TSTP Solution File: SYO605+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SYO605+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:38:28 EDT 2024
% Result : Theorem 9.80s 2.15s
% Output : CNFRefutation 9.80s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f103)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ~ ? [X1] :
! [X0] :
? [X2] :
( ( ( g_both(X2,X1)
| g_false_only(X2,X1) )
& g_false_only(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_false_only(X2,X1) )
& g_both(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_both(X2,X1) )
& g_true_only(X2,X0) ) )
& ? [X1] :
( ~ ? [X0] :
! [X2] :
( ( g_true_only(X2,X1)
& g_false_only(X2,X0) )
| ( g_false_only(X2,X1)
& g_true_only(X2,X0) ) )
& ? [X0] :
( ~ ? [X2] :
( ( ( g_both(X2,X1)
| g_false_only(X2,X1) )
& g_false_only(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_false_only(X2,X1) )
& g_both(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_both(X2,X1) )
& g_true_only(X2,X0) ) )
& ? [X2] :
( g_both(X2,X1)
& g_both(X2,X0) ) ) )
& ~ ? [X0] :
! [X1] :
( ( g_false_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_true_only(X1,X1)
& g_true_only(X1,X0) ) )
& ? [X0] :
( ~ ? [X1] :
( ( ( g_both(X1,X1)
| g_true_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_true_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
& ? [X1] :
( g_both(X1,X1)
& g_both(X1,X0) ) ) )
| ? [X1] :
! [X0] :
? [X2] :
( ( ( g_both(X2,X1)
| g_false_only(X2,X1) )
& g_false_only(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_false_only(X2,X1) )
& g_both(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_both(X2,X1) )
& g_true_only(X2,X0) ) )
| ! [X0] :
? [X1] :
( ( ( g_both(X1,X1)
| g_true_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_true_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nc4) ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [X1] :
! [X0] :
? [X2] :
( ( ( g_both(X2,X1)
| g_false_only(X2,X1) )
& g_false_only(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_false_only(X2,X1) )
& g_both(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_both(X2,X1) )
& g_true_only(X2,X0) ) )
& ? [X1] :
( ~ ? [X0] :
! [X2] :
( ( g_true_only(X2,X1)
& g_false_only(X2,X0) )
| ( g_false_only(X2,X1)
& g_true_only(X2,X0) ) )
& ? [X0] :
( ~ ? [X2] :
( ( ( g_both(X2,X1)
| g_false_only(X2,X1) )
& g_false_only(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_false_only(X2,X1) )
& g_both(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_both(X2,X1) )
& g_true_only(X2,X0) ) )
& ? [X2] :
( g_both(X2,X1)
& g_both(X2,X0) ) ) )
& ~ ? [X0] :
! [X1] :
( ( g_false_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_true_only(X1,X1)
& g_true_only(X1,X0) ) )
& ? [X0] :
( ~ ? [X1] :
( ( ( g_both(X1,X1)
| g_true_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_true_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
& ? [X1] :
( g_both(X1,X1)
& g_both(X1,X0) ) ) )
| ? [X1] :
! [X0] :
? [X2] :
( ( ( g_both(X2,X1)
| g_false_only(X2,X1) )
& g_false_only(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_false_only(X2,X1) )
& g_both(X2,X0) )
| ( ( g_true_only(X2,X1)
| g_both(X2,X1) )
& g_true_only(X2,X0) ) )
| ! [X0] :
? [X1] :
( ( ( g_both(X1,X1)
| g_true_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_true_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f3,axiom,
! [X3,X4] :
( g_true_only(X3,X4)
<=> ( ~ g_false(X3,X4)
& g_true(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',true_only_g) ).
fof(f4,axiom,
! [X3,X4] :
( g_both(X3,X4)
<=> ( g_false(X3,X4)
& g_true(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',both_g) ).
fof(f5,axiom,
! [X3,X4] :
( g_false_only(X3,X4)
<=> ( ~ g_true(X3,X4)
& g_false(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_only_g) ).
fof(f6,axiom,
! [X3,X4] :
( g_false_only(X3,X4)
| g_both(X3,X4)
| g_true_only(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exhaustion_g) ).
fof(f7,plain,
~ ( ( ~ ? [X0] :
! [X1] :
? [X2] :
( ( ( g_both(X2,X0)
| g_false_only(X2,X0) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_false_only(X2,X0) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_both(X2,X0) )
& g_true_only(X2,X1) ) )
& ? [X3] :
( ~ ? [X4] :
! [X5] :
( ( g_true_only(X5,X3)
& g_false_only(X5,X4) )
| ( g_false_only(X5,X3)
& g_true_only(X5,X4) ) )
& ? [X6] :
( ~ ? [X7] :
( ( ( g_both(X7,X3)
| g_false_only(X7,X3) )
& g_false_only(X7,X6) )
| ( ( g_true_only(X7,X3)
| g_false_only(X7,X3) )
& g_both(X7,X6) )
| ( ( g_true_only(X7,X3)
| g_both(X7,X3) )
& g_true_only(X7,X6) ) )
& ? [X8] :
( g_both(X8,X3)
& g_both(X8,X6) ) ) )
& ~ ? [X9] :
! [X10] :
( ( g_false_only(X10,X10)
& g_false_only(X10,X9) )
| ( g_true_only(X10,X10)
& g_true_only(X10,X9) ) )
& ? [X11] :
( ~ ? [X12] :
( ( ( g_both(X12,X12)
| g_true_only(X12,X12) )
& g_false_only(X12,X11) )
| ( ( g_false_only(X12,X12)
| g_true_only(X12,X12) )
& g_both(X12,X11) )
| ( ( g_false_only(X12,X12)
| g_both(X12,X12) )
& g_true_only(X12,X11) ) )
& ? [X13] :
( g_both(X13,X13)
& g_both(X13,X11) ) ) )
| ? [X14] :
! [X15] :
? [X16] :
( ( ( g_both(X16,X14)
| g_false_only(X16,X14) )
& g_false_only(X16,X15) )
| ( ( g_true_only(X16,X14)
| g_false_only(X16,X14) )
& g_both(X16,X15) )
| ( ( g_true_only(X16,X14)
| g_both(X16,X14) )
& g_true_only(X16,X15) ) )
| ! [X17] :
? [X18] :
( ( ( g_both(X18,X18)
| g_true_only(X18,X18) )
& g_false_only(X18,X17) )
| ( ( g_false_only(X18,X18)
| g_true_only(X18,X18) )
& g_both(X18,X17) )
| ( ( g_false_only(X18,X18)
| g_both(X18,X18) )
& g_true_only(X18,X17) ) ) ),
inference(rectify,[],[f2]) ).
fof(f8,plain,
! [X0,X1] :
( g_true_only(X0,X1)
<=> ( ~ g_false(X0,X1)
& g_true(X0,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f9,plain,
! [X0,X1] :
( g_both(X0,X1)
<=> ( g_false(X0,X1)
& g_true(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f10,plain,
! [X0,X1] :
( g_false_only(X0,X1)
<=> ( ~ g_true(X0,X1)
& g_false(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f11,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(rectify,[],[f6]) ).
fof(f12,plain,
( ( ? [X0] :
! [X1] :
? [X2] :
( ( ( g_both(X2,X0)
| g_false_only(X2,X0) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_false_only(X2,X0) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_both(X2,X0) )
& g_true_only(X2,X1) ) )
| ! [X3] :
( ? [X4] :
! [X5] :
( ( g_true_only(X5,X3)
& g_false_only(X5,X4) )
| ( g_false_only(X5,X3)
& g_true_only(X5,X4) ) )
| ! [X6] :
( ? [X7] :
( ( ( g_both(X7,X3)
| g_false_only(X7,X3) )
& g_false_only(X7,X6) )
| ( ( g_true_only(X7,X3)
| g_false_only(X7,X3) )
& g_both(X7,X6) )
| ( ( g_true_only(X7,X3)
| g_both(X7,X3) )
& g_true_only(X7,X6) ) )
| ! [X8] :
( ~ g_both(X8,X3)
| ~ g_both(X8,X6) ) ) )
| ? [X9] :
! [X10] :
( ( g_false_only(X10,X10)
& g_false_only(X10,X9) )
| ( g_true_only(X10,X10)
& g_true_only(X10,X9) ) )
| ! [X11] :
( ? [X12] :
( ( ( g_both(X12,X12)
| g_true_only(X12,X12) )
& g_false_only(X12,X11) )
| ( ( g_false_only(X12,X12)
| g_true_only(X12,X12) )
& g_both(X12,X11) )
| ( ( g_false_only(X12,X12)
| g_both(X12,X12) )
& g_true_only(X12,X11) ) )
| ! [X13] :
( ~ g_both(X13,X13)
| ~ g_both(X13,X11) ) ) )
& ! [X14] :
? [X15] :
! [X16] :
( ( ( ~ g_both(X16,X14)
& ~ g_false_only(X16,X14) )
| ~ g_false_only(X16,X15) )
& ( ( ~ g_true_only(X16,X14)
& ~ g_false_only(X16,X14) )
| ~ g_both(X16,X15) )
& ( ( ~ g_true_only(X16,X14)
& ~ g_both(X16,X14) )
| ~ g_true_only(X16,X15) ) )
& ? [X17] :
! [X18] :
( ( ( ~ g_both(X18,X18)
& ~ g_true_only(X18,X18) )
| ~ g_false_only(X18,X17) )
& ( ( ~ g_false_only(X18,X18)
& ~ g_true_only(X18,X18) )
| ~ g_both(X18,X17) )
& ( ( ~ g_false_only(X18,X18)
& ~ g_both(X18,X18) )
| ~ g_true_only(X18,X17) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
! [X3] :
( ! [X6] :
( ? [X7] :
( ( ( g_both(X7,X3)
| g_false_only(X7,X3) )
& g_false_only(X7,X6) )
| ( ( g_true_only(X7,X3)
| g_false_only(X7,X3) )
& g_both(X7,X6) )
| ( ( g_true_only(X7,X3)
| g_both(X7,X3) )
& g_true_only(X7,X6) ) )
| ! [X8] :
( ~ g_both(X8,X3)
| ~ g_both(X8,X6) ) )
| ~ sP0(X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f14,plain,
( ! [X11] :
( ? [X12] :
( ( ( g_both(X12,X12)
| g_true_only(X12,X12) )
& g_false_only(X12,X11) )
| ( ( g_false_only(X12,X12)
| g_true_only(X12,X12) )
& g_both(X12,X11) )
| ( ( g_false_only(X12,X12)
| g_both(X12,X12) )
& g_true_only(X12,X11) ) )
| ! [X13] :
( ~ g_both(X13,X13)
| ~ g_both(X13,X11) ) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f15,plain,
( ? [X0] :
! [X1] :
? [X2] :
( ( ( g_both(X2,X0)
| g_false_only(X2,X0) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_false_only(X2,X0) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_both(X2,X0) )
& g_true_only(X2,X1) ) )
| ~ sP2 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f16,plain,
( ? [X9] :
! [X10] :
( ( g_false_only(X10,X10)
& g_false_only(X10,X9) )
| ( g_true_only(X10,X10)
& g_true_only(X10,X9) ) )
| ~ sP3 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f17,plain,
( ( sP2
| ! [X3] :
( ? [X4] :
! [X5] :
( ( g_true_only(X5,X3)
& g_false_only(X5,X4) )
| ( g_false_only(X5,X3)
& g_true_only(X5,X4) ) )
| sP0(X3) )
| sP3
| sP1 )
& ! [X14] :
? [X15] :
! [X16] :
( ( ( ~ g_both(X16,X14)
& ~ g_false_only(X16,X14) )
| ~ g_false_only(X16,X15) )
& ( ( ~ g_true_only(X16,X14)
& ~ g_false_only(X16,X14) )
| ~ g_both(X16,X15) )
& ( ( ~ g_true_only(X16,X14)
& ~ g_both(X16,X14) )
| ~ g_true_only(X16,X15) ) )
& ? [X17] :
! [X18] :
( ( ( ~ g_both(X18,X18)
& ~ g_true_only(X18,X18) )
| ~ g_false_only(X18,X17) )
& ( ( ~ g_false_only(X18,X18)
& ~ g_true_only(X18,X18) )
| ~ g_both(X18,X17) )
& ( ( ~ g_false_only(X18,X18)
& ~ g_both(X18,X18) )
| ~ g_true_only(X18,X17) ) ) ),
inference(definition_folding,[],[f12,f16,f15,f14,f13]) ).
fof(f18,plain,
( ? [X9] :
! [X10] :
( ( g_false_only(X10,X10)
& g_false_only(X10,X9) )
| ( g_true_only(X10,X10)
& g_true_only(X10,X9) ) )
| ~ sP3 ),
inference(nnf_transformation,[],[f16]) ).
fof(f19,plain,
( ? [X0] :
! [X1] :
( ( g_false_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_true_only(X1,X1)
& g_true_only(X1,X0) ) )
| ~ sP3 ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
( ? [X0] :
! [X1] :
( ( g_false_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_true_only(X1,X1)
& g_true_only(X1,X0) ) )
=> ! [X1] :
( ( g_false_only(X1,X1)
& g_false_only(X1,sK4) )
| ( g_true_only(X1,X1)
& g_true_only(X1,sK4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
( ! [X1] :
( ( g_false_only(X1,X1)
& g_false_only(X1,sK4) )
| ( g_true_only(X1,X1)
& g_true_only(X1,sK4) ) )
| ~ sP3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f20]) ).
fof(f22,plain,
( ? [X0] :
! [X1] :
? [X2] :
( ( ( g_both(X2,X0)
| g_false_only(X2,X0) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_false_only(X2,X0) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_both(X2,X0) )
& g_true_only(X2,X1) ) )
| ~ sP2 ),
inference(nnf_transformation,[],[f15]) ).
fof(f23,plain,
( ? [X0] :
! [X1] :
? [X2] :
( ( ( g_both(X2,X0)
| g_false_only(X2,X0) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_false_only(X2,X0) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_both(X2,X0) )
& g_true_only(X2,X1) ) )
=> ! [X1] :
? [X2] :
( ( ( g_both(X2,sK5)
| g_false_only(X2,sK5) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,sK5)
| g_false_only(X2,sK5) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,sK5)
| g_both(X2,sK5) )
& g_true_only(X2,X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X1] :
( ? [X2] :
( ( ( g_both(X2,sK5)
| g_false_only(X2,sK5) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,sK5)
| g_false_only(X2,sK5) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,sK5)
| g_both(X2,sK5) )
& g_true_only(X2,X1) ) )
=> ( ( ( g_both(sK6(X1),sK5)
| g_false_only(sK6(X1),sK5) )
& g_false_only(sK6(X1),X1) )
| ( ( g_true_only(sK6(X1),sK5)
| g_false_only(sK6(X1),sK5) )
& g_both(sK6(X1),X1) )
| ( ( g_true_only(sK6(X1),sK5)
| g_both(sK6(X1),sK5) )
& g_true_only(sK6(X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
( ! [X1] :
( ( ( g_both(sK6(X1),sK5)
| g_false_only(sK6(X1),sK5) )
& g_false_only(sK6(X1),X1) )
| ( ( g_true_only(sK6(X1),sK5)
| g_false_only(sK6(X1),sK5) )
& g_both(sK6(X1),X1) )
| ( ( g_true_only(sK6(X1),sK5)
| g_both(sK6(X1),sK5) )
& g_true_only(sK6(X1),X1) ) )
| ~ sP2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f22,f24,f23]) ).
fof(f26,plain,
( ! [X11] :
( ? [X12] :
( ( ( g_both(X12,X12)
| g_true_only(X12,X12) )
& g_false_only(X12,X11) )
| ( ( g_false_only(X12,X12)
| g_true_only(X12,X12) )
& g_both(X12,X11) )
| ( ( g_false_only(X12,X12)
| g_both(X12,X12) )
& g_true_only(X12,X11) ) )
| ! [X13] :
( ~ g_both(X13,X13)
| ~ g_both(X13,X11) ) )
| ~ sP1 ),
inference(nnf_transformation,[],[f14]) ).
fof(f27,plain,
( ! [X0] :
( ? [X1] :
( ( ( g_both(X1,X1)
| g_true_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_true_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
| ! [X2] :
( ~ g_both(X2,X2)
| ~ g_both(X2,X0) ) )
| ~ sP1 ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0] :
( ? [X1] :
( ( ( g_both(X1,X1)
| g_true_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_true_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_false_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
=> ( ( ( g_both(sK7(X0),sK7(X0))
| g_true_only(sK7(X0),sK7(X0)) )
& g_false_only(sK7(X0),X0) )
| ( ( g_false_only(sK7(X0),sK7(X0))
| g_true_only(sK7(X0),sK7(X0)) )
& g_both(sK7(X0),X0) )
| ( ( g_false_only(sK7(X0),sK7(X0))
| g_both(sK7(X0),sK7(X0)) )
& g_true_only(sK7(X0),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( ! [X0] :
( ( ( g_both(sK7(X0),sK7(X0))
| g_true_only(sK7(X0),sK7(X0)) )
& g_false_only(sK7(X0),X0) )
| ( ( g_false_only(sK7(X0),sK7(X0))
| g_true_only(sK7(X0),sK7(X0)) )
& g_both(sK7(X0),X0) )
| ( ( g_false_only(sK7(X0),sK7(X0))
| g_both(sK7(X0),sK7(X0)) )
& g_true_only(sK7(X0),X0) )
| ! [X2] :
( ~ g_both(X2,X2)
| ~ g_both(X2,X0) ) )
| ~ sP1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f27,f28]) ).
fof(f30,plain,
! [X3] :
( ! [X6] :
( ? [X7] :
( ( ( g_both(X7,X3)
| g_false_only(X7,X3) )
& g_false_only(X7,X6) )
| ( ( g_true_only(X7,X3)
| g_false_only(X7,X3) )
& g_both(X7,X6) )
| ( ( g_true_only(X7,X3)
| g_both(X7,X3) )
& g_true_only(X7,X6) ) )
| ! [X8] :
( ~ g_both(X8,X3)
| ~ g_both(X8,X6) ) )
| ~ sP0(X3) ),
inference(nnf_transformation,[],[f13]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( ( ( g_both(X2,X0)
| g_false_only(X2,X0) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_false_only(X2,X0) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_both(X2,X0) )
& g_true_only(X2,X1) ) )
| ! [X3] :
( ~ g_both(X3,X0)
| ~ g_both(X3,X1) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
( ( ( g_both(X2,X0)
| g_false_only(X2,X0) )
& g_false_only(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_false_only(X2,X0) )
& g_both(X2,X1) )
| ( ( g_true_only(X2,X0)
| g_both(X2,X0) )
& g_true_only(X2,X1) ) )
=> ( ( ( g_both(sK8(X0,X1),X0)
| g_false_only(sK8(X0,X1),X0) )
& g_false_only(sK8(X0,X1),X1) )
| ( ( g_true_only(sK8(X0,X1),X0)
| g_false_only(sK8(X0,X1),X0) )
& g_both(sK8(X0,X1),X1) )
| ( ( g_true_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X0) )
& g_true_only(sK8(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ( ( g_both(sK8(X0,X1),X0)
| g_false_only(sK8(X0,X1),X0) )
& g_false_only(sK8(X0,X1),X1) )
| ( ( g_true_only(sK8(X0,X1),X0)
| g_false_only(sK8(X0,X1),X0) )
& g_both(sK8(X0,X1),X1) )
| ( ( g_true_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X0) )
& g_true_only(sK8(X0,X1),X1) )
| ! [X3] :
( ~ g_both(X3,X0)
| ~ g_both(X3,X1) ) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f31,f32]) ).
fof(f34,plain,
( ( sP2
| ! [X0] :
( ? [X1] :
! [X2] :
( ( g_true_only(X2,X0)
& g_false_only(X2,X1) )
| ( g_false_only(X2,X0)
& g_true_only(X2,X1) ) )
| sP0(X0) )
| sP3
| sP1 )
& ! [X3] :
? [X4] :
! [X5] :
( ( ( ~ g_both(X5,X3)
& ~ g_false_only(X5,X3) )
| ~ g_false_only(X5,X4) )
& ( ( ~ g_true_only(X5,X3)
& ~ g_false_only(X5,X3) )
| ~ g_both(X5,X4) )
& ( ( ~ g_true_only(X5,X3)
& ~ g_both(X5,X3) )
| ~ g_true_only(X5,X4) ) )
& ? [X6] :
! [X7] :
( ( ( ~ g_both(X7,X7)
& ~ g_true_only(X7,X7) )
| ~ g_false_only(X7,X6) )
& ( ( ~ g_false_only(X7,X7)
& ~ g_true_only(X7,X7) )
| ~ g_both(X7,X6) )
& ( ( ~ g_false_only(X7,X7)
& ~ g_both(X7,X7) )
| ~ g_true_only(X7,X6) ) ) ),
inference(rectify,[],[f17]) ).
fof(f35,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( g_true_only(X2,X0)
& g_false_only(X2,X1) )
| ( g_false_only(X2,X0)
& g_true_only(X2,X1) ) )
=> ! [X2] :
( ( g_true_only(X2,X0)
& g_false_only(X2,sK9(X0)) )
| ( g_false_only(X2,X0)
& g_true_only(X2,sK9(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X3] :
( ? [X4] :
! [X5] :
( ( ( ~ g_both(X5,X3)
& ~ g_false_only(X5,X3) )
| ~ g_false_only(X5,X4) )
& ( ( ~ g_true_only(X5,X3)
& ~ g_false_only(X5,X3) )
| ~ g_both(X5,X4) )
& ( ( ~ g_true_only(X5,X3)
& ~ g_both(X5,X3) )
| ~ g_true_only(X5,X4) ) )
=> ! [X5] :
( ( ( ~ g_both(X5,X3)
& ~ g_false_only(X5,X3) )
| ~ g_false_only(X5,sK10(X3)) )
& ( ( ~ g_true_only(X5,X3)
& ~ g_false_only(X5,X3) )
| ~ g_both(X5,sK10(X3)) )
& ( ( ~ g_true_only(X5,X3)
& ~ g_both(X5,X3) )
| ~ g_true_only(X5,sK10(X3)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
( ? [X6] :
! [X7] :
( ( ( ~ g_both(X7,X7)
& ~ g_true_only(X7,X7) )
| ~ g_false_only(X7,X6) )
& ( ( ~ g_false_only(X7,X7)
& ~ g_true_only(X7,X7) )
| ~ g_both(X7,X6) )
& ( ( ~ g_false_only(X7,X7)
& ~ g_both(X7,X7) )
| ~ g_true_only(X7,X6) ) )
=> ! [X7] :
( ( ( ~ g_both(X7,X7)
& ~ g_true_only(X7,X7) )
| ~ g_false_only(X7,sK11) )
& ( ( ~ g_false_only(X7,X7)
& ~ g_true_only(X7,X7) )
| ~ g_both(X7,sK11) )
& ( ( ~ g_false_only(X7,X7)
& ~ g_both(X7,X7) )
| ~ g_true_only(X7,sK11) ) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
( ( sP2
| ! [X0] :
( ! [X2] :
( ( g_true_only(X2,X0)
& g_false_only(X2,sK9(X0)) )
| ( g_false_only(X2,X0)
& g_true_only(X2,sK9(X0)) ) )
| sP0(X0) )
| sP3
| sP1 )
& ! [X3,X5] :
( ( ( ~ g_both(X5,X3)
& ~ g_false_only(X5,X3) )
| ~ g_false_only(X5,sK10(X3)) )
& ( ( ~ g_true_only(X5,X3)
& ~ g_false_only(X5,X3) )
| ~ g_both(X5,sK10(X3)) )
& ( ( ~ g_true_only(X5,X3)
& ~ g_both(X5,X3) )
| ~ g_true_only(X5,sK10(X3)) ) )
& ! [X7] :
( ( ( ~ g_both(X7,X7)
& ~ g_true_only(X7,X7) )
| ~ g_false_only(X7,sK11) )
& ( ( ~ g_false_only(X7,X7)
& ~ g_true_only(X7,X7) )
| ~ g_both(X7,sK11) )
& ( ( ~ g_false_only(X7,X7)
& ~ g_both(X7,X7) )
| ~ g_true_only(X7,sK11) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f34,f37,f36,f35]) ).
fof(f39,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,[],[f8]) ).
fof(f40,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,[],[f39]) ).
fof(f41,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,[],[f9]) ).
fof(f42,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,[],[f41]) ).
fof(f43,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,[],[f10]) ).
fof(f44,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,[],[f43]) ).
fof(f45,plain,
! [X1] :
( g_false_only(X1,sK4)
| g_true_only(X1,sK4)
| ~ sP3 ),
inference(cnf_transformation,[],[f21]) ).
fof(f46,plain,
! [X1] :
( g_false_only(X1,sK4)
| g_true_only(X1,X1)
| ~ sP3 ),
inference(cnf_transformation,[],[f21]) ).
fof(f47,plain,
! [X1] :
( g_false_only(X1,X1)
| g_true_only(X1,sK4)
| ~ sP3 ),
inference(cnf_transformation,[],[f21]) ).
fof(f48,plain,
! [X1] :
( g_false_only(X1,X1)
| g_true_only(X1,X1)
| ~ sP3 ),
inference(cnf_transformation,[],[f21]) ).
fof(f49,plain,
! [X1] :
( g_false_only(sK6(X1),X1)
| g_both(sK6(X1),X1)
| g_true_only(sK6(X1),X1)
| ~ sP2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f50,plain,
! [X1] :
( g_false_only(sK6(X1),X1)
| g_both(sK6(X1),X1)
| g_true_only(sK6(X1),sK5)
| g_both(sK6(X1),sK5)
| ~ sP2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f51,plain,
! [X1] :
( g_false_only(sK6(X1),X1)
| g_true_only(sK6(X1),sK5)
| g_false_only(sK6(X1),sK5)
| g_true_only(sK6(X1),X1)
| ~ sP2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f53,plain,
! [X1] :
( g_both(sK6(X1),sK5)
| g_false_only(sK6(X1),sK5)
| g_both(sK6(X1),X1)
| g_true_only(sK6(X1),X1)
| ~ sP2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f57,plain,
! [X2,X0] :
( g_false_only(sK7(X0),X0)
| g_both(sK7(X0),X0)
| g_true_only(sK7(X0),X0)
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| ~ sP1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f58,plain,
! [X2,X0] :
( g_false_only(sK7(X0),X0)
| g_both(sK7(X0),X0)
| g_false_only(sK7(X0),sK7(X0))
| g_both(sK7(X0),sK7(X0))
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| ~ sP1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f59,plain,
! [X2,X0] :
( g_false_only(sK7(X0),X0)
| g_false_only(sK7(X0),sK7(X0))
| g_true_only(sK7(X0),sK7(X0))
| g_true_only(sK7(X0),X0)
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| ~ sP1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f61,plain,
! [X2,X0] :
( g_both(sK7(X0),sK7(X0))
| g_true_only(sK7(X0),sK7(X0))
| g_both(sK7(X0),X0)
| g_true_only(sK7(X0),X0)
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| ~ sP1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f66,plain,
! [X3,X0,X1] :
( g_false_only(sK8(X0,X1),X1)
| g_both(sK8(X0,X1),X1)
| g_true_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X0)
| ~ g_both(X3,X0)
| ~ g_both(X3,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f67,plain,
! [X3,X0,X1] :
( g_false_only(sK8(X0,X1),X1)
| g_true_only(sK8(X0,X1),X0)
| g_false_only(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X1)
| ~ g_both(X3,X0)
| ~ g_both(X3,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f69,plain,
! [X3,X0,X1] :
( g_both(sK8(X0,X1),X0)
| g_false_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X1)
| g_true_only(sK8(X0,X1),X1)
| ~ g_both(X3,X0)
| ~ g_both(X3,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f73,plain,
! [X7] :
( ~ g_both(X7,X7)
| ~ g_true_only(X7,sK11) ),
inference(cnf_transformation,[],[f38]) ).
fof(f74,plain,
! [X7] :
( ~ g_false_only(X7,X7)
| ~ g_true_only(X7,sK11) ),
inference(cnf_transformation,[],[f38]) ).
fof(f75,plain,
! [X7] :
( ~ g_true_only(X7,X7)
| ~ g_both(X7,sK11) ),
inference(cnf_transformation,[],[f38]) ).
fof(f76,plain,
! [X7] :
( ~ g_false_only(X7,X7)
| ~ g_both(X7,sK11) ),
inference(cnf_transformation,[],[f38]) ).
fof(f77,plain,
! [X7] :
( ~ g_true_only(X7,X7)
| ~ g_false_only(X7,sK11) ),
inference(cnf_transformation,[],[f38]) ).
fof(f78,plain,
! [X7] :
( ~ g_both(X7,X7)
| ~ g_false_only(X7,sK11) ),
inference(cnf_transformation,[],[f38]) ).
fof(f79,plain,
! [X3,X5] :
( ~ g_both(X5,X3)
| ~ g_true_only(X5,sK10(X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f80,plain,
! [X3,X5] :
( ~ g_true_only(X5,X3)
| ~ g_true_only(X5,sK10(X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f81,plain,
! [X3,X5] :
( ~ g_false_only(X5,X3)
| ~ g_both(X5,sK10(X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f82,plain,
! [X3,X5] :
( ~ g_true_only(X5,X3)
| ~ g_both(X5,sK10(X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f83,plain,
! [X3,X5] :
( ~ g_false_only(X5,X3)
| ~ g_false_only(X5,sK10(X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f84,plain,
! [X3,X5] :
( ~ g_both(X5,X3)
| ~ g_false_only(X5,sK10(X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f88,plain,
! [X2,X0] :
( sP2
| g_true_only(X2,X0)
| g_false_only(X2,X0)
| sP0(X0)
| sP3
| sP1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f89,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f90,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f91,plain,
! [X0,X1] :
( g_true_only(X0,X1)
| g_false(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f92,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f93,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f94,plain,
! [X0,X1] :
( g_both(X0,X1)
| ~ g_false(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f95,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f96,plain,
! [X0,X1] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f97,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_true(X0,X1)
| ~ g_false(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f98,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
cnf(c_49,plain,
( ~ sP3
| g_false_only(X0,X0)
| g_true_only(X0,X0) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_50,plain,
( ~ sP3
| g_false_only(X0,X0)
| g_true_only(X0,sK4) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_51,plain,
( ~ sP3
| g_true_only(X0,X0)
| g_false_only(X0,sK4) ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_52,plain,
( ~ sP3
| g_false_only(X0,sK4)
| g_true_only(X0,sK4) ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_56,plain,
( ~ sP2
| g_true_only(sK6(X0),X0)
| g_both(sK6(X0),X0)
| g_false_only(sK6(X0),sK5)
| g_both(sK6(X0),sK5) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_58,plain,
( ~ sP2
| g_false_only(sK6(X0),X0)
| g_true_only(sK6(X0),X0)
| g_false_only(sK6(X0),sK5)
| g_true_only(sK6(X0),sK5) ),
inference(cnf_transformation,[],[f51]) ).
cnf(c_59,plain,
( ~ sP2
| g_false_only(sK6(X0),X0)
| g_both(sK6(X0),X0)
| g_true_only(sK6(X0),sK5)
| g_both(sK6(X0),sK5) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_60,plain,
( ~ sP2
| g_false_only(sK6(X0),X0)
| g_true_only(sK6(X0),X0)
| g_both(sK6(X0),X0) ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_61,plain,
( ~ g_both(X0,X0)
| ~ g_both(X0,X1)
| ~ sP1
| g_false_only(sK7(X1),sK7(X1))
| g_true_only(sK7(X1),sK7(X1))
| g_both(sK7(X1),sK7(X1)) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_64,plain,
( ~ g_both(X0,X0)
| ~ g_both(X0,X1)
| ~ sP1
| g_true_only(sK7(X1),sK7(X1))
| g_both(sK7(X1),sK7(X1))
| g_true_only(sK7(X1),X1)
| g_both(sK7(X1),X1) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_66,plain,
( ~ g_both(X0,X0)
| ~ g_both(X0,X1)
| ~ sP1
| g_false_only(sK7(X1),sK7(X1))
| g_true_only(sK7(X1),sK7(X1))
| g_false_only(sK7(X1),X1)
| g_true_only(sK7(X1),X1) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_67,plain,
( ~ g_both(X0,X0)
| ~ g_both(X0,X1)
| ~ sP1
| g_false_only(sK7(X1),sK7(X1))
| g_both(sK7(X1),sK7(X1))
| g_false_only(sK7(X1),X1)
| g_both(sK7(X1),X1) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_68,plain,
( ~ g_both(X0,X0)
| ~ g_both(X0,X1)
| ~ sP1
| g_false_only(sK7(X1),X1)
| g_true_only(sK7(X1),X1)
| g_both(sK7(X1),X1) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_72,plain,
( ~ g_both(X0,X1)
| ~ g_both(X0,X2)
| ~ sP0(X2)
| g_false_only(sK8(X2,X1),X2)
| g_true_only(sK8(X2,X1),X1)
| g_both(sK8(X2,X1),X1)
| g_both(sK8(X2,X1),X2) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_74,plain,
( ~ g_both(X0,X1)
| ~ g_both(X0,X2)
| ~ sP0(X2)
| g_false_only(sK8(X2,X1),X1)
| g_false_only(sK8(X2,X1),X2)
| g_true_only(sK8(X2,X1),X1)
| g_true_only(sK8(X2,X1),X2) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_75,plain,
( ~ g_both(X0,X1)
| ~ g_both(X0,X2)
| ~ sP0(X2)
| g_false_only(sK8(X2,X1),X1)
| g_true_only(sK8(X2,X1),X2)
| g_both(sK8(X2,X1),X1)
| g_both(sK8(X2,X1),X2) ),
inference(cnf_transformation,[],[f66]) ).
cnf(c_77,negated_conjecture,
( g_false_only(X0,X1)
| g_true_only(X0,X1)
| sP0(X1)
| sP3
| sP2
| sP1 ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_81,negated_conjecture,
( ~ g_false_only(X0,sK10(X1))
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_82,negated_conjecture,
( ~ g_false_only(X0,sK10(X1))
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_83,negated_conjecture,
( ~ g_both(X0,sK10(X1))
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_84,negated_conjecture,
( ~ g_both(X0,sK10(X1))
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_85,negated_conjecture,
( ~ g_true_only(X0,sK10(X1))
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
cnf(c_86,negated_conjecture,
( ~ g_true_only(X0,sK10(X1))
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_87,negated_conjecture,
( ~ g_both(X0,X0)
| ~ g_false_only(X0,sK11) ),
inference(cnf_transformation,[],[f78]) ).
cnf(c_88,negated_conjecture,
( ~ g_true_only(X0,X0)
| ~ g_false_only(X0,sK11) ),
inference(cnf_transformation,[],[f77]) ).
cnf(c_89,negated_conjecture,
( ~ g_false_only(X0,X0)
| ~ g_both(X0,sK11) ),
inference(cnf_transformation,[],[f76]) ).
cnf(c_90,negated_conjecture,
( ~ g_true_only(X0,X0)
| ~ g_both(X0,sK11) ),
inference(cnf_transformation,[],[f75]) ).
cnf(c_91,negated_conjecture,
( ~ g_false_only(X0,X0)
| ~ g_true_only(X0,sK11) ),
inference(cnf_transformation,[],[f74]) ).
cnf(c_92,negated_conjecture,
( ~ g_both(X0,X0)
| ~ g_true_only(X0,sK11) ),
inference(cnf_transformation,[],[f73]) ).
cnf(c_93,plain,
( ~ g_true(X0,X1)
| g_true_only(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_94,plain,
( ~ g_true_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_95,plain,
( ~ g_true_only(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_96,plain,
( ~ g_false(X0,X1)
| ~ g_true(X0,X1)
| g_both(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_97,plain,
( ~ g_both(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_98,plain,
( ~ g_both(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_99,plain,
( ~ g_false(X0,X1)
| g_false_only(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_100,plain,
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_101,plain,
( ~ g_false_only(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_102,plain,
( g_false_only(X0,X1)
| g_true_only(X0,X1)
| g_both(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
cnf(c_145,plain,
( g_false_only(X0,X1)
| g_true(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_99,c_98,c_95,c_102]) ).
cnf(c_148,plain,
( g_true_only(X0,X1)
| g_false(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_93,c_101,c_97,c_102]) ).
cnf(c_169,plain,
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_100]) ).
cnf(c_170,plain,
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(renaming,[status(thm)],[c_169]) ).
cnf(c_173,plain,
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
cnf(c_174,plain,
( ~ g_true_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(renaming,[status(thm)],[c_173]) ).
cnf(c_199,plain,
( ~ g_false_only(X0,sK10(X1))
| g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_98,c_95,c_82,c_102]) ).
cnf(c_201,plain,
( ~ g_both(X0,sK10(X1))
| g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_98,c_95,c_84,c_102]) ).
cnf(c_203,plain,
( ~ g_both(X0,sK10(X1))
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_101,c_97,c_83,c_102]) ).
cnf(c_207,plain,
( ~ g_true_only(X0,sK10(X1))
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_101,c_97,c_85,c_102]) ).
cnf(c_227,plain,
( g_true(X0,X1)
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_101,c_97,c_95,c_102]) ).
cnf(c_228,plain,
( g_false(X0,X1)
| g_true(X0,X1) ),
inference(renaming,[status(thm)],[c_227]) ).
cnf(c_293,negated_conjecture,
( ~ g_false(X0,X1)
| ~ g_true(X0,X1)
| sP0(X1)
| sP3
| sP2
| sP1 ),
inference(bin_hyper_res,[status(thm)],[c_77,c_174,c_170]) ).
cnf(c_3859,plain,
( g_true(X0,X1)
| g_false_only(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_145]) ).
cnf(c_3860,plain,
( g_false_only(X0,X1)
| g_true(X0,X1) ),
inference(renaming,[status(thm)],[c_3859]) ).
cnf(c_3863,plain,
( g_false(X0,X1)
| g_true_only(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_148]) ).
cnf(c_3864,plain,
( g_true_only(X0,X1)
| g_false(X0,X1) ),
inference(renaming,[status(thm)],[c_3863]) ).
cnf(c_3887,plain,
( ~ g_false_only(X0,sK10(X1))
| g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_199]) ).
cnf(c_3889,plain,
( ~ g_both(X0,sK10(X1))
| g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_201]) ).
cnf(c_3891,plain,
( ~ g_both(X0,sK10(X1))
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_203]) ).
cnf(c_3895,plain,
( ~ g_true_only(X0,sK10(X1))
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_207]) ).
cnf(c_3915,plain,
( g_true(X0,X1)
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_228]) ).
cnf(c_3916,plain,
( g_false(X0,X1)
| g_true(X0,X1) ),
inference(renaming,[status(thm)],[c_3915]) ).
cnf(c_7445,negated_conjecture,
( ~ g_true(X0,X1)
| ~ g_false(X0,X1)
| sP0(X1)
| ~ sP2_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP2_iProver_def])],[c_293]) ).
cnf(c_7446,negated_conjecture,
( sP3
| sP2
| sP1
| sP2_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_293]) ).
cnf(c_7455,plain,
( ~ g_true_only(sK7(sK11),sK7(sK11))
| ~ g_false_only(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_88]) ).
cnf(c_7460,plain,
( g_false_only(X0,sK11)
| g_true(X0,sK11) ),
inference(instantiation,[status(thm)],[c_3860]) ).
cnf(c_7465,plain,
( ~ g_both(sK7(sK11),sK7(sK11))
| ~ g_false_only(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_87]) ).
cnf(c_7494,plain,
( ~ g_both(X0,X1)
| ~ g_both(X0,sK11)
| ~ sP0(X1)
| g_true_only(sK8(X1,sK11),X1)
| g_both(sK8(X1,sK11),X1)
| g_false_only(sK8(X1,sK11),sK11)
| g_both(sK8(X1,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_7495,plain,
( ~ g_both(X0,X1)
| ~ g_both(X0,sK11)
| ~ sP0(X1)
| g_false_only(sK8(X1,sK11),X1)
| g_true_only(sK8(X1,sK11),X1)
| g_false_only(sK8(X1,sK11),sK11)
| g_true_only(sK8(X1,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_74]) ).
cnf(c_7502,plain,
( g_false_only(sK7(sK11),sK11)
| g_true(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7460]) ).
cnf(c_7507,plain,
( ~ g_false_only(X0,sK11)
| ~ g_true(X0,sK11) ),
inference(instantiation,[status(thm)],[c_100]) ).
cnf(c_7513,plain,
( ~ g_false_only(sK6(sK10(X0)),sK10(X0))
| g_true(sK6(sK10(X0)),X0) ),
inference(instantiation,[status(thm)],[c_3887]) ).
cnf(c_7517,plain,
( ~ g_false_only(sK8(sK10(X0),X1),sK10(X0))
| g_true(sK8(sK10(X0),X1),X0) ),
inference(instantiation,[status(thm)],[c_3887]) ).
cnf(c_7521,plain,
( g_false_only(X0,sK10(X1))
| g_true(X0,sK10(X1)) ),
inference(instantiation,[status(thm)],[c_3860]) ).
cnf(c_7528,plain,
( ~ g_false_only(sK8(X0,sK11),sK11)
| ~ g_true(sK8(X0,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7507]) ).
cnf(c_7539,plain,
( ~ sP2
| g_false_only(sK6(sK10(X0)),sK10(X0))
| g_both(sK6(sK10(X0)),sK10(X0))
| g_true_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_7575,plain,
( g_false_only(sK10(X0),sK10(X0))
| g_true(sK10(X0),sK10(X0)) ),
inference(instantiation,[status(thm)],[c_7521]) ).
cnf(c_7577,plain,
( g_false_only(sK6(sK10(X0)),sK10(X0))
| g_true(sK6(sK10(X0)),sK10(X0)) ),
inference(instantiation,[status(thm)],[c_7521]) ).
cnf(c_7630,plain,
( ~ g_false_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7517]) ).
cnf(c_7647,plain,
( ~ g_false_only(X0,sK4)
| ~ g_true(X0,sK4) ),
inference(instantiation,[status(thm)],[c_100]) ).
cnf(c_7652,plain,
( ~ g_false_only(sK7(X0),sK7(X0))
| ~ g_true(sK7(X0),sK7(X0)) ),
inference(instantiation,[status(thm)],[c_100]) ).
cnf(c_7656,plain,
( ~ g_false_only(sK8(X0,X1),X0)
| ~ g_true(sK8(X0,X1),X0) ),
inference(instantiation,[status(thm)],[c_100]) ).
cnf(c_7659,plain,
( g_true_only(X0,sK10(X1))
| g_false(X0,sK10(X1)) ),
inference(instantiation,[status(thm)],[c_3864]) ).
cnf(c_7661,plain,
( g_true_only(X0,sK11)
| g_false(X0,sK11) ),
inference(instantiation,[status(thm)],[c_3864]) ).
cnf(c_7665,plain,
( g_true_only(sK7(sK11),sK7(sK11))
| g_false(sK7(sK11),sK7(sK11)) ),
inference(instantiation,[status(thm)],[c_3864]) ).
cnf(c_7676,plain,
( g_false(sK8(X0,sK11),sK11)
| g_true(sK8(X0,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_3916]) ).
cnf(c_7678,plain,
( g_false(X0,sK10(X1))
| g_true(X0,sK10(X1)) ),
inference(instantiation,[status(thm)],[c_3916]) ).
cnf(c_7697,plain,
( g_false_only(sK8(X0,sK11),sK10(sK11))
| g_true(sK8(X0,sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_7521]) ).
cnf(c_7701,plain,
( ~ g_false_only(sK8(sK10(sK11),sK11),sK11)
| ~ g_true(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7528]) ).
cnf(c_7729,plain,
( ~ g_false_only(sK8(sK10(X0),X1),sK10(X0))
| ~ g_true(sK8(sK10(X0),X1),sK10(X0)) ),
inference(instantiation,[status(thm)],[c_7656]) ).
cnf(c_7748,plain,
( g_false(X0,sK4)
| g_true(X0,sK4) ),
inference(instantiation,[status(thm)],[c_3916]) ).
cnf(c_7752,plain,
( ~ g_false_only(sK10(sK4),sK4)
| ~ g_true(sK10(sK4),sK4) ),
inference(instantiation,[status(thm)],[c_7647]) ).
cnf(c_7763,plain,
( ~ g_true_only(X0,sK10(X1))
| ~ g_false(X0,sK10(X1)) ),
inference(instantiation,[status(thm)],[c_94]) ).
cnf(c_7765,plain,
( ~ g_false(X0,sK10(X1))
| ~ g_true(X0,sK10(X1))
| g_both(X0,sK10(X1)) ),
inference(instantiation,[status(thm)],[c_96]) ).
cnf(c_7769,plain,
( g_true_only(sK10(X0),sK10(X0))
| g_false(sK10(X0),sK10(X0)) ),
inference(instantiation,[status(thm)],[c_7659]) ).
cnf(c_7906,plain,
( g_false(sK8(sK10(X0),X1),sK10(X0))
| g_true(sK8(sK10(X0),X1),sK10(X0)) ),
inference(instantiation,[status(thm)],[c_7678]) ).
cnf(c_7922,plain,
( ~ g_false_only(sK10(X0),sK10(X0))
| ~ g_both(sK10(X0),X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_7924,plain,
( ~ g_false_only(sK6(sK10(X0)),sK10(X0))
| ~ g_both(sK6(sK10(X0)),X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_7938,plain,
( ~ g_both(sK10(X0),X0)
| ~ sP3
| g_true_only(sK10(X0),sK4) ),
inference(superposition,[status(thm)],[c_50,c_81]) ).
cnf(c_7941,plain,
( ~ g_both(sK10(X0),X0)
| ~ sP3
| g_false_only(sK10(X0),sK10(X0)) ),
inference(superposition,[status(thm)],[c_49,c_86]) ).
cnf(c_7944,plain,
( ~ g_true_only(sK6(sK10(X0)),sK10(X0))
| ~ g_both(sK6(sK10(X0)),X0) ),
inference(instantiation,[status(thm)],[c_86]) ).
cnf(c_7946,plain,
( ~ g_false_only(sK8(X0,sK11),sK10(sK11))
| ~ g_both(sK8(X0,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_7951,plain,
( g_false_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true(sK8(sK10(sK11),sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_7697]) ).
cnf(c_7985,plain,
( ~ g_true_only(sK10(X0),sK10(X0))
| ~ g_both(sK10(X0),X0) ),
inference(instantiation,[status(thm)],[c_86]) ).
cnf(c_7987,plain,
( ~ g_true_only(sK10(X0),sK10(X0))
| g_false(sK10(X0),X0) ),
inference(instantiation,[status(thm)],[c_3895]) ).
cnf(c_7991,plain,
( ~ g_false_only(sK7(X0),sK7(X0))
| ~ g_true_only(sK7(X0),sK11) ),
inference(instantiation,[status(thm)],[c_91]) ).
cnf(c_7996,plain,
( g_false_only(sK7(X0),sK7(X0))
| g_true(sK7(X0),sK7(X0)) ),
inference(instantiation,[status(thm)],[c_3860]) ).
cnf(c_8029,plain,
( ~ g_true_only(X0,sK4)
| ~ g_false(X0,sK4) ),
inference(instantiation,[status(thm)],[c_94]) ).
cnf(c_8031,plain,
( ~ g_true_only(sK7(X0),X0)
| ~ g_false(sK7(X0),X0) ),
inference(instantiation,[status(thm)],[c_94]) ).
cnf(c_8035,plain,
( ~ g_true_only(sK7(sK11),sK7(sK11))
| ~ g_false(sK7(sK11),sK7(sK11)) ),
inference(instantiation,[status(thm)],[c_94]) ).
cnf(c_8051,plain,
( ~ g_both(sK7(X0),sK7(X0))
| g_true(sK7(X0),sK7(X0)) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_8053,plain,
( ~ g_false_only(sK8(sK10(sK11),sK11),sK10(sK11))
| ~ g_true(sK8(sK10(sK11),sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_7729]) ).
cnf(c_8055,plain,
( ~ g_false(X0,sK11)
| ~ g_true(X0,sK11)
| g_both(X0,sK11) ),
inference(instantiation,[status(thm)],[c_96]) ).
cnf(c_8059,plain,
( ~ g_false(sK7(sK11),sK7(sK11))
| ~ g_true(sK7(sK11),sK7(sK11))
| g_both(sK7(sK11),sK7(sK11)) ),
inference(instantiation,[status(thm)],[c_96]) ).
cnf(c_8113,plain,
( ~ g_both(sK7(sK11),sK7(sK11))
| g_false(sK7(sK11),sK7(sK11)) ),
inference(instantiation,[status(thm)],[c_97]) ).
cnf(c_8124,plain,
( ~ sP3
| ~ g_both(sK10(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_7938,c_7922,c_7941]) ).
cnf(c_8125,plain,
( ~ g_both(sK10(X0),X0)
| ~ sP3 ),
inference(renaming,[status(thm)],[c_8124]) ).
cnf(c_8135,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_false_only(sK6(sK10(X0)),sK10(X0))
| g_both(sK6(sK10(X0)),sK10(X0)) ),
inference(superposition,[status(thm)],[c_60,c_86]) ).
cnf(c_8139,plain,
( ~ g_both(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true(sK8(sK10(sK11),sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_8203,plain,
( ~ g_false_only(sK7(sK11),sK7(sK11))
| ~ g_true_only(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7991]) ).
cnf(c_8219,plain,
( ~ g_false(sK10(X0),X0)
| ~ g_true(sK10(X0),X0)
| g_both(sK10(X0),X0) ),
inference(instantiation,[status(thm)],[c_96]) ).
cnf(c_8224,plain,
( ~ g_both(sK7(X0),X0)
| g_false(sK7(X0),X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
cnf(c_8231,plain,
( ~ g_true_only(sK7(sK11),sK11)
| ~ g_false(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8031]) ).
cnf(c_8253,plain,
( ~ g_false(sK10(X0),sK10(X0))
| ~ g_true(sK10(X0),sK10(X0))
| g_both(sK10(X0),sK10(X0)) ),
inference(instantiation,[status(thm)],[c_7765]) ).
cnf(c_8304,plain,
( ~ g_true_only(sK10(sK4),sK4)
| ~ g_false(sK10(sK4),sK4) ),
inference(instantiation,[status(thm)],[c_8029]) ).
cnf(c_8376,plain,
( ~ g_false(sK7(sK11),sK11)
| ~ g_true(sK7(sK11),sK11)
| g_both(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8055]) ).
cnf(c_8379,plain,
( ~ g_false(sK8(sK10(sK11),X0),sK11)
| ~ g_true(sK8(sK10(sK11),X0),sK11)
| g_both(sK8(sK10(sK11),X0),sK11) ),
inference(instantiation,[status(thm)],[c_8055]) ).
cnf(c_8388,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_false_only(sK6(sK10(X0)),sK10(X0))
| g_false_only(sK6(sK10(X0)),sK5)
| g_true_only(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_58,c_86]) ).
cnf(c_8431,plain,
( ~ g_both(sK7(sK11),sK7(sK11))
| ~ g_true_only(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_8621,plain,
( ~ g_false(X0,X1)
| ~ sP2_iProver_def
| g_false_only(X0,X1)
| sP0(X1) ),
inference(resolution,[status(thm)],[c_7445,c_3860]) ).
cnf(c_8625,plain,
( g_false(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true(sK8(sK10(sK11),sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_7906]) ).
cnf(c_8635,plain,
( ~ sP2_iProver_def
| g_false_only(X0,X1)
| g_true_only(X0,X1)
| sP0(X1) ),
inference(resolution,[status(thm)],[c_8621,c_3864]) ).
cnf(c_8640,plain,
( ~ g_true_only(sK7(X0),sK7(X0))
| ~ g_both(sK7(X0),sK11) ),
inference(instantiation,[status(thm)],[c_90]) ).
cnf(c_8679,plain,
( ~ g_false(X0,sK4)
| ~ sP3
| g_false_only(X0,sK4) ),
inference(superposition,[status(thm)],[c_52,c_94]) ).
cnf(c_8691,plain,
( ~ sP3
| g_true(sK10(X0),X0)
| g_true_only(sK10(X0),sK4) ),
inference(superposition,[status(thm)],[c_50,c_3887]) ).
cnf(c_8692,plain,
( ~ sP3
| g_false(sK10(X0),X0)
| g_false_only(sK10(X0),sK4) ),
inference(superposition,[status(thm)],[c_51,c_3895]) ).
cnf(c_8695,plain,
( ~ g_false(sK10(X0),X0)
| ~ sP3
| g_both(sK10(X0),X0)
| g_true_only(sK10(X0),sK4) ),
inference(superposition,[status(thm)],[c_8691,c_96]) ).
cnf(c_8696,plain,
( ~ g_false(sK10(X0),X0)
| ~ sP3
| ~ sP2_iProver_def
| g_true_only(sK10(X0),sK4)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_8691,c_7445]) ).
cnf(c_8702,plain,
( ~ sP3
| g_false_only(sK10(sK4),sK4) ),
inference(superposition,[status(thm)],[c_8692,c_8679]) ).
cnf(c_8721,plain,
( g_true_only(sK10(X0),sK4)
| ~ g_false(sK10(X0),X0)
| ~ sP3 ),
inference(global_subsumption_just,[status(thm)],[c_8696,c_8125,c_8695]) ).
cnf(c_8722,plain,
( ~ g_false(sK10(X0),X0)
| ~ sP3
| g_true_only(sK10(X0),sK4) ),
inference(renaming,[status(thm)],[c_8721]) ).
cnf(c_8729,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_false_only(sK6(sK10(X0)),sK10(X0))
| g_both(sK6(sK10(X0)),sK10(X0)) ),
inference(superposition,[status(thm)],[c_60,c_86]) ).
cnf(c_8732,plain,
( ~ sP2
| g_both(sK6(sK10(X0)),sK10(X0))
| g_false(sK6(sK10(X0)),X0)
| g_false_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_56,c_3895]) ).
cnf(c_8738,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_false_only(sK6(sK10(X0)),sK10(X0))
| g_false_only(sK6(sK10(X0)),sK5)
| g_true_only(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_58,c_86]) ).
cnf(c_8746,plain,
( ~ g_false_only(X0,X0)
| ~ sP2_iProver_def
| g_false_only(X0,sK11)
| sP0(sK11) ),
inference(resolution,[status(thm)],[c_91,c_8635]) ).
cnf(c_8845,plain,
( g_false_only(X0,sK11)
| ~ g_false_only(X0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_8746,c_91,c_89,c_7460,c_7661,c_8055]) ).
cnf(c_8846,plain,
( ~ g_false_only(X0,X0)
| g_false_only(X0,sK11) ),
inference(renaming,[status(thm)],[c_8845]) ).
cnf(c_8859,plain,
( ~ g_false(sK8(sK10(sK11),sK11),sK10(sK11))
| ~ g_true(sK8(sK10(sK11),sK11),sK10(sK11))
| g_both(sK8(sK10(sK11),sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_7765]) ).
cnf(c_8928,plain,
( g_true_only(sK7(sK11),sK11)
| g_false(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7661]) ).
cnf(c_8965,plain,
( ~ sP2
| ~ g_both(sK6(sK10(X0)),X0)
| g_both(sK6(sK10(X0)),sK10(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_8729,c_7924,c_8135]) ).
cnf(c_8966,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_both(sK6(sK10(X0)),sK10(X0)) ),
inference(renaming,[status(thm)],[c_8965]) ).
cnf(c_8968,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_true(sK6(sK10(X0)),sK10(X0)) ),
inference(superposition,[status(thm)],[c_8966,c_98]) ).
cnf(c_8971,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_true(sK6(sK10(X0)),X0) ),
inference(superposition,[status(thm)],[c_8966,c_3889]) ).
cnf(c_9038,plain,
( ~ g_both(sK10(sK11),sK11)
| g_false(sK10(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_97]) ).
cnf(c_9047,plain,
( ~ sP2
| ~ g_both(sK6(sK10(X0)),X0)
| g_false_only(sK6(sK10(X0)),sK5)
| g_true_only(sK6(sK10(X0)),sK5) ),
inference(global_subsumption_just,[status(thm)],[c_8738,c_7924,c_8388]) ).
cnf(c_9048,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_false_only(sK6(sK10(X0)),sK5)
| g_true_only(sK6(sK10(X0)),sK5) ),
inference(renaming,[status(thm)],[c_9047]) ).
cnf(c_9049,plain,
( ~ g_both(sK6(sK10(sK5)),sK5)
| ~ sP2
| g_false_only(sK6(sK10(sK5)),sK5)
| g_true_only(sK6(sK10(sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_9048]) ).
cnf(c_9206,plain,
( ~ g_both(sK8(X0,sK11),sK10(sK11))
| g_false(sK8(X0,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_3891]) ).
cnf(c_9224,plain,
( g_false_only(sK10(X0),X0)
| g_true(sK10(X0),X0) ),
inference(instantiation,[status(thm)],[c_3860]) ).
cnf(c_9225,plain,
( g_false(sK10(X0),X0)
| g_true(sK10(X0),X0) ),
inference(instantiation,[status(thm)],[c_3916]) ).
cnf(c_9258,plain,
( ~ g_both(sK7(sK11),sK11)
| g_false(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8224]) ).
cnf(c_9283,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| g_true(sK6(sK10(X0)),sK10(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_8968,c_7577,c_7924]) ).
cnf(c_9286,plain,
( ~ g_false(sK6(sK10(X0)),sK10(X0))
| ~ g_both(sK6(sK10(X0)),X0)
| g_both(sK6(sK10(X0)),sK10(X0)) ),
inference(superposition,[status(thm)],[c_9283,c_96]) ).
cnf(c_9341,plain,
( ~ g_false_only(sK10(sK11),sK10(sK11))
| ~ g_both(sK10(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7922]) ).
cnf(c_9470,plain,
( ~ sP2_iProver_def
| g_false_only(X0,sK10(X1))
| g_false(X0,X1)
| sP0(sK10(X1)) ),
inference(resolution,[status(thm)],[c_3895,c_8635]) ).
cnf(c_9505,plain,
( g_true_only(sK6(sK10(X0)),sK10(X0))
| g_false(sK6(sK10(X0)),sK10(X0)) ),
inference(instantiation,[status(thm)],[c_7659]) ).
cnf(c_9521,plain,
( ~ g_false(X0,X1)
| g_false_only(X0,X1)
| g_both(X0,X1) ),
inference(resolution,[status(thm)],[c_96,c_3860]) ).
cnf(c_9528,plain,
( ~ g_true_only(sK6(X0),sK5)
| ~ g_false(sK6(X0),sK5) ),
inference(instantiation,[status(thm)],[c_94]) ).
cnf(c_9593,plain,
( g_true_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_false(sK8(sK10(sK11),sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_7659]) ).
cnf(c_9648,plain,
( g_false(X0,X1)
| g_false_only(X0,sK10(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_9470,c_207,c_203,c_7521,c_7659,c_7765]) ).
cnf(c_9649,plain,
( g_false_only(X0,sK10(X1))
| g_false(X0,X1) ),
inference(renaming,[status(thm)],[c_9648]) ).
cnf(c_9660,plain,
( g_false(sK10(X0),X0)
| g_false_only(sK10(X0),sK11) ),
inference(resolution,[status(thm)],[c_9649,c_8846]) ).
cnf(c_9667,plain,
( ~ g_true_only(sK10(X0),X0)
| g_false_only(sK10(X0),sK11) ),
inference(resolution,[status(thm)],[c_9660,c_94]) ).
cnf(c_9716,plain,
( g_false(sK10(sK4),sK4)
| g_true(sK10(sK4),sK4) ),
inference(instantiation,[status(thm)],[c_7748]) ).
cnf(c_9763,plain,
( ~ g_false(X0,X1)
| ~ sP2_iProver_def
| g_false_only(X0,X1)
| sP0(X1) ),
inference(superposition,[status(thm)],[c_3860,c_7445]) ).
cnf(c_9788,plain,
( ~ g_true_only(sK6(sK10(sK5)),sK5)
| ~ g_false(sK6(sK10(sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_9528]) ).
cnf(c_9864,plain,
( ~ sP3
| g_true_only(sK10(X0),X0)
| g_true_only(sK10(X0),sK4) ),
inference(superposition,[status(thm)],[c_3864,c_8722]) ).
cnf(c_10098,plain,
( ~ sP2_iProver_def
| g_false_only(X0,X1)
| g_true_only(X0,X1)
| sP0(X1) ),
inference(superposition,[status(thm)],[c_3864,c_9763]) ).
cnf(c_10146,plain,
( ~ g_both(sK10(sK10(X0)),X0)
| ~ sP3
| g_true_only(sK10(sK10(X0)),sK4) ),
inference(superposition,[status(thm)],[c_9864,c_86]) ).
cnf(c_10149,plain,
( ~ sP3
| g_true_only(sK10(sK4),sK4) ),
inference(equality_factoring,[status(thm)],[c_9864]) ).
cnf(c_10255,plain,
~ sP3,
inference(global_subsumption_just,[status(thm)],[c_10146,c_7752,c_8304,c_8702,c_9716,c_10149]) ).
cnf(c_10277,plain,
( ~ sP2_iProver_def
| g_false_only(X0,sK10(X1))
| g_false(X0,X1)
| sP0(sK10(X1)) ),
inference(superposition,[status(thm)],[c_10098,c_3895]) ).
cnf(c_10340,plain,
( ~ sP2
| g_false(sK6(sK10(X0)),X0)
| g_false_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_8732,c_3891]) ).
cnf(c_10342,plain,
( ~ sP2
| g_false_only(sK6(sK10(sK5)),sK5)
| g_both(sK6(sK10(sK5)),sK5)
| g_false(sK6(sK10(sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_10340]) ).
cnf(c_10378,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| g_true(sK6(sK10(X0)),X0) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_10379,plain,
( ~ g_both(sK6(sK10(X0)),sK10(X0))
| g_true(sK6(sK10(X0)),X0) ),
inference(instantiation,[status(thm)],[c_3889]) ).
cnf(c_10381,plain,
( g_false(sK6(sK10(X0)),X0)
| g_true(sK6(sK10(X0)),X0) ),
inference(instantiation,[status(thm)],[c_3916]) ).
cnf(c_10383,plain,
( g_false(sK6(sK10(sK5)),sK5)
| g_true(sK6(sK10(sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_10381]) ).
cnf(c_10386,plain,
( ~ g_both(sK6(sK10(sK5)),sK5)
| g_true(sK6(sK10(sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_10378]) ).
cnf(c_10419,plain,
( ~ g_both(sK8(sK10(sK11),X0),sK10(sK11))
| g_true(sK8(sK10(sK11),X0),sK11) ),
inference(instantiation,[status(thm)],[c_3889]) ).
cnf(c_10426,plain,
( g_false_only(sK8(sK10(sK11),X0),sK11)
| g_true(sK8(sK10(sK11),X0),sK11) ),
inference(instantiation,[status(thm)],[c_7460]) ).
cnf(c_10428,plain,
( ~ g_false(sK8(sK10(sK11),sK11),sK11)
| ~ g_true(sK8(sK10(sK11),sK11),sK11)
| g_both(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8379]) ).
cnf(c_10449,plain,
( ~ g_true_only(sK8(X0,sK11),sK11)
| ~ g_false(sK8(X0,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_94]) ).
cnf(c_10541,plain,
( g_false(sK10(sK11),sK11)
| g_true(sK10(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_9225]) ).
cnf(c_10570,plain,
( ~ g_both(X0,sK10(sK11))
| ~ g_both(X0,sK11)
| ~ sP0(sK10(sK11))
| g_true_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_both(sK8(sK10(sK11),sK11),sK10(sK11))
| g_false_only(sK8(sK10(sK11),sK11),sK11)
| g_both(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7494]) ).
cnf(c_10704,plain,
( ~ g_true_only(sK8(sK10(X0),X1),sK10(X0))
| ~ g_both(sK8(sK10(X0),X1),X0) ),
inference(instantiation,[status(thm)],[c_86]) ).
cnf(c_10705,plain,
( ~ g_true_only(sK8(sK10(X0),X1),sK10(X0))
| ~ g_false(sK8(sK10(X0),X1),sK10(X0)) ),
inference(instantiation,[status(thm)],[c_7763]) ).
cnf(c_10706,plain,
( ~ g_true_only(sK8(sK10(X0),X1),sK10(X0))
| g_false(sK8(sK10(X0),X1),X0) ),
inference(instantiation,[status(thm)],[c_3895]) ).
cnf(c_10724,plain,
( ~ g_both(X0,X1)
| ~ g_both(X0,sK11)
| ~ sP0(X1)
| g_false_only(sK8(X1,sK11),X1)
| g_both(sK8(X1,sK11),X1)
| g_true_only(sK8(X1,sK11),sK11)
| g_both(sK8(X1,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_10857,plain,
( ~ g_both(sK8(sK10(sK11),sK11),sK10(sK11))
| g_false(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_9206]) ).
cnf(c_10905,plain,
( g_false(X0,X1)
| g_false_only(X0,sK10(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_10277,c_9649]) ).
cnf(c_10906,plain,
( g_false_only(X0,sK10(X1))
| g_false(X0,X1) ),
inference(renaming,[status(thm)],[c_10905]) ).
cnf(c_10907,plain,
( ~ g_true_only(sK10(X0),sK11)
| g_false(sK10(X0),X0) ),
inference(superposition,[status(thm)],[c_10906,c_91]) ).
cnf(c_10960,plain,
( ~ g_true_only(sK10(sK11),sK10(sK11))
| ~ g_false_only(sK10(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_88]) ).
cnf(c_10961,plain,
( ~ g_false_only(sK10(sK11),sK11)
| ~ g_true(sK10(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7507]) ).
cnf(c_10995,plain,
( ~ g_false(X0,X1)
| ~ sP2_iProver_def
| g_false_only(X0,X1)
| sP0(X1) ),
inference(superposition,[status(thm)],[c_3860,c_7445]) ).
cnf(c_11002,plain,
( ~ sP2_iProver_def
| g_false_only(X0,X1)
| g_true_only(X0,X1)
| sP0(X1) ),
inference(superposition,[status(thm)],[c_3864,c_10995]) ).
cnf(c_11008,plain,
( ~ sP2_iProver_def
| g_false_only(X0,sK10(X1))
| g_false(X0,X1)
| sP0(sK10(X1)) ),
inference(superposition,[status(thm)],[c_11002,c_3895]) ).
cnf(c_11019,plain,
( g_false(X0,X1)
| g_false_only(X0,sK10(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_11008,c_9649]) ).
cnf(c_11020,plain,
( g_false_only(X0,sK10(X1))
| g_false(X0,X1) ),
inference(renaming,[status(thm)],[c_11019]) ).
cnf(c_11021,plain,
( ~ g_true_only(sK10(X0),sK11)
| g_false(sK10(X0),X0) ),
inference(superposition,[status(thm)],[c_11020,c_91]) ).
cnf(c_11026,plain,
( ~ sP2_iProver_def
| g_false(sK10(X0),X0)
| g_false_only(sK10(X0),sK11)
| sP0(sK11) ),
inference(superposition,[status(thm)],[c_11002,c_11021]) ).
cnf(c_11027,plain,
( ~ g_false(X0,X1)
| g_false_only(X0,X1)
| g_both(X0,X1) ),
inference(superposition,[status(thm)],[c_3860,c_96]) ).
cnf(c_11030,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| ~ sP2
| g_false_only(sK6(sK10(X0)),sK10(X0))
| g_both(sK6(sK10(X0)),sK10(X0)) ),
inference(superposition,[status(thm)],[c_60,c_86]) ).
cnf(c_11054,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| g_both(sK6(sK10(X0)),sK10(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_11030,c_7944,c_9286,c_9505]) ).
cnf(c_11061,plain,
( ~ g_both(sK6(sK10(X0)),X0)
| g_false(sK6(sK10(X0)),X0) ),
inference(superposition,[status(thm)],[c_11054,c_3891]) ).
cnf(c_11063,plain,
( ~ g_both(sK6(sK10(sK5)),sK5)
| g_false(sK6(sK10(sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_11061]) ).
cnf(c_11092,plain,
( ~ sP2
| g_both(sK6(sK10(X0)),sK10(X0))
| g_true(sK6(sK10(X0)),X0)
| g_true_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_59,c_3887]) ).
cnf(c_11106,plain,
( ~ sP2
| g_true(sK6(sK10(X0)),X0)
| g_true_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(global_subsumption_just,[status(thm)],[c_11092,c_7513,c_7539,c_10379]) ).
cnf(c_11109,plain,
( ~ g_false(sK6(sK10(X0)),X0)
| ~ sP2
| g_both(sK6(sK10(X0)),X0)
| g_true_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_11106,c_96]) ).
cnf(c_11121,plain,
( g_false_only(sK10(X0),sK11)
| g_false(sK10(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_11026,c_9660]) ).
cnf(c_11122,plain,
( g_false(sK10(X0),X0)
| g_false_only(sK10(X0),sK11) ),
inference(renaming,[status(thm)],[c_11121]) ).
cnf(c_11123,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| g_false_only(sK10(X0),sK11)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_11122,c_10995]) ).
cnf(c_11148,plain,
( ~ g_true_only(sK10(X0),sK10(X0))
| ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_11123,c_88]) ).
cnf(c_11159,plain,
( g_false_only(sK10(X0),X0)
| ~ g_true_only(sK10(X0),sK10(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_11148,c_7987,c_7985,c_8219,c_9224]) ).
cnf(c_11160,plain,
( ~ g_true_only(sK10(X0),sK10(X0))
| g_false_only(sK10(X0),X0) ),
inference(renaming,[status(thm)],[c_11159]) ).
cnf(c_11162,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(X0),sK10(X0))
| g_false_only(sK10(X0),X0)
| sP0(sK10(X0)) ),
inference(superposition,[status(thm)],[c_11002,c_11160]) ).
cnf(c_11175,plain,
( ~ g_true_only(sK10(X0),sK11)
| ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| sP0(sK10(X0)) ),
inference(superposition,[status(thm)],[c_11162,c_91]) ).
cnf(c_11178,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| g_true(sK10(X0),X0)
| sP0(sK10(X0)) ),
inference(superposition,[status(thm)],[c_11162,c_3887]) ).
cnf(c_11196,plain,
( g_false_only(X0,X1)
| g_true_only(X0,X1)
| g_both(X0,X1) ),
inference(superposition,[status(thm)],[c_3864,c_11027]) ).
cnf(c_11206,plain,
( ~ g_both(X0,X1)
| g_false_only(X0,sK10(X1))
| g_both(X0,sK10(X1)) ),
inference(superposition,[status(thm)],[c_11196,c_86]) ).
cnf(c_11237,plain,
( ~ g_both(X0,X1)
| g_both(X0,sK10(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_11206,c_81,c_11206]) ).
cnf(c_11253,plain,
( ~ g_both(sK10(X0),X0)
| ~ g_true_only(sK10(X0),sK11) ),
inference(superposition,[status(thm)],[c_11237,c_92]) ).
cnf(c_11254,plain,
( ~ g_both(sK10(X0),X0)
| ~ g_false_only(sK10(X0),sK11) ),
inference(superposition,[status(thm)],[c_11237,c_87]) ).
cnf(c_11361,plain,
( ~ g_false_only(sK6(sK10(X0)),X0)
| ~ g_true(sK6(sK10(X0)),X0) ),
inference(instantiation,[status(thm)],[c_100]) ).
cnf(c_11362,plain,
( ~ g_false_only(sK6(sK10(sK5)),sK5)
| ~ g_true(sK6(sK10(sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_11361]) ).
cnf(c_11382,plain,
( ~ g_false(sK10(sK11),sK10(sK11))
| ~ g_true(sK10(sK11),sK10(sK11))
| g_both(sK10(sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_8253]) ).
cnf(c_11799,plain,
( ~ g_true_only(sK8(sK10(sK11),sK11),sK11)
| ~ g_false(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10449]) ).
cnf(c_11851,plain,
( g_false_only(sK10(X0),X0)
| ~ g_true_only(sK10(X0),sK11) ),
inference(global_subsumption_just,[status(thm)],[c_11175,c_8219,c_9224,c_10907,c_11253]) ).
cnf(c_11852,plain,
( ~ g_true_only(sK10(X0),sK11)
| g_false_only(sK10(X0),X0) ),
inference(renaming,[status(thm)],[c_11851]) ).
cnf(c_11854,plain,
( g_false_only(sK10(X0),X0)
| g_false_only(sK10(X0),sK11)
| g_both(sK10(X0),sK11) ),
inference(superposition,[status(thm)],[c_11196,c_11852]) ).
cnf(c_12099,plain,
( g_false_only(X0,X1)
| g_true_only(X0,X1)
| g_both(X0,X1) ),
inference(resolution,[status(thm)],[c_9521,c_3864]) ).
cnf(c_12282,plain,
( g_false_only(sK10(sK11),sK11)
| g_both(sK10(sK11),sK11) ),
inference(equality_factoring,[status(thm)],[c_11854]) ).
cnf(c_12341,plain,
( ~ g_true_only(sK8(sK10(sK11),X0),sK10(sK11))
| ~ g_both(sK8(sK10(sK11),X0),sK11) ),
inference(instantiation,[status(thm)],[c_10704]) ).
cnf(c_12385,plain,
( ~ g_true_only(sK8(sK10(sK11),sK11),sK10(sK11))
| ~ g_false(sK8(sK10(sK11),sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_10705]) ).
cnf(c_12469,plain,
( ~ g_true_only(X0,X0)
| g_false_only(X0,sK11)
| g_true_only(X0,sK11) ),
inference(resolution,[status(thm)],[c_90,c_12099]) ).
cnf(c_12531,plain,
( ~ g_true_only(X0,sK11)
| g_false_only(X0,X0)
| g_true_only(X0,X0) ),
inference(resolution,[status(thm)],[c_92,c_12099]) ).
cnf(c_12649,plain,
( g_true(sK10(X0),X0)
| g_false_only(sK10(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_11178,c_9224]) ).
cnf(c_12650,plain,
( g_false_only(sK10(X0),X0)
| g_true(sK10(X0),X0) ),
inference(renaming,[status(thm)],[c_12649]) ).
cnf(c_12652,plain,
( ~ g_false(sK10(X0),X0)
| ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_12650,c_7445]) ).
cnf(c_12710,plain,
( ~ g_false_only(sK8(sK10(sK11),sK11),sK10(sK11))
| ~ g_both(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7946]) ).
cnf(c_12867,plain,
( g_false_only(sK7(sK11),sK7(sK11))
| g_true(sK7(sK11),sK7(sK11)) ),
inference(instantiation,[status(thm)],[c_7996]) ).
cnf(c_12868,plain,
( ~ g_both(sK7(sK11),sK7(sK11))
| g_true(sK7(sK11),sK7(sK11)) ),
inference(instantiation,[status(thm)],[c_8051]) ).
cnf(c_12879,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| g_true_only(sK10(X0),X0)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_3864,c_12652]) ).
cnf(c_12888,plain,
( ~ g_true_only(sK7(sK11),sK7(sK11))
| ~ g_both(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_8640]) ).
cnf(c_13048,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(sK11),sK11)
| g_false(sK10(sK11),sK11)
| sP0(sK11) ),
inference(superposition,[status(thm)],[c_12879,c_11021]) ).
cnf(c_13076,plain,
g_false(sK10(sK11),sK11),
inference(global_subsumption_just,[status(thm)],[c_13048,c_9038,c_10541,c_10961,c_12282]) ).
cnf(c_13195,plain,
( ~ g_both(X0,sK10(X1))
| ~ g_both(X0,sK11)
| ~ sP0(sK10(X1))
| g_false_only(sK8(sK10(X1),sK11),sK10(X1))
| g_true_only(sK8(sK10(X1),sK11),sK10(X1))
| g_false_only(sK8(sK10(X1),sK11),sK11)
| g_true_only(sK8(sK10(X1),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7495]) ).
cnf(c_13306,plain,
( ~ g_both(X0,sK10(sK11))
| ~ g_both(X0,sK11)
| ~ sP0(sK10(sK11))
| g_false_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_both(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true_only(sK8(sK10(sK11),sK11),sK11)
| g_both(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10724]) ).
cnf(c_13539,plain,
( g_true_only(sK10(sK11),sK10(sK11))
| g_false(sK10(sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_7769]) ).
cnf(c_13558,plain,
( ~ g_true_only(X0,X0)
| g_true_only(X0,sK11) ),
inference(global_subsumption_just,[status(thm)],[c_12469,c_88,c_12469]) ).
cnf(c_13571,plain,
( ~ sP2_iProver_def
| g_false_only(X0,X0)
| g_true_only(X0,sK11)
| sP0(X0) ),
inference(resolution,[status(thm)],[c_13558,c_8635]) ).
cnf(c_13792,plain,
( ~ g_true_only(X0,sK11)
| g_true_only(X0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_12531,c_91,c_12531]) ).
cnf(c_14433,plain,
( g_false_only(X0,sK10(X1))
| g_true_only(X0,sK10(X1))
| g_true(X0,X1) ),
inference(resolution,[status(thm)],[c_3889,c_12099]) ).
cnf(c_15328,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(sK11),sK10(sK11))
| g_false_only(sK10(sK11),sK11)
| sP0(sK10(sK11)) ),
inference(resolution,[status(thm)],[c_13571,c_9667]) ).
cnf(c_15396,plain,
( g_true_only(X0,sK10(X1))
| g_true(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_14433,c_199,c_14433]) ).
cnf(c_15410,plain,
( ~ g_false_only(sK10(X0),sK11)
| g_true(sK10(X0),X0) ),
inference(resolution,[status(thm)],[c_15396,c_88]) ).
cnf(c_15479,plain,
( ~ g_false(sK10(X0),X0)
| ~ g_false_only(sK10(X0),sK11)
| ~ sP2_iProver_def
| sP0(X0) ),
inference(resolution,[status(thm)],[c_15410,c_7445]) ).
cnf(c_15481,plain,
( ~ g_false(sK10(X0),X0)
| ~ g_false_only(sK10(X0),sK11)
| g_both(sK10(X0),X0) ),
inference(resolution,[status(thm)],[c_15410,c_96]) ).
cnf(c_15603,plain,
( ~ g_false(sK10(X0),X0)
| ~ g_false_only(sK10(X0),sK11) ),
inference(global_subsumption_just,[status(thm)],[c_15479,c_11254,c_15481]) ).
cnf(c_15614,plain,
( ~ g_false_only(sK10(X0),sK11)
| g_true_only(sK10(X0),X0) ),
inference(resolution,[status(thm)],[c_15603,c_3864]) ).
cnf(c_15860,plain,
( ~ g_false_only(sK10(sK11),sK10(sK11))
| ~ g_false_only(sK10(sK11),sK11) ),
inference(resolution,[status(thm)],[c_15614,c_91]) ).
cnf(c_15861,plain,
( ~ g_false_only(sK10(sK11),sK11)
| g_true_only(sK10(sK11),sK10(sK11)) ),
inference(resolution,[status(thm)],[c_15614,c_13792]) ).
cnf(c_16124,plain,
~ g_false_only(sK10(sK11),sK11),
inference(global_subsumption_just,[status(thm)],[c_15860,c_10960,c_15861]) ).
cnf(c_16148,plain,
( ~ g_both(sK10(sK11),sK10(sK11))
| ~ g_both(sK10(sK11),sK11)
| ~ sP0(sK10(sK11))
| g_true_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_both(sK8(sK10(sK11),sK11),sK10(sK11))
| g_false_only(sK8(sK10(sK11),sK11),sK11)
| g_both(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10570]) ).
cnf(c_16219,plain,
( ~ g_false(X0,X1)
| ~ sP2_iProver_def
| g_false_only(X0,X1)
| sP0(X1) ),
inference(superposition,[status(thm)],[c_3860,c_7445]) ).
cnf(c_16241,plain,
( ~ sP2_iProver_def
| g_false_only(X0,X1)
| g_true_only(X0,X1)
| sP0(X1) ),
inference(superposition,[status(thm)],[c_3864,c_16219]) ).
cnf(c_16246,plain,
( ~ sP2_iProver_def
| g_false_only(X0,sK10(X1))
| g_false(X0,X1)
| sP0(sK10(X1)) ),
inference(superposition,[status(thm)],[c_16241,c_3895]) ).
cnf(c_16249,plain,
( ~ g_false(X0,X1)
| g_false_only(X0,X1)
| g_both(X0,X1) ),
inference(superposition,[status(thm)],[c_3860,c_96]) ).
cnf(c_16262,plain,
( ~ sP2
| g_both(sK6(sK10(X0)),sK10(X0))
| g_true(sK6(sK10(X0)),X0)
| g_true_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_59,c_3887]) ).
cnf(c_16267,plain,
( g_false(X0,X1)
| g_false_only(X0,sK10(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_16246,c_9649]) ).
cnf(c_16268,plain,
( g_false_only(X0,sK10(X1))
| g_false(X0,X1) ),
inference(renaming,[status(thm)],[c_16267]) ).
cnf(c_16269,plain,
( ~ g_true_only(sK10(X0),sK11)
| g_false(sK10(X0),X0) ),
inference(superposition,[status(thm)],[c_16268,c_91]) ).
cnf(c_16277,plain,
( ~ sP2_iProver_def
| g_false(sK10(X0),X0)
| g_false_only(sK10(X0),sK11)
| sP0(sK11) ),
inference(superposition,[status(thm)],[c_16241,c_16269]) ).
cnf(c_16295,plain,
( g_false_only(sK10(X0),sK11)
| g_false(sK10(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_16277,c_9660]) ).
cnf(c_16296,plain,
( g_false(sK10(X0),X0)
| g_false_only(sK10(X0),sK11) ),
inference(renaming,[status(thm)],[c_16295]) ).
cnf(c_16297,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| g_false_only(sK10(X0),sK11)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_16296,c_16219]) ).
cnf(c_16306,plain,
( ~ g_true_only(sK10(X0),sK10(X0))
| ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_16297,c_88]) ).
cnf(c_16313,plain,
( g_false_only(sK10(X0),X0)
| ~ g_true_only(sK10(X0),sK10(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_16306,c_11160]) ).
cnf(c_16314,plain,
( ~ g_true_only(sK10(X0),sK10(X0))
| g_false_only(sK10(X0),X0) ),
inference(renaming,[status(thm)],[c_16313]) ).
cnf(c_16315,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(X0),sK10(X0))
| g_false_only(sK10(X0),X0)
| sP0(sK10(X0)) ),
inference(superposition,[status(thm)],[c_16241,c_16314]) ).
cnf(c_16322,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| g_true(sK10(X0),X0)
| sP0(sK10(X0)) ),
inference(superposition,[status(thm)],[c_16315,c_3887]) ).
cnf(c_16337,plain,
( g_true(sK10(X0),X0)
| g_false_only(sK10(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_16322,c_9224]) ).
cnf(c_16338,plain,
( g_false_only(sK10(X0),X0)
| g_true(sK10(X0),X0) ),
inference(renaming,[status(thm)],[c_16337]) ).
cnf(c_16340,plain,
( ~ g_false(sK10(X0),X0)
| ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_16338,c_7445]) ).
cnf(c_16353,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(X0),X0)
| g_true_only(sK10(X0),X0)
| sP0(X0) ),
inference(superposition,[status(thm)],[c_3864,c_16340]) ).
cnf(c_16361,plain,
( ~ sP2_iProver_def
| g_false_only(sK10(sK11),sK11)
| g_false(sK10(sK11),sK11)
| sP0(sK11) ),
inference(superposition,[status(thm)],[c_16353,c_16269]) ).
cnf(c_16364,plain,
g_false(sK10(sK11),sK11),
inference(global_subsumption_just,[status(thm)],[c_16361,c_13076]) ).
cnf(c_16437,plain,
( g_false_only(sK10(sK11),sK11)
| g_both(sK10(sK11),sK11) ),
inference(superposition,[status(thm)],[c_16364,c_16249]) ).
cnf(c_16447,plain,
g_both(sK10(sK11),sK11),
inference(global_subsumption_just,[status(thm)],[c_16437,c_12282,c_16124]) ).
cnf(c_16452,plain,
( ~ g_both(sK10(sK11),sK10(sK11))
| ~ sP1
| g_false_only(sK7(sK11),sK7(sK11))
| g_both(sK7(sK11),sK7(sK11))
| g_false_only(sK7(sK11),sK11)
| g_both(sK7(sK11),sK11) ),
inference(superposition,[status(thm)],[c_16447,c_67]) ).
cnf(c_16453,plain,
( ~ g_both(sK10(sK11),sK10(sK11))
| ~ sP1
| g_false_only(sK7(sK11),sK7(sK11))
| g_true_only(sK7(sK11),sK7(sK11))
| g_false_only(sK7(sK11),sK11)
| g_true_only(sK7(sK11),sK11) ),
inference(superposition,[status(thm)],[c_16447,c_66]) ).
cnf(c_16454,plain,
( ~ g_both(sK10(sK11),sK10(sK11))
| ~ sP1
| g_true_only(sK7(sK11),sK7(sK11))
| g_both(sK7(sK11),sK7(sK11))
| g_true_only(sK7(sK11),sK11)
| g_both(sK7(sK11),sK11) ),
inference(superposition,[status(thm)],[c_16447,c_64]) ).
cnf(c_16457,plain,
( ~ g_both(sK10(sK11),sK10(sK11))
| ~ sP1
| g_false_only(sK7(sK11),sK7(sK11))
| g_true_only(sK7(sK11),sK7(sK11))
| g_both(sK7(sK11),sK7(sK11)) ),
inference(superposition,[status(thm)],[c_16447,c_61]) ).
cnf(c_16458,plain,
( ~ g_both(sK10(sK11),sK10(sK11))
| ~ sP1
| g_false_only(sK7(sK11),sK11)
| g_true_only(sK7(sK11),sK11)
| g_both(sK7(sK11),sK11) ),
inference(superposition,[status(thm)],[c_16447,c_68]) ).
cnf(c_16821,plain,
( ~ sP2
| g_true(sK6(sK10(X0)),X0)
| g_true_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(global_subsumption_just,[status(thm)],[c_16262,c_8971,c_10381,c_11109]) ).
cnf(c_16824,plain,
( ~ g_false(sK6(sK10(X0)),X0)
| ~ sP2
| g_both(sK6(sK10(X0)),X0)
| g_true_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_16821,c_96]) ).
cnf(c_16836,plain,
( ~ sP2
| g_true_only(sK6(sK10(X0)),X0)
| g_both(sK6(sK10(X0)),X0)
| g_true_only(sK6(sK10(X0)),sK5)
| g_both(sK6(sK10(X0)),sK5) ),
inference(superposition,[status(thm)],[c_3864,c_16824]) ).
cnf(c_16841,plain,
( ~ sP2
| g_true_only(sK6(sK10(sK5)),sK5)
| g_both(sK6(sK10(sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_16836]) ).
cnf(c_17472,plain,
( ~ g_false_only(sK7(sK11),sK7(sK11))
| ~ g_both(sK7(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_89]) ).
cnf(c_17475,plain,
( ~ g_false_only(sK7(sK11),sK7(sK11))
| ~ g_true(sK7(sK11),sK7(sK11)) ),
inference(instantiation,[status(thm)],[c_7652]) ).
cnf(c_17613,plain,
( ~ g_both(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10419]) ).
cnf(c_17713,plain,
( g_false_only(sK8(sK10(sK11),sK11),sK11)
| g_true(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_10426]) ).
cnf(c_17764,plain,
( ~ g_both(sK8(sK10(X0),X1),X0)
| g_true(sK8(sK10(X0),X1),X0) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_17870,plain,
( g_false(sK8(sK10(sK11),sK11),sK11)
| g_true(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7676]) ).
cnf(c_17914,plain,
( ~ g_true_only(sK8(sK10(sK11),X0),sK10(sK11))
| g_false(sK8(sK10(sK11),X0),sK11) ),
inference(instantiation,[status(thm)],[c_10706]) ).
cnf(c_18886,plain,
( ~ g_both(X0,sK10(sK11))
| ~ g_both(X0,sK11)
| ~ sP0(sK10(sK11))
| g_false_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_false_only(sK8(sK10(sK11),sK11),sK11)
| g_true_only(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_13195]) ).
cnf(c_19346,plain,
( g_false_only(sK10(sK11),sK10(sK11))
| g_true(sK10(sK11),sK10(sK11)) ),
inference(instantiation,[status(thm)],[c_7575]) ).
cnf(c_21096,plain,
( ~ g_true_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_false(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_17914]) ).
cnf(c_21877,plain,
( g_false_only(sK7(sK11),sK11)
| g_true_only(sK7(sK11),sK11)
| g_both(sK7(sK11),sK11) ),
inference(global_subsumption_just,[status(thm)],[c_16458,c_7502,c_8376,c_8928]) ).
cnf(c_21879,plain,
( ~ g_false(sK7(sK11),sK11)
| g_false_only(sK7(sK11),sK11)
| g_both(sK7(sK11),sK11) ),
inference(superposition,[status(thm)],[c_21877,c_94]) ).
cnf(c_22223,plain,
( ~ g_true_only(sK10(sK11),sK10(sK11))
| ~ g_both(sK10(sK11),sK11) ),
inference(instantiation,[status(thm)],[c_7985]) ).
cnf(c_23055,plain,
( ~ g_both(sK8(sK10(sK11),sK11),sK11)
| g_true(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_17764]) ).
cnf(c_23062,plain,
( ~ g_true_only(sK8(sK10(sK11),sK11),sK10(sK11))
| ~ g_both(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_12341]) ).
cnf(c_24771,plain,
( ~ g_both(sK10(sK11),sK10(sK11))
| ~ g_both(sK10(sK11),sK11)
| ~ sP0(sK10(sK11))
| g_false_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_both(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true_only(sK8(sK10(sK11),sK11),sK11)
| g_both(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_13306]) ).
cnf(c_24981,plain,
( ~ g_both(sK10(sK11),sK10(sK11))
| ~ g_both(sK10(sK11),sK11)
| ~ sP0(sK10(sK11))
| g_false_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_true_only(sK8(sK10(sK11),sK11),sK10(sK11))
| g_false_only(sK8(sK10(sK11),sK11),sK11)
| g_true_only(sK8(sK10(sK11),sK11),sK11) ),
inference(instantiation,[status(thm)],[c_18886]) ).
cnf(c_24982,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24981,c_24771,c_23062,c_23055,c_22223,c_21879,c_21096,c_19346,c_17870,c_17713,c_17613,c_17475,c_17472,c_16841,c_16452,c_16453,c_16454,c_16457,c_16148,c_16124,c_15328,c_13539,c_12888,c_12867,c_12868,c_12710,c_12385,c_12282,c_11799,c_11382,c_11362,c_11063,c_10857,c_10428,c_10386,c_10383,c_10342,c_10255,c_9788,c_9593,c_9341,c_9258,c_9049,c_8928,c_8859,c_8625,c_8431,c_8231,c_8203,c_8139,c_8113,c_8059,c_8053,c_8035,c_7951,c_7701,c_7665,c_7630,c_7465,c_7455,c_7446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO605+1 : TPTP v8.1.2. Released v7.0.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 20:03:29 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.80/2.15 % SZS status Started for theBenchmark.p
% 9.80/2.15 % SZS status Theorem for theBenchmark.p
% 9.80/2.15
% 9.80/2.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 9.80/2.15
% 9.80/2.15 ------ iProver source info
% 9.80/2.15
% 9.80/2.15 git: date: 2024-05-02 19:28:25 +0000
% 9.80/2.15 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 9.80/2.15 git: non_committed_changes: false
% 9.80/2.15
% 9.80/2.15 ------ Parsing...
% 9.80/2.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.80/2.15
% 9.80/2.15 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 9.80/2.15
% 9.80/2.15 ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.80/2.15 ------ Proving...
% 9.80/2.15 ------ Problem Properties
% 9.80/2.15
% 9.80/2.15
% 9.80/2.15 clauses 47
% 9.80/2.15 conjectures 16
% 9.80/2.15 EPR 23
% 9.80/2.15 Horn 18
% 9.80/2.15 unary 0
% 9.80/2.15 binary 19
% 9.80/2.15 lits 174
% 9.80/2.15 lits eq 0
% 9.80/2.15 fd_pure 0
% 9.80/2.15 fd_pseudo 0
% 9.80/2.15 fd_cond 0
% 9.80/2.15 fd_pseudo_cond 0
% 9.80/2.15 AC symbols 0
% 9.80/2.15
% 9.80/2.15 ------ Input Options Time Limit: Unbounded
% 9.80/2.15
% 9.80/2.15
% 9.80/2.15 ------
% 9.80/2.15 Current options:
% 9.80/2.15 ------
% 9.80/2.15
% 9.80/2.15
% 9.80/2.15
% 9.80/2.15
% 9.80/2.15 ------ Proving...
% 9.80/2.15
% 9.80/2.15
% 9.80/2.15 % SZS status Theorem for theBenchmark.p
% 9.80/2.15
% 9.80/2.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.80/2.16
% 9.80/2.16
%------------------------------------------------------------------------------