%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO604+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 : Thu Sep 24 03:42:48 PM UTC 2026
% Result : Theorem 153.23s 29.84s
% Output : CNFRefutation 153.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 15
% Syntax : Number of formulae : 225 ( 13 unt; 11 def)
% Number of atoms : 1171 ( 0 equ)
% Maximal formula atoms : 59 ( 5 avg)
% Number of connectives : 1535 ( 589 ~; 632 |; 296 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 2 con; 0-2 aty)
% Number of variables : 578 ( 474 !; 104 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ~ ? [A] :
! [B] :
( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& g_false_only(B,A) )
| ( ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) )
& g_true_only(B,A) ) )
& ? [A] :
( ~ ? [B] :
( ( ( ( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) )
& g_true_only(B,A) ) )
& ? [B] :
( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
& g_both(B,A) ) ) )
| ! [A] :
? [B] :
( ( ( ( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) )
& g_true_only(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [A] :
! [B] :
( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& g_false_only(B,A) )
| ( ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) )
& g_true_only(B,A) ) )
& ? [A] :
( ~ ? [B] :
( ( ( ( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) )
& g_true_only(B,A) ) )
& ? [B] :
( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
& g_both(B,A) ) ) )
| ! [A] :
? [B] :
( ( ( ( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ( ~ ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) )
& g_true_only(B,A) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [X_2,X_1] :
( g_both(X_2,X_1)
<=> ( g_false(X_2,X_1)
& g_true(X_2,X_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X_2,X_1] :
( g_false_only(X_2,X_1)
<=> ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X_2,X_1] :
( g_false_only(X_2,X_1)
| g_both(X_2,X_1)
| g_true_only(X_2,X_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
( ( ? [A] :
! [B] :
( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& g_false_only(B,A) )
| ( ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) )
& g_true_only(B,A) ) )
| ! [A] :
( ? [B] :
( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) )
& g_true_only(B,A) ) )
| ! [B] :
( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) ) )
| ~ g_both(B,A) ) ) )
& ? [A] :
! [B] :
( ( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) ) ) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_false_only(B,A) )
& ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_both(B,A) )
& ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) ) ) ) )
| ~ g_true_only(B,A) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f8,definition,
! [B,C] :
( sP0_prd(C,B)
<=> ( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f9,definition,
! [B,C] :
( sP1_prd(C,B)
<=> ( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f10,definition,
! [B,C] :
( sP2_prd(C,B)
<=> ( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f11,definition,
! [B,C] :
( sP3_prd(C,B)
<=> ( g_true_only(C,B)
& g_true_only(B,C) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f12,definition,
! [A,B] :
( sP4_prd(B,A)
<=> ( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) )
& g_true_only(B,A) ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f13,definition,
! [A,B] :
( sP5_prd(B,A)
<=> ( ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) )
& g_true_only(B,A) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f14,plain,
( ( ? [A] :
! [B] :
( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& g_false_only(B,A) )
| sP5_prd(B,A) )
| ! [A] :
( ? [B] : sP4_prd(B,A)
| ! [B] :
( ? [C] : sP3_prd(C,B)
| ! [C] : sP2_prd(C,B)
| ~ g_both(B,A) ) ) )
& ? [A] :
! [B] :
( ( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] : sP1_prd(C,B) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_false_only(B,A) )
& ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_both(B,A) )
& ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] : sP0_prd(C,B) ) )
| ~ g_true_only(B,A) ) ) ),
inference(formula_renaming,[status(thm)],[f7,f13,f12,f11,f10,f9,f8]) ).
fof(f15,plain,
( ( ? [A] :
! [B] :
( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
& g_false_only(B,A) )
| sP5_prd(B,A) )
| ! [A] :
( ? [B] : sP4_prd(B,A)
| ! [B] :
( ? [C] : sP3_prd(C,B)
| ! [C] : sP2_prd(C,B)
| ~ g_both(B,A) ) ) )
& ? [A] :
( ! [B] :
( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] : sP1_prd(C,B) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_false_only(B,A) )
& ! [B] :
( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_both(B,A) )
& ! [B] :
( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] : sP0_prd(C,B) ) )
| ~ g_true_only(B,A) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
( ( ! [B] :
( ( g_true_only(sK8_skl(B),B)
& g_true_only(B,sK8_skl(B))
& g_false_only(B,sK7_skl) )
| sP5_prd(B,sK7_skl) )
| ! [A] :
( sP4_prd(sK6_skl(A),A)
| ! [B] :
( sP3_prd(sK5_skl(B,A),B)
| ! [C] : sP2_prd(C,B)
| ~ g_both(B,A) ) ) )
& ! [B] :
( ( ( ( g_true_only(sK4_skl(B),B)
& g_true_only(B,sK4_skl(B)) )
| ! [C] : sP1_prd(C,B) )
& ~ g_false_only(sK3_skl(B),B)
& ~ g_false_only(B,sK3_skl(B)) )
| ~ g_false_only(B,sK0_skl) )
& ! [B] :
( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ~ g_false_only(sK2_skl(B),B)
& ~ g_false_only(B,sK2_skl(B)) )
| ~ g_both(B,sK0_skl) )
& ! [B] :
( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ( ( g_true_only(sK1_skl(B),B)
& g_true_only(B,sK1_skl(B)) )
| ! [C] : sP0_prd(C,B) ) )
| ~ g_true_only(B,sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK0_skl),skolemize(C,sK1_skl(B)),skolemize(C,sK2_skl(B)),skolemize(C,sK3_skl(B)),skolemize(C,sK4_skl(B)),skolemize(C,sK5_skl(B,A)),skolemize(B,sK6_skl(A)),skolemize(A,sK7_skl),skolemize(C,sK8_skl(B))],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( sP0_prd(X1,X0)
| ~ g_true_only(X0,sK0_skl)
| g_true_only(X0,sK1_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ g_true_only(X1,sK0_skl)
| g_true_only(sK1_skl(X1),X1)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( ~ g_true_only(X1,X0)
| ~ g_true_only(X1,sK0_skl)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [X0] :
( ~ g_both(X0,sK0_skl)
| ~ g_false_only(X0,sK2_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f21,plain,
! [X0] :
( ~ g_both(X0,sK0_skl)
| ~ g_false_only(sK2_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f22,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| ~ g_true_only(X1,X0)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f23,plain,
! [X0] :
( ~ g_false_only(X0,sK0_skl)
| ~ g_false_only(X0,sK3_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f24,plain,
! [X0] :
( ~ g_false_only(X0,sK0_skl)
| ~ g_false_only(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f25,plain,
! [X0,X1] :
( ~ g_false_only(X1,sK0_skl)
| g_true_only(X1,sK4_skl(X1))
| sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f26,plain,
! [X0,X1] :
( g_true_only(sK4_skl(X0),X0)
| sP1_prd(X1,X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( sP5_prd(X3,sK7_skl)
| sP4_prd(sK6_skl(X1),X1)
| g_true_only(X3,sK8_skl(X3))
| sP2_prd(X2,X0)
| sP3_prd(sK5_skl(X0,X1),X0)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( sP3_prd(sK5_skl(X1,X2),X1)
| sP4_prd(sK6_skl(X2),X2)
| sP5_prd(X0,sK7_skl)
| sP2_prd(X3,X1)
| ~ g_both(X1,X2)
| g_true_only(sK8_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
! [X_2,X_1] :
( ( ~ g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_both(X_2,X_1) )
& ( ( g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_both(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
( ! [X_2,X_1] :
( ~ g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_both(X_2,X_1) )
& ! [X_2,X_1] :
( ( g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_both(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
! [X_2,X_1] :
( ( g_true(X_2,X_1)
| ~ g_false(X_2,X_1)
| g_false_only(X_2,X_1) )
& ( ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) )
| ~ g_false_only(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f41,plain,
( ! [X_2,X_1] :
( g_true(X_2,X_1)
| ~ g_false(X_2,X_1)
| g_false_only(X_2,X_1) )
& ! [X_2,X_1] :
( ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) )
| ~ g_false_only(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( g_both(X0,X1)
| g_false_only(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
! [B,C] :
( ( ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
| sP0_prd(C,B) )
& ( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) )
| ~ sP0_prd(C,B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f47,plain,
( ! [B,C] :
( ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
| sP0_prd(C,B) )
& ! [B,C] :
( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) )
| ~ sP0_prd(C,B) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sP0_prd(X1,X0)
| g_false_only(X1,X0)
| g_false_only(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_false_only(X1,X0)
| ~ g_both(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0,X1] :
( sP0_prd(X1,X0)
| g_both(X1,X0)
| g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f53,plain,
! [B,C] :
( ( ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
| sP1_prd(C,B) )
& ( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) )
| ~ sP1_prd(C,B) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f54,plain,
( ! [B,C] :
( ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
| sP1_prd(C,B) )
& ! [B,C] :
( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) )
| ~ sP1_prd(C,B) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ~ g_both(X1,X0)
| g_false_only(X1,X0)
| ~ sP1_prd(X0,X1)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( g_false_only(X1,X0)
| ~ g_both(X1,X0)
| ~ sP1_prd(X1,X0)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
! [X0,X1] :
( g_both(X1,X0)
| sP1_prd(X1,X0)
| g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f60,plain,
! [B,C] :
( ( ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
| sP2_prd(C,B) )
& ( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) )
| ~ sP2_prd(C,B) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f61,plain,
( ! [B,C] :
( ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
| sP2_prd(C,B) )
& ! [B,C] :
( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) )
| ~ sP2_prd(C,B) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| ~ g_both(X0,X1)
| g_false_only(X1,X0)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f67,plain,
! [B,C] :
( ( ~ g_true_only(C,B)
| ~ g_true_only(B,C)
| sP3_prd(C,B) )
& ( ( g_true_only(C,B)
& g_true_only(B,C) )
| ~ sP3_prd(C,B) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f68,plain,
( ! [B,C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C)
| sP3_prd(C,B) )
& ! [B,C] :
( ( g_true_only(C,B)
& g_true_only(B,C) )
| ~ sP3_prd(C,B) ) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( g_true_only(X1,X0)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( g_true_only(X0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f71,plain,
! [X0,X1] :
( sP3_prd(X0,X1)
| ~ g_true_only(X1,X0)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f72,definition,
! [A,B] :
( sP6_prd(B,A)
<=> ( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) )
& g_true_only(B,A) ) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f73,plain,
! [A,B] :
( sP4_prd(B,A)
<=> ( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| sP6_prd(B,A) ) ),
inference(formula_renaming,[status(thm)],[f12,f72]) ).
fof(f74,definition,
! [B,C] :
( sP7_prd(C,B)
<=> ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f75,plain,
! [A,B] :
( sP4_prd(B,A)
<=> ( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] : sP7_prd(C,B) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| sP6_prd(B,A) ) ),
inference(formula_renaming,[status(thm)],[f73,f74]) ).
fof(f76,plain,
! [A,B] :
( ( ( ( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] : ~ sP7_prd(C,B) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_false_only(B,A) )
& ~ sP6_prd(B,A) )
| sP4_prd(B,A) )
& ( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] : sP7_prd(C,B) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| sP6_prd(B,A)
| ~ sP4_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
( ! [A,B] :
( ( ( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] : ~ sP7_prd(C,B) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_false_only(B,A) )
& ~ sP6_prd(B,A) )
| sP4_prd(B,A) )
& ! [A,B] :
( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] : sP7_prd(C,B) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| sP6_prd(B,A)
| ~ sP4_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f78,plain,
( ! [A,B] :
( ( ( ( ( ( g_true_only(sK11_skl(B,A),B)
& g_true_only(B,sK11_skl(B,A)) )
| ! [C] : ~ sP7_prd(C,B) )
& ~ g_false_only(sK10_skl(B,A),B)
& ~ g_false_only(B,sK10_skl(B,A)) )
| ~ g_false_only(B,A) )
& ~ sP6_prd(B,A) )
| sP4_prd(B,A) )
& ! [A,B] :
( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& sP7_prd(sK9_skl(B,A),B) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_false_only(B,A) )
| sP6_prd(B,A)
| ~ sP4_prd(B,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(C,sK9_skl(B,A)),skolemize(C,sK10_skl(B,A)),skolemize(C,sK11_skl(B,A))],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ~ sP4_prd(X0,X1)
| g_false_only(X0,X1)
| sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( g_false_only(X1,X0)
| ~ g_true_only(X1,X2)
| ~ sP4_prd(X1,X3)
| sP6_prd(X1,X3)
| ~ g_true_only(X2,X1)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f87,plain,
! [A,B] :
( ( ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) )
| ~ g_true_only(B,A)
| sP5_prd(B,A) )
& ( ( ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) )
& g_true_only(B,A) )
| ~ sP5_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f88,plain,
( ! [A,B] :
( ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) )
| ~ g_true_only(B,A)
| sP5_prd(B,A) )
& ! [A,B] :
( ( ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) )
& g_true_only(B,A) )
| ~ sP5_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f89,plain,
( ! [A,B] :
( ( ~ g_false_only(sK12_skl(B,A),B)
& ~ g_false_only(B,sK12_skl(B,A)) )
| ~ g_true_only(B,A)
| sP5_prd(B,A) )
& ! [A,B] :
( ( ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) )
& g_true_only(B,A) )
| ~ sP5_prd(B,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(C,sK12_skl(B,A))],[f88]) ).
fof(f91,plain,
! [X0,X1,X2] :
( g_false_only(X0,X2)
| g_false_only(X2,X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f94,definition,
! [B] :
( sP8_prd(B)
<=> ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f95,plain,
! [A,B] :
( sP6_prd(B,A)
<=> ( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( sP8_prd(B)
& g_true_only(B,A) ) ) ),
inference(formula_renaming,[status(thm)],[f72,f94]) ).
fof(f96,plain,
! [A,B] :
( ( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_both(B,A) )
& ( ~ sP8_prd(B)
| ~ g_true_only(B,A) ) )
| sP6_prd(B,A) )
& ( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( sP8_prd(B)
& g_true_only(B,A) )
| ~ sP6_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
( ! [A,B] :
( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C) ) )
| ~ g_both(B,A) )
& ( ~ sP8_prd(B)
| ~ g_true_only(B,A) ) )
| sP6_prd(B,A) )
& ! [A,B] :
( ( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( sP8_prd(B)
& g_true_only(B,A) )
| ~ sP6_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
( ! [A,B] :
( ( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ~ g_false_only(sK14_skl(B,A),B)
& ~ g_false_only(B,sK14_skl(B,A)) )
| ~ g_both(B,A) )
& ( ~ sP8_prd(B)
| ~ g_true_only(B,A) ) )
| sP6_prd(B,A) )
& ! [A,B] :
( ( ( ( g_true_only(sK13_skl(B,A),B)
& g_true_only(B,sK13_skl(B,A)) )
| ! [C] :
( g_false_only(C,B)
| g_false_only(B,C) ) )
& g_both(B,A) )
| ( sP8_prd(B)
& g_true_only(B,A) )
| ~ sP6_prd(B,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(C,sK13_skl(B,A)),skolemize(C,sK14_skl(B,A))],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ sP6_prd(X0,X1)
| g_true_only(X0,X1)
| g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( g_true_only(X0,X2)
| g_true_only(X0,sK13_skl(X0,X2))
| g_false_only(X1,X0)
| ~ sP6_prd(X0,X2)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1,X2] :
( g_true_only(sK13_skl(X0,X1),X0)
| g_false_only(X2,X0)
| ~ sP6_prd(X0,X1)
| g_false_only(X0,X2)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f102,plain,
! [X0,X1] :
( g_both(X0,X1)
| sP8_prd(X0)
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f103,plain,
! [X0,X1,X2] :
( sP8_prd(X0)
| ~ sP6_prd(X0,X2)
| g_true_only(X0,sK13_skl(X0,X2))
| g_false_only(X1,X0)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f104,plain,
! [X0,X1,X2] :
( g_false_only(X1,X0)
| sP8_prd(X1)
| ~ sP6_prd(X1,X2)
| g_true_only(sK13_skl(X1,X2),X1)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f116,definition,
! [B] :
( sP9_prd(B)
<=> ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] :
( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f117,plain,
! [B] :
( sP8_prd(B)
<=> ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| sP9_prd(B) ) ),
inference(formula_renaming,[status(thm)],[f94,f116]) ).
fof(f118,plain,
! [B] :
( ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ~ sP9_prd(B) )
| sP8_prd(B) )
& ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| sP9_prd(B)
| ~ sP8_prd(B) ) ),
inference(NNF_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
( ! [B] :
( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ~ sP9_prd(B) )
| sP8_prd(B) )
& ! [B] :
( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| sP9_prd(B)
| ~ sP8_prd(B) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
( ! [B] :
( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ~ sP9_prd(B) )
| sP8_prd(B) )
& ! [B] :
( ( g_true_only(sK15_skl(B),B)
& g_true_only(B,sK15_skl(B)) )
| sP9_prd(B)
| ~ sP8_prd(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(C,sK15_skl(B))],[f119]) ).
fof(f121,plain,
! [X0] :
( ~ sP8_prd(X0)
| sP9_prd(X0)
| g_true_only(X0,sK15_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [X0] :
( g_true_only(sK15_skl(X0),X0)
| ~ sP8_prd(X0)
| sP9_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f125,definition,
! [B,C] :
( sP10_prd(C,B)
<=> ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f126,plain,
! [B] :
( sP9_prd(B)
<=> ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] : sP10_prd(C,B) ) ),
inference(formula_renaming,[status(thm)],[f116,f125]) ).
fof(f127,plain,
! [B] :
( ( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] : ~ sP10_prd(C,B)
| sP9_prd(B) )
& ( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] : sP10_prd(C,B) )
| ~ sP9_prd(B) ) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
( ! [B] :
( ? [C] :
( g_true_only(C,B)
& g_true_only(B,C) )
| ! [C] : ~ sP10_prd(C,B)
| sP9_prd(B) )
& ! [B] :
( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& ? [C] : sP10_prd(C,B) )
| ~ sP9_prd(B) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ! [B] :
( ( g_true_only(sK17_skl(B),B)
& g_true_only(B,sK17_skl(B)) )
| ! [C] : ~ sP10_prd(C,B)
| sP9_prd(B) )
& ! [B] :
( ( ! [C] :
( ~ g_true_only(C,B)
| ~ g_true_only(B,C) )
& sP10_prd(sK16_skl(B),B) )
| ~ sP9_prd(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl]),skolemize(C,sK16_skl(B)),skolemize(C,sK17_skl(B))],[f128]) ).
fof(f130,plain,
! [X0] :
( sP10_prd(sK16_skl(X0),X0)
| ~ sP9_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ~ g_true_only(X1,X0)
| ~ sP9_prd(X0)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
! [X0,X1] :
( g_true_only(X1,sK17_skl(X1))
| sP9_prd(X1)
| ~ sP10_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
! [X0,X1] :
( g_true_only(sK17_skl(X0),X0)
| ~ sP10_prd(X1,X0)
| sP9_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f134,plain,
! [B,C] :
( ( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) )
| sP10_prd(C,B) )
& ( ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
| ~ sP10_prd(C,B) ) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f135,plain,
( ! [B,C] :
( g_false_only(C,B)
| g_false_only(B,C)
| ( ~ g_both(C,B)
& ~ g_both(B,C) )
| sP10_prd(C,B) )
& ! [B,C] :
( ( ~ g_false_only(C,B)
& ~ g_false_only(B,C)
& ( g_both(C,B)
| g_both(B,C) ) )
| ~ sP10_prd(C,B) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( g_both(X1,X0)
| ~ sP10_prd(X1,X0)
| g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sP10_prd(X1,X0)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f138,plain,
! [X0,X1] :
( ~ sP10_prd(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f139,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_false_only(X1,X0)
| ~ g_both(X1,X0)
| sP10_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f140,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_false_only(X0,X1)
| g_false_only(X1,X0)
| sP10_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f155,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[f43,f37]) ).
fof(f169,plain,
! [X0,X1] :
( g_false_only(X0,sK2_skl(X0))
| ~ sP5_prd(X0,X1)
| ~ g_both(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f21,f91]) ).
fof(f171,plain,
! [X0,X1] :
( ~ g_false_only(X0,sK0_skl)
| g_false_only(X0,sK3_skl(X0))
| ~ sP5_prd(X0,X1) ),
inference(resolution,[status(thm)],[f24,f91]) ).
fof(f197,plain,
! [X0,X1] :
( ~ sP0_prd(X0,X1)
| g_false_only(X1,X0)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f155]) ).
fof(f207,plain,
! [X0,X1] :
( ~ sP0_prd(X0,X1)
| ~ g_both(X0,X1)
| ~ sP10_prd(X0,X1) ),
inference(resolution,[status(thm)],[f197,f137]) ).
fof(f210,plain,
! [X0,X1] :
( sP8_prd(X0)
| ~ sP6_prd(X0,X1)
| g_true_only(X0,sK13_skl(X0,X1))
| g_false_only(sK2_skl(X0),X0)
| ~ g_both(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f20,f103]) ).
fof(f211,plain,
! [X0,X1] :
( ~ sP6_prd(X0,X1)
| g_true_only(X0,sK13_skl(X0,X1))
| ~ g_both(X0,sK0_skl)
| sP8_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f21]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ~ g_false_only(X1,sK0_skl)
| g_false_only(X1,sK3_skl(X1))
| ~ g_true_only(X1,X0)
| ~ sP4_prd(X1,X2)
| sP6_prd(X1,X2)
| ~ g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[f81,f24]) ).
fof(f238,plain,
! [X0,X1,X2] :
( ~ sP4_prd(X1,X2)
| ~ g_true_only(X1,X0)
| ~ g_false_only(X1,sK0_skl)
| sP6_prd(X1,X2)
| ~ g_true_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f23]) ).
fof(f268,plain,
! [X0,X1] :
( ~ sP2_prd(X0,X1)
| g_false_only(X1,X0)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f155]) ).
fof(f299,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| g_false_only(X0,sK2_skl(X0))
| sP8_prd(X0)
| ~ sP6_prd(X0,X1)
| g_true_only(sK13_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f104,f21]) ).
fof(f313,plain,
! [X0,X1] :
( g_true_only(sK13_skl(X0,X1),X0)
| ~ sP6_prd(X0,X1)
| sP8_prd(X0)
| ~ g_both(X0,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f299,f20]) ).
fof(f369,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| g_true_only(X0,X1)
| g_true_only(X0,sK13_skl(X0,X1))
| g_false_only(sK2_skl(X0),X0)
| ~ sP6_prd(X0,X1) ),
inference(resolution,[status(thm)],[f100,f20]) ).
fof(f384,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| ~ sP6_prd(X0,X1)
| g_true_only(X0,X1)
| g_true_only(X0,sK13_skl(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f21]) ).
fof(f394,plain,
! [X0,X1] :
( ~ g_both(X1,X0)
| ~ sP1_prd(X1,X0)
| g_false_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f155]) ).
fof(f406,plain,
! [X0,X1] :
( ~ sP10_prd(X0,X1)
| ~ g_both(X0,X1)
| ~ sP1_prd(X0,X1) ),
inference(resolution,[status(thm)],[f394,f137]) ).
fof(f491,plain,
! [X0,X1] :
( ~ sP1_prd(X0,X1)
| ~ g_both(X1,X0)
| g_false_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f155]) ).
fof(f502,plain,
! [X0,X1] :
( ~ g_both(X1,X0)
| ~ sP1_prd(X0,X1)
| ~ sP10_prd(X0,X1) ),
inference(resolution,[status(thm)],[f491,f138]) ).
fof(f668,plain,
! [X0,X1] :
( g_false_only(X1,X0)
| ~ sP0_prd(X1,X0)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f155]) ).
fof(f679,plain,
! [X0,X1] :
( ~ sP10_prd(X1,X0)
| ~ sP0_prd(X1,X0)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[f668,f138]) ).
fof(f865,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| g_true_only(sK13_skl(X0,X1),X0)
| g_false_only(sK2_skl(X0),X0)
| ~ sP6_prd(X0,X1)
| g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[f101,f20]) ).
fof(f876,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| g_true_only(sK13_skl(X0,X1),X0)
| g_true_only(X0,X1)
| ~ sP6_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f865,f21]) ).
fof(f1088,plain,
! [X0,X1] :
( g_false_only(X1,X0)
| sP10_prd(X0,X1)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f155]) ).
fof(f1094,plain,
! [X0] :
( sP10_prd(sK3_skl(X0),X0)
| ~ g_both(sK3_skl(X0),X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f1088,f23]) ).
fof(f1206,plain,
! [X0,X1] :
( ~ g_true_only(X1,X0)
| g_true_only(X1,sK0_skl)
| g_false_only(X1,sK0_skl)
| ~ g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[f22,f45]) ).
fof(f1231,plain,
! [X0,X1] :
( g_false_only(X1,X0)
| sP10_prd(X1,X0)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f155]) ).
fof(f1233,plain,
! [X0] :
( ~ g_both(X0,sK3_skl(X0))
| sP10_prd(sK3_skl(X0),X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f1231,f24]) ).
fof(f1378,plain,
! [X0,X1] :
( g_both(X0,X1)
| ~ sP10_prd(X0,X1)
| ~ sP1_prd(X0,X1)
| ~ sP10_prd(X0,X1) ),
inference(resolution,[status(thm)],[f502,f136]) ).
fof(f1391,plain,
! [X0,X1] :
( g_both(X0,X1)
| ~ sP1_prd(X0,X1)
| ~ sP10_prd(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1378]) ).
fof(f1392,plain,
! [X0,X1] :
( ~ sP1_prd(X0,X1)
| ~ sP10_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1391,f406]) ).
fof(f1397,plain,
! [X0,X1] :
( g_true_only(X0,sK4_skl(X0))
| ~ sP10_prd(X1,X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f1392,f25]) ).
fof(f1398,plain,
! [X0,X1] :
( ~ sP10_prd(X1,X0)
| ~ g_false_only(X0,sK0_skl)
| g_true_only(sK4_skl(X0),X0) ),
inference(resolution,[status(thm)],[f1392,f26]) ).
fof(f1830,plain,
! [X0,X1,X2] :
( sP3_prd(sK5_skl(X0,X1),X0)
| sP4_prd(sK6_skl(X1),X1)
| sP5_prd(sK0_skl,sK7_skl)
| sP2_prd(X2,X0)
| ~ g_both(X0,X1)
| ~ g_true_only(sK0_skl,sK8_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f19,f29]) ).
fof(f1848,plain,
! [X0] :
( ~ sP3_prd(X0,sK0_skl)
| ~ g_true_only(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f19,f70]) ).
fof(f1850,plain,
! [X0] :
( ~ sP3_prd(sK0_skl,X0)
| ~ g_true_only(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f19,f69]) ).
fof(f1858,plain,
! [X0] :
( ~ sP8_prd(X0)
| sP9_prd(X0)
| ~ g_true_only(X0,sK0_skl)
| ~ g_true_only(sK15_skl(X0),X0) ),
inference(resolution,[status(thm)],[f19,f121]) ).
fof(f1859,plain,
! [X0,X1] :
( sP0_prd(X1,X0)
| ~ g_true_only(X0,sK0_skl)
| ~ g_true_only(X0,sK0_skl)
| ~ g_true_only(sK1_skl(X0),X0) ),
inference(resolution,[status(thm)],[f19,f17]) ).
fof(f1867,plain,
~ g_true_only(sK0_skl,sK0_skl),
inference(factoring,[status(thm)],[f19]) ).
fof(f1869,plain,
! [X0] : ~ sP3_prd(sK0_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f1850,f70]) ).
fof(f1870,plain,
! [X0] :
( ~ g_true_only(X0,sK0_skl)
| sP9_prd(X0)
| ~ sP8_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1858,f122]) ).
fof(f1872,plain,
! [X0,X1,X2] :
( sP4_prd(sK6_skl(X1),X1)
| sP5_prd(sK0_skl,sK7_skl)
| sP2_prd(X2,X0)
| sP3_prd(sK5_skl(X0,X1),X0)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1830,f28]) ).
fof(f1874,plain,
! [X0,X1] :
( sP0_prd(X1,X0)
| ~ g_true_only(X0,sK0_skl)
| ~ g_true_only(sK1_skl(X0),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1859]) ).
fof(f1875,plain,
! [X0,X1] :
( ~ g_true_only(X1,sK0_skl)
| sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1874,f18]) ).
fof(f1878,plain,
! [X0] : ~ sP3_prd(X0,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1848,f69]) ).
fof(f1895,plain,
! [X0] :
( ~ g_true_only(X0,sK0_skl)
| ~ g_true_only(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f1869,f71]) ).
fof(f2118,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| ~ sP5_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f20]) ).
fof(f2129,plain,
! [X0,X1] :
( g_true_only(X0,sK0_skl)
| g_false_only(X0,sK0_skl)
| ~ sP5_prd(X0,X1) ),
inference(resolution,[status(thm)],[f2118,f45]) ).
fof(f2148,plain,
! [X0,X1] :
( ~ g_false_only(X0,sK0_skl)
| ~ sP5_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f23]) ).
fof(f2405,plain,
! [X0,X1] :
( g_both(X0,X1)
| ~ sP10_prd(X0,X1)
| ~ sP10_prd(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f679,f136]) ).
fof(f2419,plain,
! [X0,X1] :
( g_both(X0,X1)
| ~ sP10_prd(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f2405]) ).
fof(f2420,plain,
! [X0,X1] :
( ~ sP10_prd(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2419,f207]) ).
fof(f2431,plain,
! [X0,X1] :
( ~ g_true_only(X1,sK0_skl)
| ~ sP10_prd(X0,X1) ),
inference(resolution,[status(thm)],[f2420,f1875]) ).
fof(f2435,plain,
! [X0] :
( ~ sP9_prd(X0)
| ~ g_true_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f2431,f130]) ).
fof(f2446,plain,
! [X0] :
( ~ sP8_prd(X0)
| ~ g_true_only(X0,sK0_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f1870,f2435]) ).
fof(f3285,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| ~ g_true_only(X0,sK13_skl(X0,X1))
| ~ sP6_prd(X0,X1)
| sP8_prd(X0)
| ~ g_both(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f313,f22]) ).
fof(f3293,plain,
! [X0,X1] :
( ~ g_true_only(X0,sK13_skl(X0,X1))
| ~ sP6_prd(X0,X1)
| sP8_prd(X0)
| ~ g_both(X0,sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f3285]) ).
fof(f3294,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| sP8_prd(X0)
| ~ sP6_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3293,f211]) ).
fof(f4099,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| ~ g_true_only(X0,sK13_skl(X0,X1))
| ~ g_both(X0,sK0_skl)
| g_true_only(X0,X1)
| ~ sP6_prd(X0,X1) ),
inference(resolution,[status(thm)],[f876,f22]) ).
fof(f4118,plain,
! [X0,X1] :
( ~ g_true_only(X0,sK13_skl(X0,X1))
| ~ g_both(X0,sK0_skl)
| g_true_only(X0,X1)
| ~ sP6_prd(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f4099]) ).
fof(f4119,plain,
! [X0,X1] :
( ~ g_both(X0,sK0_skl)
| g_true_only(X0,X1)
| ~ sP6_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f4118,f384]) ).
fof(f4687,plain,
! [X0] :
( ~ sP8_prd(X0)
| ~ g_both(X0,sK0_skl)
| ~ sP6_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f4119,f2446]) ).
fof(f4735,plain,
! [X0] :
( ~ g_both(X0,sK0_skl)
| ~ sP6_prd(X0,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f4687,f3294]) ).
fof(f4809,plain,
! [X0] :
( ~ sP6_prd(X0,sK0_skl)
| g_true_only(X0,sK0_skl)
| ~ sP6_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f4735,f99]) ).
fof(f4810,plain,
! [X0] :
( sP8_prd(X0)
| ~ sP6_prd(X0,sK0_skl)
| ~ sP6_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f4735,f102]) ).
fof(f4811,plain,
! [X0] :
( ~ sP6_prd(X0,sK0_skl)
| g_true_only(X0,sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f4809]) ).
fof(f4812,plain,
! [X0] :
( ~ sP6_prd(X0,sK0_skl)
| sP8_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4810]) ).
fof(f4826,plain,
! [X0] :
( ~ sP8_prd(X0)
| ~ sP6_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f4811,f2446]) ).
fof(f4874,plain,
! [X0] : ~ sP6_prd(X0,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f4826,f4812]) ).
fof(f5044,plain,
! [X0,X1,X2] :
( ~ sP4_prd(X0,X1)
| ~ g_true_only(X2,X0)
| ~ g_true_only(X0,X2)
| sP6_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f238,f5045]) ).
fof(f5045,plain,
! [X0,X1] :
( ~ g_true_only(X1,X0)
| ~ g_true_only(X0,X1)
| g_false_only(X0,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1206,f19]) ).
fof(f7958,plain,
! [X0,X1] :
( g_true_only(X0,sK0_skl)
| ~ sP5_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2129,f2148]) ).
fof(f7961,plain,
! [X0] : ~ sP5_prd(sK0_skl,X0),
inference(resolution,[status(thm)],[f7958,f1895]) ).
fof(f8047,plain,
! [X0,X1,X2] :
( ~ g_both(X0,X1)
| sP4_prd(sK6_skl(X1),X1)
| sP2_prd(X2,X0)
| sP3_prd(sK5_skl(X0,X1),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1872,f7961]) ).
fof(f8176,plain,
! [X0,X1] :
( ~ g_true_only(X1,X0)
| ~ sP4_prd(X0,sK0_skl)
| ~ g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[f5044,f4874]) ).
fof(f8229,plain,
! [X0,X1] :
( sP9_prd(X0)
| ~ sP10_prd(X1,X0)
| ~ g_true_only(sK17_skl(X0),X0)
| ~ sP4_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f8176,f132]) ).
fof(f8300,plain,
! [X0,X1] :
( ~ sP10_prd(X1,X0)
| ~ sP4_prd(X0,sK0_skl)
| sP9_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8229,f133]) ).
fof(f8372,plain,
! [X0,X1] :
( sP2_prd(X1,sK0_skl)
| ~ g_both(sK0_skl,X0)
| sP4_prd(sK6_skl(X0),X0) ),
inference(resolution,[status(thm)],[f8047,f1878]) ).
fof(f9663,plain,
! [X0] :
( ~ g_true_only(sK4_skl(sK0_skl),sK0_skl)
| ~ sP10_prd(X0,sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f1397,f1895]) ).
fof(f9690,plain,
! [X0,X1] :
( ~ g_true_only(sK4_skl(X0),X0)
| ~ sP9_prd(X0)
| ~ sP10_prd(X1,X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f1397,f131]) ).
fof(f9704,plain,
! [X0,X1] :
( ~ g_false_only(X0,sK0_skl)
| ~ sP10_prd(X1,X0)
| ~ sP9_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f9690,f1398]) ).
fof(f9705,plain,
! [X0] :
( ~ sP10_prd(X0,sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f9663,f1398]) ).
fof(f9745,plain,
( ~ g_both(sK0_skl,sK3_skl(sK0_skl))
| ~ g_false_only(sK0_skl,sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f9705,f1233]) ).
fof(f9746,plain,
( ~ g_both(sK3_skl(sK0_skl),sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f9705,f1094]) ).
fof(f9757,plain,
( ~ g_both(sK3_skl(sK0_skl),sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f9746]) ).
fof(f9758,plain,
( ~ g_both(sK0_skl,sK3_skl(sK0_skl))
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f9745]) ).
fof(f9826,plain,
! [X0] :
( ~ sP9_prd(X0)
| ~ g_false_only(X0,sK0_skl)
| ~ sP9_prd(X0) ),
inference(resolution,[status(thm)],[f9704,f130]) ).
fof(f9875,plain,
! [X0] :
( ~ g_false_only(X0,sK0_skl)
| ~ sP9_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f9826]) ).
fof(f9907,plain,
! [X0] :
( ~ sP4_prd(X0,sK0_skl)
| sP6_prd(X0,sK0_skl)
| ~ sP9_prd(X0) ),
inference(resolution,[status(thm)],[f9875,f79]) ).
fof(f9911,plain,
! [X0] :
( ~ sP4_prd(X0,sK0_skl)
| ~ sP9_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f9907,f4874]) ).
fof(f9924,plain,
! [X0,X1] :
( ~ sP10_prd(X1,X0)
| ~ sP4_prd(X0,sK0_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f8300,f9911]) ).
fof(f9951,plain,
! [X0] :
( ~ g_both(X0,sK3_skl(X0))
| ~ sP4_prd(X0,sK0_skl)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f9924,f1233]) ).
fof(f9952,plain,
! [X0] :
( ~ sP4_prd(X0,sK0_skl)
| ~ g_both(sK3_skl(X0),X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f9924,f1094]) ).
fof(f10980,plain,
( g_false_only(sK3_skl(sK0_skl),sK0_skl)
| g_true_only(sK3_skl(sK0_skl),sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f9757,f45]) ).
fof(f10988,plain,
( g_true_only(sK3_skl(sK0_skl),sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f10980,f24]) ).
fof(f11010,plain,
( g_false_only(sK0_skl,sK3_skl(sK0_skl))
| g_true_only(sK0_skl,sK3_skl(sK0_skl))
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f9758,f45]) ).
fof(f11018,plain,
( ~ g_false_only(sK0_skl,sK0_skl)
| g_true_only(sK0_skl,sK3_skl(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f11010,f23]) ).
fof(f11411,plain,
( ~ g_true_only(sK3_skl(sK0_skl),sK0_skl)
| ~ g_true_only(sK3_skl(sK0_skl),sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f11018,f19]) ).
fof(f11420,plain,
( ~ g_true_only(sK3_skl(sK0_skl),sK0_skl)
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f11411]) ).
fof(f11421,plain,
~ g_false_only(sK0_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f11420,f10988]) ).
fof(f11449,plain,
( ~ sP1_prd(sK0_skl,sK0_skl)
| ~ g_both(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f11421,f394]) ).
fof(f11452,plain,
( ~ g_both(sK0_skl,sK0_skl)
| ~ sP2_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f11421,f268]) ).
fof(f11454,plain,
( ~ g_both(sK0_skl,sK0_skl)
| ~ sP0_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f11421,f197]) ).
fof(f11494,plain,
( g_false_only(sK0_skl,sK0_skl)
| g_true_only(sK0_skl,sK0_skl)
| ~ sP1_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f11449,f45]) ).
fof(f11504,plain,
( g_false_only(sK0_skl,sK0_skl)
| ~ sP1_prd(sK0_skl,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f11494,f1867]) ).
fof(f11557,plain,
( g_both(sK0_skl,sK0_skl)
| sP1_prd(sK0_skl,sK0_skl)
| ~ sP0_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f11454,f57]) ).
fof(f11561,plain,
( ~ sP0_prd(sK0_skl,sK0_skl)
| sP1_prd(sK0_skl,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f11557,f11454]) ).
fof(f11585,plain,
( g_false_only(sK0_skl,sK0_skl)
| g_true_only(sK0_skl,sK0_skl)
| ~ sP2_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f11452,f45]) ).
fof(f11593,plain,
( ~ sP2_prd(sK0_skl,sK0_skl)
| g_false_only(sK0_skl,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f11585,f1867]) ).
fof(f11633,plain,
~ sP1_prd(sK0_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f11504,f11421]) ).
fof(f11657,plain,
~ sP0_prd(sK0_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f11561,f11633]) ).
fof(f11680,plain,
~ sP2_prd(sK0_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f11593,f11421]) ).
fof(f22731,plain,
! [X0] :
( g_false_only(X0,sK3_skl(X0))
| g_true_only(X0,sK3_skl(X0))
| ~ sP4_prd(X0,sK0_skl)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f9951,f45]) ).
fof(f22740,plain,
! [X0] :
( ~ g_false_only(X0,sK0_skl)
| ~ sP4_prd(X0,sK0_skl)
| g_true_only(X0,sK3_skl(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f22731,f23]) ).
fof(f22819,plain,
! [X0] :
( g_false_only(sK3_skl(X0),X0)
| g_true_only(sK3_skl(X0),X0)
| ~ sP4_prd(X0,sK0_skl)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f9952,f45]) ).
fof(f22827,plain,
! [X0] :
( ~ sP4_prd(X0,sK0_skl)
| g_true_only(sK3_skl(X0),X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f22819,f24]) ).
fof(f26829,plain,
! [X0] :
( ~ sP4_prd(X0,sK0_skl)
| ~ g_true_only(X0,sK3_skl(X0))
| ~ sP4_prd(X0,sK0_skl)
| ~ g_false_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f22827,f8176]) ).
fof(f26862,plain,
! [X0] :
( ~ g_true_only(X0,sK3_skl(X0))
| ~ sP4_prd(X0,sK0_skl)
| ~ g_false_only(X0,sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f26829]) ).
fof(f26863,plain,
! [X0] :
( ~ g_false_only(X0,sK0_skl)
| ~ sP4_prd(X0,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f26862,f22740]) ).
fof(f26915,plain,
! [X0] :
( ~ sP4_prd(X0,sK0_skl)
| sP6_prd(X0,sK0_skl)
| ~ sP4_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f26863,f79]) ).
fof(f26924,plain,
! [X0] :
( sP6_prd(X0,sK0_skl)
| ~ sP4_prd(X0,sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f26915]) ).
fof(f26925,plain,
! [X0] : ~ sP4_prd(X0,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f26924,f4874]) ).
fof(f26926,plain,
! [X0] :
( ~ g_both(sK0_skl,sK0_skl)
| sP2_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f26925,f8372]) ).
fof(f26951,plain,
~ g_both(sK0_skl,sK0_skl),
inference(resolution,[status(thm)],[f26926,f11680]) ).
fof(f27002,plain,
( sP0_prd(sK0_skl,sK0_skl)
| g_both(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f26951,f50]) ).
fof(f27007,plain,
sP0_prd(sK0_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f27002,f26951]) ).
fof(f27013,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f27007,f11657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO604+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n001.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Mon Sep 21 12:09:25 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.39 % Drodi V4.1.1
% 153.23/29.84 % Refutation found
% 153.23/29.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 153.23/29.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 76.22/29.90 % Elapsed time: 19.495345 seconds
% 76.22/29.90 % CPU time: 154.568093 seconds
% 76.22/29.90 % Total memory used: 310.822 MB
% 76.22/29.90 % Net memory used: 271.166 MB
%------------------------------------------------------------------------------