ( g_true_only(sK5(X1),X1)
& g_true_only(X1,sK5(X1))
& g_false_only(X1,sK4) )
| ( ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) )
& g_true_only(X1,sK4) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X3,sK5(X1))],[f15]) ).
fof(f17,plain,
! [X10] :
( ~ sP2(X10)
| ? [X14] :
( sP1(X10,X14)
| ( ( ? [X19] :
( g_true_only(X19,X14)
& g_true_only(X14,X19) )
| ! [X18] :
( g_false_only(X18,X14)
| g_false_only(X14,X18) ) )
& g_both(X14,X10) )
| ( sP0(X14)
& g_true_only(X14,X10) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0] :
( ~ sP2(X0)
| ? [X1] :
( sP1(X0,X1)
| ( ( ? [X3] :
( g_true_only(X3,X1)
& g_true_only(X1,X3) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_both(X1,X0) )
| ( sP0(X1)
& g_true_only(X1,X0) ) ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0] :
( ~ sP2(X0)
| sP1(X0,sK6(X0))
| ( ( ( g_true_only(sK7(X0),sK6(X0))
& g_true_only(sK6(X0),sK7(X0)) )
| ! [X2] :
( g_false_only(X2,sK6(X0))
| g_false_only(sK6(X0),X2) ) )
& g_both(sK6(X0),X0) )
| ( sP0(sK6(X0))
& g_true_only(sK6(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X1,sK6(X0)),skolemize(X3,sK7(X0))],[f18]) ).
fof(f20,plain,
! [X10,X14] :
( ~ sP1(X10,X14)
| ( ( ( ! [X22] :
( ~ g_true_only(X22,X14)
| ~ g_true_only(X14,X22) )
& ? [X21] :
( ~ g_false_only(X21,X14)
& ~ g_false_only(X14,X21)
& ( g_both(X21,X14)
| g_both(X14,X21) ) ) )
| ! [X20] :
( g_false_only(X20,X14)
| g_false_only(X14,X20) ) )
& g_false_only(X14,X10) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ( ( ( ! [X4] :
( ~ g_true_only(X4,X1)
| ~ g_true_only(X1,X4) )
& ? [X3] :
( ~ g_false_only(X3,X1)
& ~ g_false_only(X1,X3)
& ( g_both(X3,X1)
| g_both(X1,X3) ) ) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_false_only(X1,X0) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ( ( ( ! [X4] :
( ~ g_true_only(X4,X1)
| ~ g_true_only(X1,X4) )
& ~ g_false_only(sK8(X1),X1)
& ~ g_false_only(X1,sK8(X1))
& ( g_both(sK8(X1),X1)
| g_both(X1,sK8(X1)) ) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2) ) )
& g_false_only(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X1))],[f21]) ).
fof(f26,plain,
( ( sP3
| ! [X10] :
( sP2(X10)
| ! [X11] :
( ( g_true_only(sK16(X11),X11)
& g_true_only(X11,sK16(X11)) )
| ! [X12] :
( g_false_only(X12,X11)
| g_false_only(X11,X12)
| ( ~ g_both(X12,X11)
& ~ g_both(X11,X12) ) )
| ~ g_both(X11,X10) ) ) )
& ! [X1] :
( ( ( ( ( g_true_only(sK15(X1),X1)
& g_true_only(X1,sK15(X1)) )
| ! [X8] :
( g_false_only(X8,X1)
| g_false_only(X1,X8)
| ( ~ g_both(X8,X1)
& ~ g_both(X1,X8) ) ) )
& ~ g_false_only(sK14(X1),X1)
& ~ g_false_only(X1,sK14(X1)) )
| ~ g_false_only(X1,sK11) )
& ( ( ! [X6] :
( ~ g_true_only(X6,X1)
| ~ g_true_only(X1,X6) )
& ~ g_false_only(sK13(X1),X1)
& ~ g_false_only(X1,sK13(X1)) )
| ~ g_both(X1,sK11) )
& ( ( ! [X4] :
( ~ g_true_only(X4,X1)
| ~ g_true_only(X1,X4) )
& ( ( g_true_only(sK12(X1),X1)
& g_true_only(X1,sK12(X1)) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2)
| ( ~ g_both(X2,X1)
& ~ g_both(X1,X2) ) ) ) )
| ~ g_true_only(X1,sK11) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15,sK16]),skolemize(X0,sK11),skolemize(X3,sK12(X1)),skolemize(X5,sK13(X1)),skolemize(X7,sK14(X1)),skolemize(X9,sK15(X1)),skolemize(X13,sK16(X11))],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ g_true_only(X0,X1)
| ( ~ g_false(X0,X1)
& g_true(X0,X1) ) )
& ( g_false(X0,X1)
| ~ g_true(X0,X1)
| g_true_only(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0,X1] :
( ( ~ g_true_only(X0,X1)
| ( ~ g_false(X0,X1)
& g_true(X0,X1) ) )
& ( g_false(X0,X1)
| ~ g_true(X0,X1)
| g_true_only(X0,X1) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( ~ g_both(X0,X1)
| ( g_false(X0,X1)
& g_true(X0,X1) ) )
& ( ~ g_false(X0,X1)
| ~ g_true(X0,X1)
| g_both(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0,X1] :
( ( ~ g_both(X0,X1)
| ( g_false(X0,X1)
& g_true(X0,X1) ) )
& ( ~ g_false(X0,X1)
| ~ g_true(X0,X1)
| g_both(X0,X1) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( ~ g_false_only(X0,X1)
| ( ~ g_true(X0,X1)
& g_false(X0,X1) ) )
& ( g_true(X0,X1)
| ~ g_false(X0,X1)
| g_false_only(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ g_false_only(X0,X1)
| ( ~ g_true(X0,X1)
& g_false(X0,X1) ) )
& ( g_true(X0,X1)
| ~ g_false(X0,X1)
| g_false_only(X0,X1) ) ),
inference(flattening,[],[f31]) ).
fof(f35,plain,
! [X2,X1] :
( ~ sP3
| g_false_only(X1,sK4)
| g_false_only(X2,X1)
| g_false_only(X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X1] :
( ~ sP3
| g_true_only(sK5(X1),X1)
| g_true_only(X1,sK4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X1] :
( ~ sP3
| g_true_only(X1,sK5(X1))
| g_true_only(X1,sK4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X0] :
( ~ sP2(X0)
| sP1(X0,sK6(X0))
| g_both(sK6(X0),X0)
| sP0(sK6(X0)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X2,X0] :
( ~ sP2(X0)
| sP1(X0,sK6(X0))
| g_true_only(sK7(X0),sK6(X0))
| g_false_only(X2,sK6(X0))
| g_false_only(sK6(X0),X2)
| g_true_only(sK6(X0),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X2,X0] :
( ~ sP2(X0)
| sP1(X0,sK6(X0))
| g_true_only(sK6(X0),sK7(X0))
| g_false_only(X2,sK6(X0))
| g_false_only(sK6(X0),X2)
| g_true_only(sK6(X0),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0] :
( ~ sP2(X0)
| sP1(X0,sK6(X0))
| g_both(sK6(X0),X0)
| g_true_only(sK6(X0),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1)
| ~ g_true_only(X4,X1)
| ~ g_true_only(X1,X4)
| g_false_only(X2,X1)
| g_false_only(X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| ~ g_false_only(sK8(X1),X1)
| g_false_only(X2,X1)
| g_false_only(X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| ~ g_false_only(X1,sK8(X1))
| g_false_only(X2,X1)
| g_false_only(X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f49,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| g_false_only(X1,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f60,plain,
! [X10,X11,X12] :
( sP3
| sP2(X10)
| g_true_only(sK16(X11),X11)
| g_false_only(X12,X11)
| g_false_only(X11,X12)
| ~ g_both(X11,X12)
| ~ g_both(X11,X10) ),
inference(cnf_transformation,[],[f26]) ).
fof(f61,plain,
! [X10,X11,X12] :
( sP3
| sP2(X10)
| g_true_only(X11,sK16(X11))
| g_false_only(X12,X11)
| g_false_only(X11,X12)
| ~ g_both(X11,X12)
| ~ g_both(X11,X10) ),
inference(cnf_transformation,[],[f26]) ).
fof(f62,plain,
! [X1,X8] :
( g_true_only(sK15(X1),X1)
| g_false_only(X8,X1)
| g_false_only(X1,X8)
| ~ g_both(X8,X1)
| ~ g_false_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f63,plain,
! [X1,X8] :
( g_true_only(X1,sK15(X1))
| g_false_only(X8,X1)
| g_false_only(X1,X8)
| ~ g_both(X8,X1)
| ~ g_false_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f64,plain,
! [X1,X8] :
( g_true_only(sK15(X1),X1)
| g_false_only(X8,X1)
| g_false_only(X1,X8)
| ~ g_both(X1,X8)
| ~ g_false_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f65,plain,
! [X1,X8] :
( g_true_only(X1,sK15(X1))
| g_false_only(X8,X1)
| g_false_only(X1,X8)
| ~ g_both(X1,X8)
| ~ g_false_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f66,plain,
! [X1] :
( ~ g_false_only(sK14(X1),X1)
| ~ g_false_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f67,plain,
! [X1] :
( ~ g_false_only(X1,sK14(X1))
| ~ g_false_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f68,plain,
! [X1,X6] :
( ~ g_true_only(X6,X1)
| ~ g_true_only(X1,X6)
| ~ g_both(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f69,plain,
! [X1] :
( ~ g_false_only(sK13(X1),X1)
| ~ g_both(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f70,plain,
! [X1] :
( ~ g_false_only(X1,sK13(X1))
| ~ g_both(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f71,plain,
! [X1,X4] :
( ~ g_true_only(X4,X1)
| ~ g_true_only(X1,X4)
| ~ g_true_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f72,plain,
! [X2,X1] :
( g_true_only(sK12(X1),X1)
| g_false_only(X2,X1)
| g_false_only(X1,X2)
| ~ g_both(X2,X1)
| ~ g_true_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f73,plain,
! [X2,X1] :
( g_true_only(X1,sK12(X1))
| g_false_only(X2,X1)
| g_false_only(X1,X2)
| ~ g_both(X2,X1)
| ~ g_true_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f74,plain,
! [X2,X1] :
( g_true_only(sK12(X1),X1)
| g_false_only(X2,X1)
| g_false_only(X1,X2)
| ~ g_both(X1,X2)
| ~ g_true_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f75,plain,
! [X2,X1] :
( g_true_only(X1,sK12(X1))
| g_false_only(X2,X1)
| g_false_only(X1,X2)
| ~ g_both(X1,X2)
| ~ g_true_only(X1,sK11) ),
inference(cnf_transformation,[],[f26]) ).
fof(f76,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f77,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f78,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f79,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_true(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f80,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f81,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f82,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| ~ g_true(X0,X1)
| g_both(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f83,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f84,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f85,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_false(X0,X1)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_50,plain,
! [X0: $i] :
( g_true_only(X0,sK4)
| g_true_only(X0,sK5(X0))
| ~ sP3 ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_51,plain,
! [X0: $i] :
( g_true_only(X0,sK4)
| g_true_only(sK5(X0),X0)
| ~ sP3 ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( g_false_only(X0,sK4)
| g_false_only(X1,X0)
| g_false_only(X0,X1)
| ~ sP3 ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
! [X0: $i] :
( sP1(X0,sK6(X0))
| g_both(sK6(X0),X0)
| g_true_only(sK6(X0),X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( sP1(X0,sK6(X0))
| g_false_only(X1,sK6(X0))
| g_false_only(sK6(X0),X1)
| g_true_only(sK6(X0),X0)
| g_true_only(sK6(X0),sK7(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( sP1(X0,sK6(X0))
| g_false_only(X1,sK6(X0))
| g_false_only(sK6(X0),X1)
| g_true_only(sK6(X0),X0)
| g_true_only(sK7(X0),sK6(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_58,plain,
! [X0: $i] :
( sP0(sK6(X0))
| sP1(X0,sK6(X0))
| g_both(sK6(X0),X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( g_false_only(X2,X0)
| g_false_only(X0,X2)
| ~ sP1(X1,X0)
| ~ g_false_only(X0,sK8(X0)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( g_false_only(X2,X0)
| g_false_only(X0,X2)
| ~ sP1(X1,X0)
| ~ g_false_only(sK8(X0),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( g_false_only(X3,X0)
| g_false_only(X0,X3)
| ~ sP1(X2,X0)
| ~ g_true_only(X1,X0)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_74,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X0,sK12(X0))
| ~ g_true_only(X0,sK11)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_75,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(sK12(X0),X0)
| ~ g_true_only(X0,sK11)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_76,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X1,sK12(X1))
| ~ g_true_only(X1,sK11)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(sK12(X1),X1)
| ~ g_true_only(X1,sK11)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_78,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ g_true_only(X0,sK11)
| ~ g_true_only(X1,X0)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_79,negated_conjecture,
! [X0: $i] :
( ~ g_both(X0,sK11)
| ~ g_false_only(X0,sK13(X0)) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_80,negated_conjecture,
! [X0: $i] :
( ~ g_both(X0,sK11)
| ~ g_false_only(sK13(X0),X0) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_81,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ g_both(X0,sK11)
| ~ g_true_only(X1,X0)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_82,negated_conjecture,
! [X0: $i] :
( ~ g_false_only(X0,sK11)
| ~ g_false_only(X0,sK14(X0)) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_83,negated_conjecture,
! [X0: $i] :
( ~ g_false_only(X0,sK11)
| ~ g_false_only(sK14(X0),X0) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_84,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X0,sK15(X0))
| ~ g_false_only(X0,sK11)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_85,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(sK15(X0),X0)
| ~ g_false_only(X0,sK11)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_86,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X1,sK15(X1))
| ~ g_false_only(X1,sK11)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_87,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(sK15(X1),X1)
| ~ g_false_only(X1,sK11)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_88,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( sP3
| sP2(X1)
| g_false_only(X2,X0)
| g_false_only(X0,X2)
| g_true_only(X0,sK16(X0))
| ~ g_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_89,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( sP3
| sP2(X1)
| g_false_only(X2,X0)
| g_false_only(X0,X2)
| g_true_only(sK16(X0),X0)
| ~ g_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( g_both(X0,X1)
| g_false_only(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( g_both(X0,X1)
| ~ g_false(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| g_false_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_110,plain,
( ~ g_false_only(sK11,sK11)
| ~ g_false_only(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_111,plain,
( ~ g_false_only(sK11,sK11)
| ~ g_false_only(sK11,sK14(sK11)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_114,plain,
( g_both(sK11,sK11)
| g_false_only(sK11,sK11)
| g_true_only(sK11,sK11) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_117,plain,
( g_true(sK11,sK11)
| g_false_only(sK11,sK11)
| ~ g_false(sK11,sK11) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_122,plain,
~ g_true_only(sK11,sK11),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_129,plain,
( sP0(sK6(sK11))
| sP1(sK11,sK6(sK11))
| g_both(sK6(sK11),sK11)
| ~ sP2(sK11) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_132,plain,
( sP1(sK11,sK6(sK11))
| g_both(sK6(sK11),sK11)
| g_true_only(sK6(sK11),sK11)
| ~ sP2(sK11) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| g_false_only(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_99,c_97,c_94,c_92]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_93,c_100,c_93,c_139]) ).
tcf(c_144,plain,
( g_false(sK11,sK11)
| g_true_only(sK11,sK11) ),
inference(instantiation,[status(thm)],[c_142]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ g_false_only(X1,sK11)
| g_true_only(sK15(X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_87,c_97,c_101,c_87]) ).
tcf(c_146,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_true_only(sK15(X1),X1)
| ~ g_false_only(X1,sK11)
| ~ g_both(X0,X1) ),
inference(renaming,[status(thm)],[c_145]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ g_false_only(X1,sK11)
| g_true_only(X1,sK15(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_97,c_101,c_86]) ).
tcf(c_148,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_true_only(X1,sK15(X1))
| ~ g_false_only(X1,sK11)
| ~ g_both(X0,X1) ),
inference(renaming,[status(thm)],[c_147]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ g_false_only(X0,sK11)
| g_true_only(sK15(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_97,c_101,c_85]) ).
tcf(c_150,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_true_only(sK15(X0),X0)
| ~ g_false_only(X0,sK11)
| ~ g_both(X0,X1) ),
inference(renaming,[status(thm)],[c_149]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ g_false_only(X0,sK11)
| g_true_only(X0,sK15(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_84,c_97,c_101,c_84]) ).
tcf(c_152,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_true_only(X0,sK15(X0))
| ~ g_false_only(X0,sK11)
| ~ g_both(X0,X1) ),
inference(renaming,[status(thm)],[c_151]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ g_true_only(X1,sK11)
| g_true_only(sK12(X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_77,c_97,c_101,c_77]) ).
tcf(c_154,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_true_only(sK12(X1),X1)
| ~ g_true_only(X1,sK11)
| ~ g_both(X0,X1) ),
inference(renaming,[status(thm)],[c_153]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ g_true_only(X1,sK11)
| g_true_only(X1,sK12(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_76,c_97,c_101,c_76]) ).
tcf(c_156,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_true_only(X1,sK12(X1))
| ~ g_true_only(X1,sK11)
| ~ g_both(X0,X1) ),
inference(renaming,[status(thm)],[c_155]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ g_true_only(X0,sK11)
| g_true_only(sK12(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_75,c_97,c_101,c_75]) ).
tcf(c_158,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_true_only(sK12(X0),X0)
| ~ g_true_only(X0,sK11)
| ~ g_both(X0,X1) ),
inference(renaming,[status(thm)],[c_157]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ g_true_only(X0,sK11)
| g_true_only(X0,sK12(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_97,c_101,c_74]) ).
tcf(c_160,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_true_only(X0,sK12(X0))
| ~ g_true_only(X0,sK11)
| ~ g_both(X0,X1) ),
inference(renaming,[status(thm)],[c_159]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] :
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_101]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(renaming,[status(thm)],[c_161]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( g_true_only(X0,X1)
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_142]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1) ),
inference(renaming,[status(thm)],[c_167]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| ~ g_both(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_97]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_100,c_94,c_93,c_139]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] :
( g_false_only(X0,sK4)
| g_false_only(X1,X0)
| ~ sP3
| ~ g_true(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_52,c_162]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( g_false(X1,X0)
| g_false_only(X3,X1)
| g_false_only(X1,X3)
| ~ sP1(X2,X1)
| ~ g_true_only(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_65,c_168]) ).
tcf(c_283,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false(X1,X0)
| ~ g_true_only(X1,sK11)
| ~ g_true_only(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_78,c_168]) ).
tcf(c_284,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false(X1,X0)
| ~ g_both(X1,sK11)
| ~ g_true_only(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_81,c_168]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i] :
( ~ g_both(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(resolution,[status(thm)],[c_171,c_162]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP3
| sP2(X1)
| g_false_only(X2,X0)
| g_true_only(sK16(X0),X0)
| ~ g_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_89,c_817]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP3
| sP2(X1)
| g_false_only(X2,X0)
| g_true_only(X0,sK16(X0))
| ~ g_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_88,c_817]) ).
tcf(c_1846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP2(X1)
| g_false_only(X3,sK4)
| g_false_only(X4,X3)
| g_false_only(X2,X0)
| g_true_only(X0,sK16(X0))
| ~ g_true(X3,X4)
| ~ g_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[c_871,c_277]) ).
tcf(c_1847,plain,
( sP2(sK11)
| g_false_only(sK11,sK11)
| g_false_only(sK11,sK4)
| g_true_only(sK11,sK16(sK11))
| ~ g_true(sK11,sK11)
| ~ g_both(sK11,sK11) ),
inference(instantiation,[status(thm)],[c_1846]) ).
tcf(c_1993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP2(X1)
| g_false_only(X3,sK4)
| g_false_only(X4,X3)
| g_false_only(X2,X0)
| g_true_only(sK16(X0),X0)
| ~ g_true(X3,X4)
| ~ g_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[c_870,c_277]) ).
tcf(c_1994,plain,
( sP2(sK11)
| g_false_only(sK11,sK11)
| g_false_only(sK11,sK4)
| g_true_only(sK16(sK11),sK11)
| ~ g_true(sK11,sK11)
| ~ g_both(sK11,sK11) ),
inference(instantiation,[status(thm)],[c_1993]) ).
tcf(c_4406,plain,
! [X0: $i,X1: $i] :
( g_false_only(X0,X1)
| g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_139]) ).
tcf(c_4407,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| g_false_only(X0,X1) ),
inference(renaming,[status(thm)],[c_4406]) ).
tcf(c_4410,plain,
! [X0: $i,X1: $i] :
( g_true_only(X0,X1)
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_142]) ).
tcf(c_4411,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1) ),
inference(renaming,[status(thm)],[c_4410]) ).
tcf(c_4436,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_193]) ).
tcf(c_4518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( g_false(X3,X1)
| g_false(X1,X3)
| g_false_only(X2,X1)
| g_false_only(X1,X2)
| ~ sP1(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_280,c_4411]) ).
tcf(c_4521,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false(X1,X0)
| g_false(X0,X1)
| ~ g_true_only(X0,sK11) ),
inference(bin_hyper_res,[status(thm)],[c_283,c_4411]) ).
tcf(c_4522,negated_conjecture,
! [X0: $i,X1: $i] :
( g_false(X1,X0)
| g_false(X0,X1)
| ~ g_both(X0,sK11) ),
inference(bin_hyper_res,[status(thm)],[c_284,c_4411]) ).
tcf(c_8349,plain,
! [X0: $i] :
( g_false_only(X0,sK14(X0))
| g_true_only(sK15(X0),X0)
| ~ g_false_only(X0,sK11)
| ~ g_both(sK14(X0),X0) ),
inference(instantiation,[status(thm)],[c_146]) ).
tcf(c_8350,plain,
( g_false_only(sK11,sK14(sK11))
| g_true_only(sK15(sK11),sK11)
| ~ g_false_only(sK11,sK11)
| ~ g_both(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8349]) ).
tcf(c_8352,plain,
! [X0: $i] :
( g_false_only(X0,sK14(X0))
| g_true_only(X0,sK15(X0))
| ~ g_false_only(X0,sK11)
| ~ g_both(sK14(X0),X0) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_8353,plain,
( g_false_only(sK11,sK14(sK11))
| g_true_only(sK11,sK15(sK11))
| ~ g_false_only(sK11,sK11)
| ~ g_both(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8352]) ).
tcf(c_8357,plain,
! [X0: $i] :
( g_false_only(sK14(X0),X0)
| g_true_only(sK15(X0),X0)
| ~ g_false_only(X0,sK11)
| ~ g_both(X0,sK14(X0)) ),
inference(instantiation,[status(thm)],[c_150]) ).
tcf(c_8361,plain,
! [X0: $i] :
( g_false_only(sK14(X0),X0)
| g_true_only(X0,sK15(X0))
| ~ g_false_only(X0,sK11)
| ~ g_both(X0,sK14(X0)) ),
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_8395,plain,
! [X0: $i] :
( g_true(X0,sK14(X0))
| g_false_only(X0,sK14(X0)) ),
inference(instantiation,[status(thm)],[c_4407]) ).
tcf(c_8397,plain,
! [X0: $i] :
( g_true(sK14(X0),X0)
| g_false_only(sK14(X0),X0) ),
inference(instantiation,[status(thm)],[c_4407]) ).
tcf(c_8398,plain,
( g_true(sK14(sK11),sK11)
| g_false_only(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8397]) ).
tcf(c_8399,plain,
! [X0: $i,X1: $i] :
( g_false_only(X0,sK14(X0))
| g_false_only(sK14(X0),X0)
| ~ sP1(X1,X0)
| ~ g_false_only(X0,sK8(X0)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_8403,plain,
! [X0: $i,X1: $i] :
( g_false_only(X0,sK14(X0))
| g_false_only(sK14(X0),X0)
| ~ sP1(X1,X0)
| ~ g_false_only(sK8(X0),X0) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_8419,plain,
! [X0: $i] :
( g_both(sK14(X0),X0)
| ~ g_false(sK14(X0),X0)
| ~ g_true(sK14(X0),X0) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_8422,plain,
( g_both(sK14(sK11),sK11)
| ~ g_false(sK14(sK11),sK11)
| ~ g_true(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8419]) ).
tcf(c_8550,plain,
! [X0: $i] :
( g_false(sK14(X0),X0)
| g_true_only(sK14(X0),X0) ),
inference(instantiation,[status(thm)],[c_4411]) ).
tcf(c_8559,plain,
( g_false(sK14(sK11),sK11)
| g_true_only(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8550]) ).
tcf(c_8606,plain,
! [X0: $i] :
( ~ g_false(sK14(X0),sK12(sK14(X0)))
| ~ g_true_only(sK14(X0),sK12(sK14(X0))) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8607,plain,
( ~ g_false(sK14(sK11),sK12(sK14(sK11)))
| ~ g_true_only(sK14(sK11),sK12(sK14(sK11))) ),
inference(instantiation,[status(thm)],[c_8606]) ).
tcf(c_8608,plain,
! [X0: $i] :
( ~ g_false(sK12(sK14(X0)),sK14(X0))
| ~ g_true_only(sK12(sK14(X0)),sK14(X0)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8609,plain,
( ~ g_false(sK12(sK14(sK11)),sK14(sK11))
| ~ g_true_only(sK12(sK14(sK11)),sK14(sK11)) ),
inference(instantiation,[status(thm)],[c_8608]) ).
tcf(c_8633,plain,
( ~ g_false(sK11,sK15(sK11))
| ~ g_true_only(sK11,sK15(sK11)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8634,plain,
( ~ g_false(sK15(sK11),sK11)
| ~ g_true_only(sK15(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8640,plain,
! [X0: $i] :
( ~ g_false(sK15(X0),X0)
| ~ g_true_only(sK15(X0),X0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8647,plain,
! [X0: $i] :
( ~ g_false(X0,sK15(X0))
| ~ g_true_only(X0,sK15(X0)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8700,plain,
! [X0: $i] :
( g_false(sK14(X0),sK12(sK14(X0)))
| g_false(sK12(sK14(X0)),sK14(X0))
| ~ g_true_only(sK14(X0),sK11) ),
inference(instantiation,[status(thm)],[c_4521]) ).
tcf(c_8701,plain,
( g_false(sK14(sK11),sK12(sK14(sK11)))
| g_false(sK12(sK14(sK11)),sK14(sK11))
| ~ g_true_only(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8700]) ).
tcf(c_8740,plain,
! [X0: $i] :
( ~ g_false(X0,sK16(X0))
| ~ g_true_only(X0,sK16(X0)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8741,plain,
( ~ g_false(sK11,sK16(sK11))
| ~ g_true_only(sK11,sK16(sK11)) ),
inference(instantiation,[status(thm)],[c_8740]) ).
tcf(c_8742,plain,
! [X0: $i] :
( ~ g_false(sK16(X0),X0)
| ~ g_true_only(sK16(X0),X0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8743,plain,
( ~ g_false(sK16(sK11),sK11)
| ~ g_true_only(sK16(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8742]) ).
tcf(c_8799,plain,
! [X0: $i] :
( ~ g_both(sK6(X0),sK11)
| ~ g_false_only(sK6(X0),sK13(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_8801,plain,
( ~ g_both(sK6(sK11),sK11)
| ~ g_false_only(sK6(sK11),sK13(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_8799]) ).
tcf(c_8803,plain,
! [X0: $i] :
( g_false_only(sK6(X0),sK14(sK6(X0)))
| g_true_only(sK15(sK6(X0)),sK6(X0))
| ~ g_false_only(sK6(X0),sK11)
| ~ g_both(sK14(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_8349]) ).
tcf(c_8804,plain,
! [X0: $i] :
( g_false_only(sK14(sK6(X0)),sK6(X0))
| g_true_only(sK15(sK6(X0)),sK6(X0))
| ~ g_false_only(sK6(X0),sK11)
| ~ g_both(sK6(X0),sK14(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_8357]) ).
tcf(c_8807,plain,
( g_false_only(sK14(sK6(sK11)),sK6(sK11))
| g_true_only(sK15(sK6(sK11)),sK6(sK11))
| ~ g_false_only(sK6(sK11),sK11)
| ~ g_both(sK6(sK11),sK14(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_8804]) ).
tcf(c_8808,plain,
( g_false_only(sK6(sK11),sK14(sK6(sK11)))
| g_true_only(sK15(sK6(sK11)),sK6(sK11))
| ~ g_false_only(sK6(sK11),sK11)
| ~ g_both(sK14(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_8803]) ).
tcf(c_8811,plain,
! [X0: $i] :
( ~ g_false_only(sK6(X0),sK11)
| ~ g_false_only(sK6(X0),sK14(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_8813,plain,
( ~ g_false_only(sK6(sK11),sK11)
| ~ g_false_only(sK6(sK11),sK14(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_8811]) ).
tcf(c_8845,plain,
! [X0: $i] :
( g_false_only(sK14(sK6(X0)),sK6(X0))
| g_true_only(sK6(X0),sK15(sK6(X0)))
| ~ g_false_only(sK6(X0),sK11)
| ~ g_both(sK6(X0),sK14(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_8361]) ).
tcf(c_8846,plain,
! [X0: $i] :
( g_false_only(sK6(X0),sK14(sK6(X0)))
| g_true_only(sK6(X0),sK15(sK6(X0)))
| ~ g_false_only(sK6(X0),sK11)
| ~ g_both(sK14(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_8352]) ).
tcf(c_8852,plain,
( g_false_only(sK6(sK11),sK14(sK6(sK11)))
| g_true_only(sK6(sK11),sK15(sK6(sK11)))
| ~ g_false_only(sK6(sK11),sK11)
| ~ g_both(sK14(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_8846]) ).
tcf(c_8853,plain,
( g_false_only(sK14(sK6(sK11)),sK6(sK11))
| g_true_only(sK6(sK11),sK15(sK6(sK11)))
| ~ g_false_only(sK6(sK11),sK11)
| ~ g_both(sK6(sK11),sK14(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_8845]) ).
tcf(c_9247,plain,
! [X0: $i,X1: $i] :
( g_both(sK6(X0),X1)
| ~ g_false(sK6(X0),X1)
| ~ g_true(sK6(X0),X1) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_9312,plain,
! [X0: $i] :
( g_true_only(X0,sK4)
| ~ sP3
| ~ g_false(X0,sK5(X0)) ),
inference(superposition,[status(thm)],[c_50,c_95]) ).
tcf(c_9316,plain,
( g_true_only(sK11,sK4)
| ~ sP3
| ~ g_false(sK11,sK5(sK11)) ),
inference(instantiation,[status(thm)],[c_9312]) ).
tcf(c_9343,plain,
! [X0: $i] :
( g_false_only(sK6(X0),X0)
| ~ sP1(X0,sK6(X0)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_9348,plain,
( g_false_only(sK6(sK11),sK11)
| ~ sP1(sK11,sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_9343]) ).
tcf(c_9351,plain,
! [X0: $i] :
( g_false_only(sK6(X0),sK14(sK6(X0)))
| g_false_only(sK14(sK6(X0)),sK6(X0))
| ~ sP1(X0,sK6(X0))
| ~ g_false_only(sK8(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_8403]) ).
tcf(c_9352,plain,
! [X0: $i] :
( g_false_only(sK6(X0),sK14(sK6(X0)))
| g_false_only(sK14(sK6(X0)),sK6(X0))
| ~ sP1(X0,sK6(X0))
| ~ g_false_only(sK6(X0),sK8(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_8399]) ).
tcf(c_9353,plain,
( g_false_only(sK6(sK11),sK14(sK6(sK11)))
| g_false_only(sK14(sK6(sK11)),sK6(sK11))
| ~ sP1(sK11,sK6(sK11))
| ~ g_false_only(sK6(sK11),sK8(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_9352]) ).
tcf(c_9354,plain,
( g_false_only(sK6(sK11),sK14(sK6(sK11)))
| g_false_only(sK14(sK6(sK11)),sK6(sK11))
| ~ sP1(sK11,sK6(sK11))
| ~ g_false_only(sK8(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_9351]) ).
tcf(c_9361,plain,
! [X0: $i] :
( g_true_only(X0,sK4)
| ~ sP3
| ~ g_false(sK5(X0),X0) ),
inference(superposition,[status(thm)],[c_51,c_95]) ).
tcf(c_9362,plain,
! [X0: $i] :
( g_true_only(sK11,sK4)
| g_false(X0,sK5(sK11))
| g_false(sK5(sK11),X0)
| ~ sP3 ),
inference(superposition,[status(thm)],[c_51,c_4521]) ).
tcf(c_9370,plain,
( g_true_only(sK11,sK4)
| ~ sP3
| ~ g_false(sK5(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_9361]) ).
tcf(c_9371,plain,
( g_true_only(sK11,sK4)
| g_false(sK11,sK5(sK11))
| g_false(sK5(sK11),sK11)
| ~ sP3 ),
inference(instantiation,[status(thm)],[c_9362]) ).
tcf(c_9454,plain,
! [X0: $i] :
( g_both(sK14(sK6(X0)),sK6(X0))
| ~ g_false(sK14(sK6(X0)),sK6(X0))
| ~ g_true(sK14(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_8419]) ).
tcf(c_9455,plain,
( g_both(sK14(sK6(sK11)),sK6(sK11))
| ~ g_false(sK14(sK6(sK11)),sK6(sK11))
| ~ g_true(sK14(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_9454]) ).
tcf(c_9475,plain,
! [X0: $i,X1: $i] :
( g_both(X0,X1)
| g_false_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(superposition,[status(thm)],[c_4407,c_96]) ).
tcf(c_9592,plain,
! [X0: $i] :
( g_false(X0,sK16(X0))
| g_false(sK16(X0),X0)
| ~ g_both(X0,sK11) ),
inference(instantiation,[status(thm)],[c_4522]) ).
tcf(c_9594,plain,
( g_false(sK11,sK16(sK11))
| g_false(sK16(sK11),sK11)
| ~ g_both(sK11,sK11) ),
inference(instantiation,[status(thm)],[c_9592]) ).
tcf(c_9665,plain,
( g_true_only(sK11,sK4)
| ~ sP3 ),
inference(global_subsumption_just,[status(thm)],[c_9362,c_9316,c_9370,c_9371]) ).
tcf(c_9671,plain,
( ~ sP3
| ~ g_false(sK11,sK4) ),
inference(superposition,[status(thm)],[c_9665,c_95]) ).
tcf(c_9687,plain,
! [X0: $i] :
( g_both(sK6(X0),sK14(sK6(X0)))
| ~ g_false(sK6(X0),sK14(sK6(X0)))
| ~ g_true(sK6(X0),sK14(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_9247]) ).
tcf(c_9690,plain,
! [X0: $i] :
( g_true(sK6(X0),sK14(sK6(X0)))
| g_false_only(sK6(X0),sK14(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_8395]) ).
tcf(c_9691,plain,
( g_both(sK6(sK11),sK14(sK6(sK11)))
| ~ g_false(sK6(sK11),sK14(sK6(sK11)))
| ~ g_true(sK6(sK11),sK14(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_9687]) ).
tcf(c_9692,plain,
( g_true(sK6(sK11),sK14(sK6(sK11)))
| g_false_only(sK6(sK11),sK14(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_9690]) ).
tcf(c_9696,plain,
! [X0: $i] :
( ~ g_false_only(sK6(X0),sK11)
| ~ g_false_only(sK14(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_9697,plain,
( ~ g_false_only(sK6(sK11),sK11)
| ~ g_false_only(sK14(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_9696]) ).
tcf(c_9756,plain,
( g_true(sK11,sK4)
| ~ sP3 ),
inference(superposition,[status(thm)],[c_4436,c_9671]) ).
tcf(c_9772,plain,
( ~ sP3
| ~ g_false_only(sK11,sK4) ),
inference(superposition,[status(thm)],[c_9756,c_101]) ).
tcf(c_9796,plain,
! [X0: $i] :
( g_true(sK14(sK6(X0)),sK6(X0))
| g_false_only(sK14(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_8397]) ).
tcf(c_9797,plain,
( g_true(sK14(sK6(sK11)),sK6(sK11))
| g_false_only(sK14(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_9796]) ).
tcf(c_9942,plain,
! [X0: $i] :
( ~ g_both(sK6(X0),sK11)
| ~ g_false_only(sK13(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_9944,plain,
( ~ g_both(sK6(sK11),sK11)
| ~ g_false_only(sK13(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_9942]) ).
tcf(c_9994,plain,
! [X0: $i,X1: $i] :
( g_both(X0,X1)
| g_false_only(X0,X1)
| g_true_only(X0,X1) ),
inference(superposition,[status(thm)],[c_4411,c_9475]) ).
tcf(c_10051,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP3
| sP2(X2)
| g_false_only(X1,X0)
| g_false_only(X0,X2)
| g_true_only(X0,X2)
| g_true_only(X0,sK16(X0))
| ~ g_both(X0,X1) ),
inference(superposition,[status(thm)],[c_9994,c_871]) ).
tcf(c_10052,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP3
| sP2(X2)
| g_false_only(X1,X0)
| g_false_only(X0,X2)
| g_true_only(X0,X2)
| g_true_only(sK16(X0),X0)
| ~ g_both(X0,X1) ),
inference(superposition,[status(thm)],[c_9994,c_870]) ).
tcf(c_10055,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X0,X1)
| g_true_only(X0,sK12(X0))
| ~ g_true_only(X0,sK11) ),
inference(superposition,[status(thm)],[c_9994,c_160]) ).
tcf(c_10056,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X0,X1)
| g_true_only(sK12(X0),X0)
| ~ g_true_only(X0,sK11) ),
inference(superposition,[status(thm)],[c_9994,c_158]) ).
tcf(c_10057,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X1,X0)
| g_true_only(X0,sK12(X0))
| ~ g_true_only(X0,sK11) ),
inference(superposition,[status(thm)],[c_9994,c_156]) ).
tcf(c_10058,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X1,X0)
| g_true_only(sK12(X0),X0)
| ~ g_true_only(X0,sK11) ),
inference(superposition,[status(thm)],[c_9994,c_154]) ).
tcf(c_10284,plain,
! [X0: $i] :
( ~ g_false(sK6(X0),sK7(X0))
| ~ g_true_only(sK6(X0),sK7(X0)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_10285,plain,
( ~ g_false(sK6(sK11),sK7(sK11))
| ~ g_true_only(sK6(sK11),sK7(sK11)) ),
inference(instantiation,[status(thm)],[c_10284]) ).
tcf(c_10329,plain,
! [X0: $i] :
( sP1(X0,sK6(X0))
| g_true_only(sK6(X0),X0)
| g_true_only(sK7(X0),sK6(X0))
| g_false_only(sK6(X0),sK13(sK6(X0)))
| g_false_only(sK13(sK6(X0)),sK6(X0))
| ~ sP2(X0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_10330,plain,
! [X0: $i] :
( sP1(X0,sK6(X0))
| g_true_only(sK6(X0),X0)
| g_true_only(sK6(X0),sK7(X0))
| g_false_only(sK6(X0),sK13(sK6(X0)))
| g_false_only(sK13(sK6(X0)),sK6(X0))
| ~ sP2(X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_10337,plain,
( sP1(sK11,sK6(sK11))
| g_true_only(sK6(sK11),sK11)
| g_true_only(sK6(sK11),sK7(sK11))
| g_false_only(sK6(sK11),sK13(sK6(sK11)))
| g_false_only(sK13(sK6(sK11)),sK6(sK11))
| ~ sP2(sK11) ),
inference(instantiation,[status(thm)],[c_10330]) ).
tcf(c_10338,plain,
( sP1(sK11,sK6(sK11))
| g_true_only(sK6(sK11),sK11)
| g_true_only(sK7(sK11),sK6(sK11))
| g_false_only(sK6(sK11),sK13(sK6(sK11)))
| g_false_only(sK13(sK6(sK11)),sK6(sK11))
| ~ sP2(sK11) ),
inference(instantiation,[status(thm)],[c_10329]) ).
tcf(c_10380,plain,
! [X0: $i] :
( g_false(sK7(X0),sK6(X0))
| g_false(sK6(X0),sK7(X0))
| ~ g_both(sK6(X0),sK11) ),
inference(instantiation,[status(thm)],[c_4522]) ).
tcf(c_10383,plain,
( g_false(sK7(sK11),sK6(sK11))
| g_false(sK6(sK11),sK7(sK11))
| ~ g_both(sK6(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10380]) ).
tcf(c_10452,plain,
! [X0: $i] :
( ~ g_false(sK6(X0),X0)
| ~ g_true_only(sK6(X0),X0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_10453,plain,
( ~ g_false(sK6(sK11),sK11)
| ~ g_true_only(sK6(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10452]) ).
tcf(c_10455,plain,
! [X0: $i] :
( g_false_only(X0,sK6(sK11))
| g_true_only(sK6(sK11),sK12(sK6(sK11)))
| ~ g_true_only(sK6(sK11),sK11)
| ~ g_both(sK6(sK11),X0) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_10609,plain,
! [X0: $i] :
( g_false_only(sK6(sK11),X0)
| g_true_only(sK6(sK11),sK12(sK6(sK11)))
| ~ g_true_only(sK6(sK11),sK11)
| ~ g_both(X0,sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_10610,plain,
! [X0: $i] :
( g_false_only(sK6(sK11),X0)
| g_true_only(sK12(sK6(sK11)),sK6(sK11))
| ~ g_true_only(sK6(sK11),sK11)
| ~ g_both(X0,sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_10623,plain,
( ~ g_false(sK6(sK11),sK12(sK6(sK11)))
| ~ g_true_only(sK6(sK11),sK12(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_10624,plain,
( ~ g_false(sK12(sK6(sK11)),sK6(sK11))
| ~ g_true_only(sK12(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_10857,plain,
! [X0: $i] :
( g_false(sK6(X0),sK11)
| ~ g_both(sK6(X0),sK11) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_10862,plain,
( g_false(sK6(sK11),sK11)
| ~ g_both(sK6(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10857]) ).
tcf(c_10876,plain,
! [X0: $i,X1: $i] :
( g_false(X1,sK6(X0))
| g_false(sK6(X0),X1)
| ~ g_true_only(sK6(X0),sK11) ),
inference(instantiation,[status(thm)],[c_4521]) ).
tcf(c_10926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( g_false(X3,sK6(X1))
| g_false(sK6(X1),X3)
| g_false_only(X2,sK6(X1))
| g_false_only(sK6(X1),X2)
| ~ sP1(X0,sK6(X1)) ),
inference(instantiation,[status(thm)],[c_4518]) ).
tcf(c_11053,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| ~ g_true_only(X0,sK11)
| g_true_only(X0,sK12(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_10055,c_78,c_10057,c_10055]) ).
tcf(c_11054,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(X0,sK12(X0))
| ~ g_true_only(X0,sK11) ),
inference(renaming,[status(thm)],[c_11053]) ).
tcf(c_11081,plain,
! [X0: $i] :
( g_false_only(X0,sK14(X0))
| g_true_only(sK14(X0),sK12(sK14(X0)))
| ~ g_false_only(X0,sK11)
| ~ g_true_only(sK14(X0),sK11) ),
inference(superposition,[status(thm)],[c_11054,c_83]) ).
tcf(c_11195,plain,
( g_false_only(sK11,sK14(sK11))
| g_true_only(sK14(sK11),sK12(sK14(sK11)))
| ~ g_false_only(sK11,sK11)
| ~ g_true_only(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_11081]) ).
tcf(c_11383,plain,
( g_false_only(sK9(sK6(sK11)),sK6(sK11))
| g_true_only(sK6(sK11),sK12(sK6(sK11)))
| ~ g_true_only(sK6(sK11),sK11)
| ~ g_both(sK6(sK11),sK9(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_10455]) ).
tcf(c_11387,plain,
( g_false_only(sK6(sK11),sK9(sK6(sK11)))
| g_true_only(sK6(sK11),sK12(sK6(sK11)))
| ~ g_true_only(sK6(sK11),sK11)
| ~ g_both(sK9(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_10609]) ).
tcf(c_11427,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,sK6(X0))
| g_true_only(sK12(sK6(X0)),sK6(X0))
| ~ g_true_only(sK6(X0),sK11)
| ~ g_both(sK6(X0),X1) ),
inference(instantiation,[status(thm)],[c_158]) ).
tcf(c_11585,plain,
! [X0: $i] :
( ~ g_false(sK6(X0),sK15(sK6(X0)))
| ~ g_true_only(sK6(X0),sK15(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_8647]) ).
tcf(c_11586,plain,
( ~ g_false(sK6(sK11),sK15(sK6(sK11)))
| ~ g_true_only(sK6(sK11),sK15(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_11585]) ).
tcf(c_11588,plain,
! [X0: $i] :
( ~ g_false(sK15(sK6(X0)),sK6(X0))
| ~ g_true_only(sK15(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_8640]) ).
tcf(c_11589,plain,
( ~ g_false(sK15(sK6(sK11)),sK6(sK11))
| ~ g_true_only(sK15(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_11588]) ).
tcf(c_11730,plain,
! [X0: $i] :
( ~ g_false(sK6(X0),sK10(sK6(X0)))
| ~ g_true_only(sK6(X0),sK10(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_11731,plain,
( ~ g_false(sK6(sK11),sK10(sK6(sK11)))
| ~ g_true_only(sK6(sK11),sK10(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_11730]) ).
tcf(c_11732,plain,
! [X0: $i] :
( ~ g_false(sK10(sK6(X0)),sK6(X0))
| ~ g_true_only(sK10(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_11733,plain,
( ~ g_false(sK10(sK6(sK11)),sK6(sK11))
| ~ g_true_only(sK10(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_11732]) ).
tcf(c_11801,plain,
! [X0: $i,X1: $i,X2: $i] :
( g_false(X2,sK6(X1))
| g_false(sK6(X1),X2)
| g_false_only(sK6(X1),sK8(sK6(X1)))
| g_false_only(sK8(sK6(X1)),sK6(X1))
| ~ sP1(X0,sK6(X1)) ),
inference(instantiation,[status(thm)],[c_10926]) ).
tcf(c_11951,plain,
! [X0: $i] :
( g_false_only(sK9(sK6(X0)),sK6(X0))
| g_true_only(sK12(sK6(X0)),sK6(X0))
| ~ g_true_only(sK6(X0),sK11)
| ~ g_both(sK6(X0),sK9(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_11427]) ).
tcf(c_11952,plain,
( g_false_only(sK9(sK6(sK11)),sK6(sK11))
| g_true_only(sK12(sK6(sK11)),sK6(sK11))
| ~ g_true_only(sK6(sK11),sK11)
| ~ g_both(sK6(sK11),sK9(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_11951]) ).
tcf(c_11972,plain,
( g_false(sK6(sK11),sK12(sK6(sK11)))
| g_false(sK12(sK6(sK11)),sK6(sK11))
| ~ g_true_only(sK6(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10876]) ).
tcf(c_12100,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| ~ g_true_only(X0,sK11)
| g_true_only(sK12(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_10056,c_78,c_10058,c_10056]) ).
tcf(c_12101,plain,
! [X0: $i,X1: $i] :
( g_false_only(X1,X0)
| g_false_only(X0,X1)
| g_true_only(sK12(X0),X0)
| ~ g_true_only(X0,sK11) ),
inference(renaming,[status(thm)],[c_12100]) ).
tcf(c_12128,plain,
! [X0: $i] :
( g_false_only(X0,sK14(X0))
| g_true_only(sK12(sK14(X0)),sK14(X0))
| ~ g_false_only(X0,sK11)
| ~ g_true_only(sK14(X0),sK11) ),
inference(superposition,[status(thm)],[c_12101,c_83]) ).
tcf(c_12248,plain,
( g_false_only(sK11,sK14(sK11))
| g_true_only(sK12(sK14(sK11)),sK14(sK11))
| ~ g_false_only(sK11,sK11)
| ~ g_true_only(sK14(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_12128]) ).
tcf(c_12891,plain,
! [X0: $i,X1: $i] :
( g_false(sK6(X1),sK15(sK6(X1)))
| g_false(sK15(sK6(X1)),sK6(X1))
| g_false_only(sK6(X1),sK8(sK6(X1)))
| g_false_only(sK8(sK6(X1)),sK6(X1))
| ~ sP1(X0,sK6(X1)) ),
inference(instantiation,[status(thm)],[c_11801]) ).
tcf(c_12892,plain,
( g_false(sK6(sK11),sK15(sK6(sK11)))
| g_false(sK15(sK6(sK11)),sK6(sK11))
| g_false_only(sK6(sK11),sK8(sK6(sK11)))
| g_false_only(sK8(sK6(sK11)),sK6(sK11))
| ~ sP1(sK11,sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_12891]) ).
tcf(c_13112,plain,
! [X0: $i] :
( g_false(sK6(X0),sK10(sK6(X0)))
| g_false(sK10(sK6(X0)),sK6(X0))
| ~ g_true_only(sK6(X0),sK11) ),
inference(instantiation,[status(thm)],[c_10876]) ).
tcf(c_13115,plain,
( g_false(sK6(sK11),sK10(sK6(sK11)))
| g_false(sK10(sK6(sK11)),sK6(sK11))
| ~ g_true_only(sK6(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_13112]) ).
tcf(c_13143,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP3
| sP2(X2)
| g_false_only(X1,X0)
| g_false_only(X0,X2)
| g_false_only(X0,X1)
| g_true_only(X0,X2)
| g_true_only(X0,X1)
| g_true_only(X0,sK16(X0)) ),
inference(superposition,[status(thm)],[c_9994,c_10051]) ).
tcf(c_13152,plain,
( sP3
| sP2(sK11)
| g_false_only(sK11,sK11)
| g_true_only(sK11,sK11)
| g_true_only(sK11,sK16(sK11)) ),
inference(instantiation,[status(thm)],[c_13143]) ).
tcf(c_13306,plain,
( g_false_only(sK6(sK11),sK9(sK6(sK11)))
| g_true_only(sK12(sK6(sK11)),sK6(sK11))
| ~ g_true_only(sK6(sK11),sK11)
| ~ g_both(sK9(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_10610]) ).
tcf(c_13394,plain,
( ~ g_false(sK7(sK11),sK6(sK11))
| ~ g_true_only(sK7(sK11),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_13935,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP3
| sP2(X2)
| g_false_only(X1,X0)
| g_false_only(X0,X2)
| g_false_only(X0,X1)
| g_true_only(X0,X2)
| g_true_only(X0,X1)
| g_true_only(sK16(X0),X0) ),
inference(superposition,[status(thm)],[c_9994,c_10052]) ).
tcf(c_13944,plain,
( sP3
| sP2(sK11)
| g_false_only(sK11,sK11)
| g_true_only(sK11,sK11)
| g_true_only(sK16(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_13935]) ).
tcf(c_14474,plain,
! [X0: $i,X1: $i] :
( g_false(sK6(X1),sK14(sK6(X1)))
| g_false(sK14(sK6(X1)),sK6(X1))
| g_false_only(sK6(X1),sK8(sK6(X1)))
| g_false_only(sK8(sK6(X1)),sK6(X1))
| ~ sP1(X0,sK6(X1)) ),
inference(instantiation,[status(thm)],[c_11801]) ).
tcf(c_14480,plain,
( g_false(sK6(sK11),sK14(sK6(sK11)))
| g_false(sK14(sK6(sK11)),sK6(sK11))
| g_false_only(sK6(sK11),sK8(sK6(sK11)))
| g_false_only(sK8(sK6(sK11)),sK6(sK11))
| ~ sP1(sK11,sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_14474]) ).
tcf(c_15788,plain,
( g_false(sK11,sK15(sK11))
| g_false(sK15(sK11),sK11)
| ~ g_true_only(sK15(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_4521]) ).
fof(f9,definition,
! [X14] :
( ~ sP0(X14)
| ? [X17] :
( g_true_only(X17,X14)
& g_true_only(X14,X17) )
| ( ! [X16] :
( ~ g_true_only(X16,X14)
| ~ g_true_only(X14,X16) )
& ? [X15] :
( ~ g_false_only(X15,X14)
& ~ g_false_only(X14,X15)
& ( g_both(X15,X14)
| g_both(X14,X15) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,definition,
! [X10,X14] :
( ~ sP1(X10,X14)
| ( ( ( ! [X22] :
( ~ g_true_only(X22,X14)
| ~ g_true_only(X14,X22) )
& ? [X21] :
( ~ g_false_only(X21,X14)
& ~ g_false_only(X14,X21)
& ( g_both(X21,X14)
| g_both(X14,X21) ) ) )
| ! [X20] :
( g_false_only(X20,X14)
| g_false_only(X14,X20) ) )
& g_false_only(X14,X10) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f11,definition,
! [X10] :
( ~ sP2(X10)
| ? [X14] :
( sP1(X10,X14)
| ( ( ? [X19] :
( g_true_only(X19,X14)
& g_true_only(X14,X19) )
| ! [X18] :
( g_false_only(X18,X14)
| g_false_only(X14,X18) ) )
& g_both(X14,X10) )
| ( sP0(X14)
& g_true_only(X14,X10) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f12,definition,
( ~ sP3
| ? [X23] :
! [X24] :
( ( ? [X26] :
( g_true_only(X26,X24)
& g_true_only(X24,X26) )
& g_false_only(X24,X23) )
| ( ! [X25] :
( g_false_only(X25,X24)
| g_false_only(X24,X25) )
& g_true_only(X24,X23) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f13,plain,
( ( sP3
| ! [X10] :
( sP2(X10)
| ! [X11] :
( ? [X13] :
( g_true_only(X13,X11)
& g_true_only(X11,X13) )
| ! [X12] :
( g_false_only(X12,X11)
| g_false_only(X11,X12)
| ( ~ g_both(X12,X11)
& ~ g_both(X11,X12) ) )
| ~ g_both(X11,X10) ) ) )
& ? [X0] :
! [X1] :
( ( ( ( ? [X9] :
( g_true_only(X9,X1)
& g_true_only(X1,X9) )
| ! [X8] :
( g_false_only(X8,X1)
| g_false_only(X1,X8)
| ( ~ g_both(X8,X1)
& ~ g_both(X1,X8) ) ) )
& ? [X7] :
( ~ g_false_only(X7,X1)
& ~ g_false_only(X1,X7) ) )
| ~ g_false_only(X1,X0) )
& ( ( ! [X6] :
( ~ g_true_only(X6,X1)
| ~ g_true_only(X1,X6) )
& ? [X5] :
( ~ g_false_only(X5,X1)
& ~ g_false_only(X1,X5) ) )
| ~ g_both(X1,X0) )
& ( ( ! [X4] :
( ~ g_true_only(X4,X1)
| ~ g_true_only(X1,X4) )
& ( ? [X3] :
( g_true_only(X3,X1)
& g_true_only(X1,X3) )
| ! [X2] :
( g_false_only(X2,X1)
| g_false_only(X1,X2)
| ( ~ g_both(X2,X1)
& ~ g_both(X1,X2) ) ) ) )
| ~ g_true_only(X1,X0) ) ) ),
inference(definition_folding,[],[f8,f12,f11,f10,f9]) ).
fof(f23,plain,
! [X14] :
( ~ sP0(X14)
| ? [X17] :
( g_true_only(X17,X14)
& g_true_only(X14,X17) )
| ( ! [X16] :
( ~ g_true_only(X16,X14)
| ~ g_true_only(X14,X16) )
& ? [X15] :
( ~ g_false_only(X15,X14)
& ~ g_false_only(X14,X15)
& ( g_both(X15,X14)
| g_both(X14,X15) ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f24,plain,
! [X0] :
( ~ sP0(X0)
| ? [X3] :
( g_true_only(X3,X0)
& g_true_only(X0,X3) )
| ( ! [X2] :
( ~ g_true_only(X2,X0)
| ~ g_true_only(X0,X2) )
& ? [X1] :
( ~ g_false_only(X1,X0)
& ~ g_false_only(X0,X1)
& ( g_both(X1,X0)
| g_both(X0,X1) ) ) ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ sP0(X0)
| ( g_true_only(sK10(X0),X0)
& g_true_only(X0,sK10(X0)) )
| ( ! [X2] :
( ~ g_true_only(X2,X0)
| ~ g_true_only(X0,X2) )
& ~ g_false_only(sK9(X0),X0)
& ~ g_false_only(X0,sK9(X0))
& ( g_both(sK9(X0),X0)
| g_both(X0,sK9(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X1,sK9(X0)),skolemize(X3,sK10(X0))],[f24]) ).
fof(f52,plain,
! [X0] :
( ~ sP0(X0)
| g_true_only(sK10(X0),X0)
| ~ g_false_only(sK9(X0),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f53,plain,
! [X0] :
( ~ sP0(X0)
| g_true_only(X0,sK10(X0))
| ~ g_false_only(sK9(X0),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f54,plain,
! [X0] :
( ~ sP0(X0)
| g_true_only(sK10(X0),X0)
| ~ g_false_only(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f55,plain,
! [X0] :
( ~ sP0(X0)
| g_true_only(X0,sK10(X0))
| ~ g_false_only(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
! [X0] :
( ~ sP0(X0)
| g_true_only(sK10(X0),X0)
| g_both(sK9(X0),X0)
| g_both(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f57,plain,
! [X0] :
( ~ sP0(X0)
| g_true_only(X0,sK10(X0))
| g_both(sK9(X0),X0)
| g_both(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_66,plain,
! [X0: $i] :
( g_both(X0,sK9(X0))
| g_both(sK9(X0),X0)
| g_true_only(X0,sK10(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_67,plain,
! [X0: $i] :
( g_both(X0,sK9(X0))
| g_both(sK9(X0),X0)
| g_true_only(sK10(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_68,plain,
! [X0: $i] :
( g_true_only(X0,sK10(X0))
| ~ sP0(X0)
| ~ g_false_only(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_69,plain,
! [X0: $i] :
( g_true_only(sK10(X0),X0)
| ~ sP0(X0)
| ~ g_false_only(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_70,plain,
! [X0: $i] :
( g_true_only(X0,sK10(X0))
| ~ sP0(X0)
| ~ g_false_only(sK9(X0),X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_71,plain,
! [X0: $i] :
( g_true_only(sK10(X0),X0)
| ~ sP0(X0)
| ~ g_false_only(sK9(X0),X0) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_10342,plain,
! [X0: $i] :
( g_both(sK6(X0),sK9(sK6(X0)))
| g_both(sK9(sK6(X0)),sK6(X0))
| g_true_only(sK10(sK6(X0)),sK6(X0))
| ~ sP0(sK6(X0)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_10343,plain,
! [X0: $i] :
( g_both(sK6(X0),sK9(sK6(X0)))
| g_both(sK9(sK6(X0)),sK6(X0))
| g_true_only(sK6(X0),sK10(sK6(X0)))
| ~ sP0(sK6(X0)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_10344,plain,
! [X0: $i] :
( g_true_only(sK10(sK6(X0)),sK6(X0))
| ~ sP0(sK6(X0))
| ~ g_false_only(sK9(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_10345,plain,
! [X0: $i] :
( g_true_only(sK6(X0),sK10(sK6(X0)))
| ~ sP0(sK6(X0))
| ~ g_false_only(sK9(sK6(X0)),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_10346,plain,
! [X0: $i] :
( g_true_only(sK10(sK6(X0)),sK6(X0))
| ~ sP0(sK6(X0))
| ~ g_false_only(sK6(X0),sK9(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_10347,plain,
! [X0: $i] :
( g_true_only(sK6(X0),sK10(sK6(X0)))
| ~ sP0(sK6(X0))
| ~ g_false_only(sK6(X0),sK9(sK6(X0))) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_10348,plain,
( g_true_only(sK6(sK11),sK10(sK6(sK11)))
| ~ sP0(sK6(sK11))
| ~ g_false_only(sK6(sK11),sK9(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_10347]) ).
tcf(c_10349,plain,
( g_true_only(sK10(sK6(sK11)),sK6(sK11))
| ~ sP0(sK6(sK11))
| ~ g_false_only(sK6(sK11),sK9(sK6(sK11))) ),
inference(instantiation,[status(thm)],[c_10346]) ).
tcf(c_10350,plain,
( g_true_only(sK6(sK11),sK10(sK6(sK11)))
| ~ sP0(sK6(sK11))
| ~ g_false_only(sK9(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_10345]) ).
tcf(c_10351,plain,
( g_true_only(sK10(sK6(sK11)),sK6(sK11))
| ~ sP0(sK6(sK11))
| ~ g_false_only(sK9(sK6(sK11)),sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_10344]) ).
tcf(c_10352,plain,
( g_both(sK6(sK11),sK9(sK6(sK11)))
| g_both(sK9(sK6(sK11)),sK6(sK11))
| g_true_only(sK6(sK11),sK10(sK6(sK11)))
| ~ sP0(sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_10343]) ).
tcf(c_10353,plain,
( g_both(sK6(sK11),sK9(sK6(sK11)))
| g_both(sK9(sK6(sK11)),sK6(sK11))
| g_true_only(sK10(sK6(sK11)),sK6(sK11))
| ~ sP0(sK6(sK11)) ),
inference(instantiation,[status(thm)],[c_10342]) ).
tcf(c_17944,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15788,c_14480,c_13944,c_13394,c_13306,c_13152,c_13115,c_12892,c_12248,c_11972,c_11952,c_11733,c_11731,c_11589,c_11586,c_11387,c_11383,c_11195,c_10862,c_10624,c_10623,c_10453,c_10383,c_10353,c_10352,c_10351,c_10350,c_10349,c_10348,c_10338,c_10337,c_10285,c_9944,c_9797,c_9772,c_9697,c_9692,c_9691,c_9594,c_9455,c_9354,c_9353,c_9348,c_8853,c_8852,c_8813,c_8808,c_8807,c_8801,c_8743,c_8741,c_8701,c_8634,c_8633,c_8609,c_8607,c_8559,c_8422,c_8398,c_8353,c_8350,c_1994,c_1847,c_144,c_132,c_129,c_122,c_117,c_114,c_111,c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO604+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 03:17:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 6.02/1.65 % SZS status Started for theBenchmark.p
% 6.02/1.65 % SZS status Theorem for theBenchmark.p
% 6.02/1.65
% 6.02/1.65 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.02/1.65
% 6.02/1.65 % ------ iProver source info
% 6.02/1.65
% 6.02/1.65 % git: date: 2026-07-19 20:42:38 +0200
% 6.02/1.65 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.02/1.65 % git: non_committed_changes: false
% 6.02/1.65
% 6.02/1.65 % ------ Parsing...
% 6.02/1.65 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.02/1.65
% 6.02/1.65 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.02/1.65
% 6.02/1.65 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.02/1.65 % ------ Proving...
% 6.02/1.65 % ------ Problem Properties
% 6.02/1.65
% 6.02/1.65 %
% 6.02/1.65 % clauses 51
% 6.02/1.65 % conjectures 14
% 6.02/1.65 % EPR 14
% 6.02/1.65 % Horn 14
% 6.02/1.65 % unary 0
% 6.02/1.65 % binary 12
% 6.02/1.65 % lits 188
% 6.02/1.65 % lits eq 0
% 6.02/1.65 % fd_pure 0
% 6.02/1.65 % fd_pseudo 0
% 6.02/1.66 % fd_cond 0
% 6.02/1.66 % fd_pseudo_cond 0
% 6.02/1.66 % AC symbols 0
% 6.02/1.66
% 6.02/1.66 % ------ Schedule dynamic 5 is on
% 6.02/1.66
% 6.02/1.66 % ------ no equalities: superposition off
% 6.02/1.66
% 6.02/1.66 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.02/1.66
% 6.02/1.66
% 6.02/1.66 % ------
% 6.02/1.66 % Current options:
% 6.02/1.66 % ------
% 6.02/1.66
% 6.02/1.66
% 6.02/1.66 %
% 6.02/1.66
% 6.02/1.66 % ------ Proving...
% 6.02/1.66 %
% 6.02/1.66
% 6.02/1.66 % SZS status Theorem for theBenchmark.p
% 6.02/1.66
% 6.02/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.02/1.67
% 6.02/1.67
%------------------------------------------------------------------------------