%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEV515+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 08:50:15 AM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 94 ( 10 unt; 0 def)
% Number of atoms : 600 ( 0 equ)
% Maximal formula atoms : 164 ( 6 avg)
% Number of connectives : 645 ( 139 ~; 431 |; 72 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 155 ( 0 sgn 86 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(true_only_g,axiom,
! [X_2,X_1] :
( g_true_only(X_2,X_1)
<=> ( ~ g_false(X_2,X_1)
& g_true(X_2,X_1) ) ),
file('theBenchmark.p',true_only_g) ).
fof(both_g,axiom,
! [X_2,X_1] :
( g_both(X_2,X_1)
<=> ( g_false(X_2,X_1)
& g_true(X_2,X_1) ) ),
file('theBenchmark.p',both_g) ).
fof(false_only_g,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('theBenchmark.p',false_only_g) ).
fof(exhaustion_g,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('theBenchmark.p',exhaustion_g) ).
fof(nc1,conjecture,
( ( ~ ? [A] :
! [B] :
( ( g_true_only(B,B)
& g_false_only(B,A) )
| ( g_false_only(B,B)
& g_true_only(B,A) ) )
& ? [A] :
( ~ ? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) )
& ? [B] :
( g_both(B,B)
& g_both(B,A) ) ) )
| ! [A] :
? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) ) ),
file('theBenchmark.p',nc1) ).
fof(nc1_neg,negated_conjecture,
~ ( ( ~ ? [A] :
! [B] :
( ( g_true_only(B,B)
& g_false_only(B,A) )
| ( g_false_only(B,B)
& g_true_only(B,A) ) )
& ? [A] :
( ~ ? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) )
& ? [B] :
( g_both(B,B)
& g_both(B,A) ) ) )
| ! [A] :
? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) ) ),
inference(assume_negation,[status(cth)],[nc1]) ).
cnf(c_7,plain,
( g_true(A,B)
| ~ g_true_only(A,B) ),
inference(clausify,[status(thm)],[true_only_g]) ).
cnf(c_8,plain,
( g_true(A,B)
| ~ g_both(A,B) ),
inference(clausify,[status(thm)],[both_g]) ).
cnf(c_10,plain,
( ~ g_true(A,B)
| ~ g_false_only(A,B) ),
inference(clausify,[status(thm)],[false_only_g]) ).
cnf(c_14,plain,
( ~ g_true_only(A,B)
| ~ g_false_only(A,B) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_15,plain,
( ~ g_both(A,B)
| ~ g_false_only(A,B) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
fof(nnf_5,plain,
( ( ? [A] :
! [B] :
( ( g_true_only(B,B)
& g_false_only(B,A) )
| ( g_false_only(B,B)
& g_true_only(B,A) ) )
| ! [X2] :
( ? [X4] :
( ( ( g_both(X4,X4)
| g_false_only(X4,X4) )
& g_false_only(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_false_only(X4,X4) )
& g_both(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_both(X4,X4) )
& g_true_only(X4,X2) ) )
| ! [X3] :
( ~ g_both(X3,X3)
| ~ g_both(X3,X2) ) ) )
& ? [X0] :
! [X1] :
( ( ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_false_only(X1,X0) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_both(X1,X0) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) )
| ~ g_true_only(X1,X0) ) ) ),
inference(fof_nnf,[status(thm)],[nc1_neg]) ).
fof(sk_nc1_neg_sk,plain,
( ( ! [B] :
( ( g_true_only(B,B)
& g_false_only(B,sK1) )
| ( g_false_only(B,B)
& g_true_only(B,sK1) ) )
| ! [X2] :
( ( ( g_both(sK0(X2),sK0(X2))
| g_false_only(sK0(X2),sK0(X2)) )
& g_false_only(sK0(X2),X2) )
| ( ( g_true_only(sK0(X2),sK0(X2))
| g_false_only(sK0(X2),sK0(X2)) )
& g_both(sK0(X2),X2) )
| ( ( g_true_only(sK0(X2),sK0(X2))
| g_both(sK0(X2),sK0(X2)) )
& g_true_only(sK0(X2),X2) )
| ! [X3] :
( ~ g_both(X3,X3)
| ~ g_both(X3,X2) ) ) )
& ! [X1] :
( ( ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_false_only(X1,sK2) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_both(X1,sK2) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) )
| ~ g_true_only(X1,sK2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(X0,sK2),skolemize(X4,sK0(X2)),skolemize(A,sK1)],[nnf_5]) ).
fof(sk_nc1_neg,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_false_only(VAR_2,VAR_2)
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),sK0(VAR_1))
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_false_only(VAR_2,VAR_2)
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),sK0(VAR_1))
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_true_only(VAR_2,sK1)
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),sK0(VAR_1))
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_true_only(VAR_2,sK1)
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),sK0(VAR_1))
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_false_only(VAR_2,VAR_2)
| g_false_only(sK0(VAR_1),VAR_1)
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),sK0(VAR_1))
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_false_only(VAR_2,VAR_2)
| g_false_only(sK0(VAR_1),VAR_1)
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),sK0(VAR_1))
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_true_only(VAR_2,sK1)
| g_false_only(sK0(VAR_1),VAR_1)
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),sK0(VAR_1))
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_true_only(VAR_2,sK1)
| g_false_only(sK0(VAR_1),VAR_1)
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),sK0(VAR_1))
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_false_only(VAR_2,VAR_2)
| g_false_only(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_false_only(VAR_2,VAR_2)
| g_false_only(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_true_only(VAR_2,sK1)
| g_false_only(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_true_only(VAR_2,sK1)
| g_false_only(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),sK0(VAR_1))
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_false_only(VAR_2,VAR_2)
| g_both(sK0(VAR_1),sK0(VAR_1))
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_false_only(VAR_2,VAR_2)
| g_both(sK0(VAR_1),sK0(VAR_1))
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_true_only(VAR_2,sK1)
| g_both(sK0(VAR_1),sK0(VAR_1))
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_true_only(VAR_2,sK1)
| g_both(sK0(VAR_1),sK0(VAR_1))
| g_false_only(sK0(VAR_1),sK0(VAR_1))
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_false_only(VAR_2,VAR_2)
| g_false_only(sK0(VAR_1),VAR_1)
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_false_only(VAR_2,VAR_2)
| g_false_only(sK0(VAR_1),VAR_1)
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_true_only(VAR_2,VAR_2)
| g_true_only(VAR_2,sK1)
| g_false_only(sK0(VAR_1),VAR_1)
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( g_false_only(VAR_2,sK1)
| g_true_only(VAR_2,sK1)
| g_false_only(sK0(VAR_1),VAR_1)
| g_both(sK0(VAR_1),VAR_1)
| g_true_only(sK0(VAR_1),VAR_1)
| ~ g_both(VAR_0,VAR_0)
| ~ g_both(VAR_0,VAR_1) )
& ! [VAR_0] :
( ~ g_both(VAR_0,VAR_0)
| ~ g_false_only(VAR_0,sK2) )
& ! [VAR_0] :
( ~ g_false_only(VAR_0,VAR_0)
| ~ g_false_only(VAR_0,sK2) )
& ! [VAR_0] :
( ~ g_true_only(VAR_0,VAR_0)
| ~ g_both(VAR_0,sK2) )
& ! [VAR_0] :
( ~ g_false_only(VAR_0,VAR_0)
| ~ g_both(VAR_0,sK2) )
& ! [VAR_0] :
( ~ g_true_only(VAR_0,VAR_0)
| ~ g_true_only(VAR_0,sK2) )
& ! [VAR_0] :
( ~ g_both(VAR_0,VAR_0)
| ~ g_true_only(VAR_0,sK2) ) ),
inference(cnf_transformation,[status(thm)],[sk_nc1_neg_sk]) ).
cnf(c_21,negated_conjecture,
( g_false_only(C,sK1)
| g_false_only(C,C)
| g_false_only(sK0(B),B)
| g_both(sK0(B),B)
| g_true_only(sK0(B),sK0(B))
| g_both(sK0(B),sK0(B))
| ~ g_both(A,A)
| ~ g_both(A,B) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_22,negated_conjecture,
( g_true_only(C,C)
| g_true_only(C,sK1)
| g_false_only(sK0(B),B)
| g_both(sK0(B),B)
| g_true_only(sK0(B),sK0(B))
| g_both(sK0(B),sK0(B))
| ~ g_both(A,A)
| ~ g_both(A,B) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_24,negated_conjecture,
( g_true_only(C,C)
| g_false_only(C,C)
| g_false_only(sK0(B),B)
| g_true_only(sK0(B),sK0(B))
| g_false_only(sK0(B),sK0(B))
| g_true_only(sK0(B),B)
| ~ g_both(A,A)
| ~ g_both(A,B) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_28,negated_conjecture,
( g_false_only(C,sK1)
| g_false_only(C,C)
| g_both(sK0(B),sK0(B))
| g_false_only(sK0(B),sK0(B))
| g_both(sK0(B),B)
| g_true_only(sK0(B),B)
| ~ g_both(A,A)
| ~ g_both(A,B) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_29,negated_conjecture,
( g_true_only(C,C)
| g_true_only(C,sK1)
| g_both(sK0(B),sK0(B))
| g_false_only(sK0(B),sK0(B))
| g_both(sK0(B),B)
| g_true_only(sK0(B),B)
| ~ g_both(A,A)
| ~ g_both(A,B) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_35,negated_conjecture,
( ~ g_both(A,A)
| ~ g_false_only(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_36,negated_conjecture,
( ~ g_false_only(A,A)
| ~ g_false_only(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_37,negated_conjecture,
( ~ g_true_only(A,A)
| ~ g_both(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_38,negated_conjecture,
( ~ g_false_only(A,A)
| ~ g_both(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_39,negated_conjecture,
( ~ g_true_only(A,A)
| ~ g_true_only(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_40,negated_conjecture,
( ~ g_both(A,A)
| ~ g_true_only(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_nc1_neg]) ).
cnf(c_41,plain,
( g_false_only(A,B)
| g_both(A,B)
| g_true_only(A,B) ),
inference(clausify,[status(thm)],[exhaustion_g]) ).
cnf(c_43,plain,
( g_false(A,B)
| ~ g_both(A,B) ),
inference(clausify,[status(thm)],[both_g]) ).
cnf(c_44,plain,
( ~ g_false(A,B)
| ~ g_true_only(A,B) ),
inference(clausify,[status(thm)],[true_only_g]) ).
cnf(c_46,plain,
( g_false_only(B,sK1)
| g_false_only(B,B)
| g_false_only(sK0(A),A)
| g_both(sK0(A),A)
| g_true_only(sK0(A),sK0(A))
| g_both(sK0(A),sK0(A))
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_21]) ).
cnf(c_48,plain,
( g_true_only(B,B)
| g_true_only(B,sK1)
| g_false_only(sK0(A),A)
| g_both(sK0(A),A)
| g_true_only(sK0(A),sK0(A))
| g_both(sK0(A),sK0(A))
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_22]) ).
cnf(c_52,plain,
( g_true_only(B,B)
| g_false_only(B,B)
| g_false_only(sK0(A),A)
| g_true_only(sK0(A),sK0(A))
| g_false_only(sK0(A),sK0(A))
| g_true_only(sK0(A),A)
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_57,plain,
( g_false_only(B,sK1)
| g_false_only(B,B)
| g_both(sK0(A),sK0(A))
| g_false_only(sK0(A),sK0(A))
| g_both(sK0(A),A)
| g_true_only(sK0(A),A)
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_60,plain,
( g_true_only(B,B)
| g_true_only(B,sK1)
| g_both(sK0(A),sK0(A))
| g_false_only(sK0(A),sK0(A))
| g_both(sK0(A),A)
| g_true_only(sK0(A),A)
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_63,plain,
~ g_false_only(sK2,sK2),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_64,plain,
~ g_true_only(sK2,sK2),
inference(factor,[status(thm)],[c_39]) ).
cnf(c_65,plain,
( g_false_only(sK1,sK1)
| g_false_only(sK0(A),A)
| g_both(sK0(A),A)
| g_true_only(sK0(A),sK0(A))
| g_both(sK0(A),sK0(A))
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_67,plain,
( g_true_only(sK1,sK1)
| g_false_only(sK0(A),A)
| g_both(sK0(A),A)
| g_true_only(sK0(A),sK0(A))
| g_both(sK0(A),sK0(A))
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_48]) ).
cnf(c_191,plain,
( g_true_only(sK0(A),sK0(A))
| g_false_only(sK0(A),A)
| g_true_only(sK0(A),sK0(A))
| g_false_only(sK0(A),sK0(A))
| g_true_only(sK0(A),A)
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_52]) ).
cnf(c_68,plain,
( g_false_only(sK0(A),A)
| g_true_only(sK0(A),sK0(A))
| g_false_only(sK0(A),sK0(A))
| g_true_only(sK0(A),A)
| ~ g_both(A,A) ),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_70,plain,
( g_false_only(sK1,sK1)
| g_both(sK0(A),sK0(A))
| g_false_only(sK0(A),sK0(A))
| g_both(sK0(A),A)
| g_true_only(sK0(A),A)
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_71,plain,
( g_true_only(sK1,sK1)
| g_both(sK0(A),sK0(A))
| g_false_only(sK0(A),sK0(A))
| g_both(sK0(A),A)
| g_true_only(sK0(A),A)
| ~ g_both(A,A) ),
inference(factor,[status(thm)],[c_60]) ).
cnf(c_72,plain,
( ~ g_both(A,A)
| g_false_only(A,sK2)
| g_both(A,sK2) ),
inference(resolve,[status(thm)],[c_41,c_40]) ).
cnf(c_73,plain,
( ~ g_true_only(A,sK2)
| g_false_only(A,A)
| g_both(A,A) ),
inference(resolve,[status(thm)],[c_41,c_39]) ).
cnf(c_74,plain,
( ~ g_true_only(A,A)
| g_false_only(A,sK2)
| g_both(A,sK2) ),
inference(resolve,[status(thm)],[c_41,c_39]) ).
cnf(c_192,plain,
( g_false_only(sK2,sK2)
| g_both(sK2,sK2) ),
inference(resolve,[status(thm)],[c_64,c_41]) ).
cnf(c_76,plain,
g_both(sK2,sK2),
inference(resolve,[status(thm)],[c_63,c_192]) ).
cnf(c_78,plain,
( g_true_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2)
| g_true_only(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_76,c_71]) ).
cnf(c_79,plain,
( g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2)
| g_true_only(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_76,c_70]) ).
cnf(c_81,plain,
( g_false_only(sK0(sK2),sK2)
| g_true_only(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_true_only(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_76,c_68]) ).
cnf(c_82,plain,
( g_true_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_true_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_76,c_67]) ).
cnf(c_84,plain,
( g_false_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_true_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_76,c_65]) ).
cnf(c_193,plain,
( g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK0(sK2))
| g_true_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_78,c_73]) ).
cnf(c_194,plain,
( g_false_only(sK0(sK2),sK0(sK2))
| g_true_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_111,plain,
( g_true_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_195,plain,
( g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_79,c_73]) ).
cnf(c_196,plain,
( g_false_only(sK0(sK2),sK0(sK2))
| g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(copy,[status(thm)],[c_195]) ).
cnf(c_112,plain,
( g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_117,plain,
( ~ g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_111,c_14]) ).
cnf(c_119,plain,
( ~ g_false_only(sK0(sK2),sK2)
| g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_112,c_36]) ).
cnf(c_120,plain,
( ~ g_both(sK0(sK2),sK2)
| g_false_only(sK0(sK2),sK2)
| g_false_only(sK0(sK2),sK0(sK2))
| g_true_only(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_81,c_37]) ).
cnf(c_197,plain,
( g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_true_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_82,c_74]) ).
cnf(c_198,plain,
( g_false_only(sK0(sK2),sK2)
| g_true_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_197]) ).
cnf(c_121,plain,
( g_true_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_126,plain,
( ~ g_false_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_121,c_14]) ).
cnf(c_199,plain,
( g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_false_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_84,c_74]) ).
cnf(c_200,plain,
( g_false_only(sK0(sK2),sK2)
| g_false_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_199]) ).
cnf(c_128,plain,
( g_false_only(sK1,sK1)
| g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_201,plain,
( g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2)
| g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_128,c_119]) ).
cnf(c_202,plain,
( g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_201]) ).
cnf(c_203,plain,
( g_false_only(sK1,sK1)
| g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_130,plain,
( g_false_only(sK1,sK1)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_204,plain,
( g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_130,c_126]) ).
cnf(c_205,plain,
( g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_131,plain,
( g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_205]) ).
cnf(c_206,plain,
( g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_130,c_117]) ).
cnf(c_207,plain,
( g_both(sK0(sK2),sK0(sK2))
| g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_206]) ).
cnf(c_132,plain,
( g_false_only(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_207]) ).
cnf(c_142,plain,
( ~ g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_132,c_36]) ).
cnf(c_208,plain,
( g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(resolve,[status(thm)],[c_142,c_131]) ).
cnf(c_209,plain,
( g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_208]) ).
cnf(c_143,plain,
( g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK0(sK2)) ),
inference(copy,[status(thm)],[c_209]) ).
cnf(c_210,plain,
( g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_143,c_72]) ).
cnf(c_144,plain,
( g_false_only(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2) ),
inference(copy,[status(thm)],[c_210]) ).
cnf(c_178,plain,
( ~ g_both(sK0(sK2),sK0(sK2))
| g_both(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_144,c_35]) ).
cnf(c_211,plain,
( g_both(sK0(sK2),sK2)
| g_both(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_178,c_143]) ).
cnf(c_181,plain,
g_both(sK0(sK2),sK2),
inference(copy,[status(thm)],[c_211]) ).
cnf(c_182,plain,
( g_false_only(sK0(sK2),sK2)
| g_false_only(sK0(sK2),sK0(sK2))
| g_true_only(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_181,c_120]) ).
cnf(c_184,plain,
g_false(sK0(sK2),sK2),
inference(resolve,[status(thm)],[c_181,c_43]) ).
cnf(c_185,negated_conjecture,
~ g_false_only(sK0(sK2),sK0(sK2)),
inference(resolve,[status(thm)],[c_38,c_181]) ).
cnf(c_187,plain,
~ g_false_only(sK0(sK2),sK2),
inference(resolve,[status(thm)],[c_15,c_181]) ).
cnf(c_212,plain,
( g_false_only(sK0(sK2),sK2)
| g_true_only(sK0(sK2),sK2) ),
inference(resolve,[status(thm)],[c_185,c_182]) ).
cnf(c_189,plain,
g_true_only(sK0(sK2),sK2),
inference(resolve,[status(thm)],[c_187,c_212]) ).
cnf(c_213,plain,
~ g_true_only(sK0(sK2),sK2),
inference(resolve,[status(thm)],[c_184,c_44]) ).
cnf(c_190,plain,
$false,
inference(resolve,[status(thm)],[c_189,c_213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV515+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 11:06:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 571653 was started by sandbox2 on n017,
% 0.09/0.37 % Sat Sep 26 11:06:03 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 67.
% 0.14/0.40 % Level of proof is 16.
% 0.14/0.40 % Maximum clause weight is 40.000.
% 0.14/0.40 % Given clauses 105.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------