%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU280+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:45:40 AM UTC 2026
% Result : Theorem 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of formulae : 90 ( 8 unt; 0 def)
% Number of atoms : 347 ( 139 equ)
% Maximal formula atoms : 70 ( 3 avg)
% Number of connectives : 390 ( 133 ~; 206 |; 46 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 65 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_tarski__e6_22__wellord2__1,axiom,
! [A] :
( ! [B,C,D] :
( ( ordinal(D)
& B = D
& ordinal(C)
& B = C )
=> C = D )
=> ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ordinal(C)
& D = C
& in(D,A) ) ) ),
file('theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
fof(s1_xboole_0__e6_22__wellord2,conjecture,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( ordinal(C)
& in(C,A) ) ),
file('theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
fof(s1_xboole_0__e6_22__wellord2_neg,negated_conjecture,
~ ! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( ordinal(C)
& in(C,A) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e6_22__wellord2]) ).
fof(nnf_5,plain,
! [A] :
( ? [B] :
! [C] :
( ( ! [D] :
( ~ ordinal(C)
| D != C
| ~ in(D,A) )
| in(C,B) )
& ( ? [X3] :
( ordinal(C)
& X3 = C
& in(X3,A) )
| ~ in(C,B) ) )
| ? [X0,X1,X2] :
( X2 != X1
& ordinal(X2)
& X2 = X0
& ordinal(X1)
& X0 = X1 ) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e6_22__wellord2__1]) ).
fof(sk_s1_tarski__e6_22__wellord2__1_sk,plain,
! [A] :
( ! [C] :
( ( ! [D] :
( ~ ordinal(C)
| D != C
| ~ in(D,A) )
| in(C,sK2(A)) )
& ( ( ordinal(C)
& sK3(A,C) = C
& in(sK3(A,C),A) )
| ~ in(C,sK2(A)) ) )
| ( sK4(A) != sK1(A)
& ordinal(sK4(A))
& sK4(A) = sK0(A)
& ordinal(sK1(A))
& sK0(A) = sK1(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK4,sK2,sK3]),skolemize(X0,sK0(A)),skolemize(X1,sK1(A)),skolemize(X2,sK4(A)),skolemize(B,sK2(A)),skolemize(X3,sK3(A,C))],[nnf_5]) ).
fof(sk_s1_tarski__e6_22__wellord2__1,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ ordinal(VAR_1)
| VAR_2 != VAR_1
| ~ in(VAR_2,VAR_0)
| in(VAR_1,sK2(VAR_0))
| sK4(VAR_0) != sK1(VAR_0) )
& ! [VAR_0,VAR_1] :
( ordinal(VAR_1)
| ~ in(VAR_1,sK2(VAR_0))
| sK4(VAR_0) != sK1(VAR_0) )
& ! [VAR_0,VAR_1] :
( sK3(VAR_0,VAR_1) = VAR_1
| ~ in(VAR_1,sK2(VAR_0))
| sK4(VAR_0) != sK1(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_0)
| ~ in(VAR_1,sK2(VAR_0))
| sK4(VAR_0) != sK1(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ ordinal(VAR_1)
| VAR_2 != VAR_1
| ~ in(VAR_2,VAR_0)
| in(VAR_1,sK2(VAR_0))
| ordinal(sK4(VAR_0)) )
& ! [VAR_0,VAR_1] :
( ordinal(VAR_1)
| ~ in(VAR_1,sK2(VAR_0))
| ordinal(sK4(VAR_0)) )
& ! [VAR_0,VAR_1] :
( sK3(VAR_0,VAR_1) = VAR_1
| ~ in(VAR_1,sK2(VAR_0))
| ordinal(sK4(VAR_0)) )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_0)
| ~ in(VAR_1,sK2(VAR_0))
| ordinal(sK4(VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ ordinal(VAR_1)
| VAR_2 != VAR_1
| ~ in(VAR_2,VAR_0)
| in(VAR_1,sK2(VAR_0))
| sK4(VAR_0) = sK0(VAR_0) )
& ! [VAR_0,VAR_1] :
( ordinal(VAR_1)
| ~ in(VAR_1,sK2(VAR_0))
| sK4(VAR_0) = sK0(VAR_0) )
& ! [VAR_0,VAR_1] :
( sK3(VAR_0,VAR_1) = VAR_1
| ~ in(VAR_1,sK2(VAR_0))
| sK4(VAR_0) = sK0(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_0)
| ~ in(VAR_1,sK2(VAR_0))
| sK4(VAR_0) = sK0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ ordinal(VAR_1)
| VAR_2 != VAR_1
| ~ in(VAR_2,VAR_0)
| in(VAR_1,sK2(VAR_0))
| ordinal(sK1(VAR_0)) )
& ! [VAR_0,VAR_1] :
( ordinal(VAR_1)
| ~ in(VAR_1,sK2(VAR_0))
| ordinal(sK1(VAR_0)) )
& ! [VAR_0,VAR_1] :
( sK3(VAR_0,VAR_1) = VAR_1
| ~ in(VAR_1,sK2(VAR_0))
| ordinal(sK1(VAR_0)) )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_0)
| ~ in(VAR_1,sK2(VAR_0))
| ordinal(sK1(VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ ordinal(VAR_1)
| VAR_2 != VAR_1
| ~ in(VAR_2,VAR_0)
| in(VAR_1,sK2(VAR_0))
| sK0(VAR_0) = sK1(VAR_0) )
& ! [VAR_0,VAR_1] :
( ordinal(VAR_1)
| ~ in(VAR_1,sK2(VAR_0))
| sK0(VAR_0) = sK1(VAR_0) )
& ! [VAR_0,VAR_1] :
( sK3(VAR_0,VAR_1) = VAR_1
| ~ in(VAR_1,sK2(VAR_0))
| sK0(VAR_0) = sK1(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_0)
| ~ in(VAR_1,sK2(VAR_0))
| sK0(VAR_0) = sK1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1_sk]) ).
cnf(c_12,plain,
( in(sK3(A,B),A)
| ~ in(B,sK2(A))
| sK0(A) = sK1(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_13,plain,
( in(sK3(A,B),A)
| ~ in(B,sK2(A))
| sK1(A) = sK0(A) ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_14,plain,
( sK3(A,B) = B
| ~ in(B,sK2(A))
| sK0(A) = sK1(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_15,plain,
( sK3(A,B) = B
| ~ in(B,sK2(A))
| sK1(A) = sK0(A) ),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_16,plain,
( ordinal(B)
| ~ in(B,sK2(A))
| sK0(A) = sK1(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_17,plain,
( ordinal(B)
| ~ in(B,sK2(A))
| sK1(A) = sK0(A) ),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_18,plain,
( ~ ordinal(B)
| C != B
| ~ in(C,A)
| in(B,sK2(A))
| sK0(A) = sK1(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_19,plain,
( ~ ordinal(B)
| C != B
| ~ in(C,A)
| in(B,sK2(A))
| sK1(A) = sK0(A) ),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_24,plain,
( in(sK3(A,B),A)
| ~ in(B,sK2(A))
| sK4(A) = sK0(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_25,plain,
( sK3(A,B) = B
| ~ in(B,sK2(A))
| sK4(A) = sK0(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_26,plain,
( ordinal(B)
| ~ in(B,sK2(A))
| sK4(A) = sK0(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_27,plain,
( ~ ordinal(B)
| C != B
| ~ in(C,A)
| in(B,sK2(A))
| sK4(A) = sK0(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_32,plain,
( in(sK3(A,B),A)
| ~ in(B,sK2(A))
| sK4(A) != sK1(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_33,plain,
( sK3(A,B) = B
| ~ in(B,sK2(A))
| sK4(A) != sK1(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_34,plain,
( ordinal(B)
| ~ in(B,sK2(A))
| sK4(A) != sK1(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
cnf(c_35,plain,
( ~ ordinal(B)
| C != B
| ~ in(C,A)
| in(B,sK2(A))
| sK4(A) != sK1(A) ),
inference(split_conjunct,[status(thm)],[sk_s1_tarski__e6_22__wellord2__1]) ).
fof(nnf_6,plain,
? [A] :
! [B] :
? [C] :
( ( ~ ordinal(C)
| ~ in(C,A)
| ~ in(C,B) )
& ( ( ordinal(C)
& in(C,A) )
| in(C,B) ) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e6_22__wellord2_neg]) ).
fof(sk_s1_xboole_0__e6_22__wellord2_neg_sk,plain,
! [B] :
( ( ~ ordinal(sK5(B))
| ~ in(sK5(B),sK6)
| ~ in(sK5(B),B) )
& ( ( ordinal(sK5(B))
& in(sK5(B),sK6) )
| in(sK5(B),B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(A,sK6),skolemize(C,sK5(B))],[nnf_6]) ).
fof(sk_s1_xboole_0__e6_22__wellord2_neg,plain,
( ! [VAR_0] :
( ~ ordinal(sK5(VAR_0))
| ~ in(sK5(VAR_0),sK6)
| ~ in(sK5(VAR_0),VAR_0) )
& ! [VAR_0] :
( ordinal(sK5(VAR_0))
| in(sK5(VAR_0),VAR_0) )
& ! [VAR_0] :
( in(sK5(VAR_0),sK6)
| in(sK5(VAR_0),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_s1_xboole_0__e6_22__wellord2_neg_sk]) ).
cnf(c_36,negated_conjecture,
( in(sK5(A),sK6)
| in(sK5(A),A) ),
inference(split_conjunct,[status(thm)],[sk_s1_xboole_0__e6_22__wellord2_neg]) ).
cnf(c_37,negated_conjecture,
( ordinal(sK5(A))
| in(sK5(A),A) ),
inference(split_conjunct,[status(thm)],[sk_s1_xboole_0__e6_22__wellord2_neg]) ).
cnf(c_38,negated_conjecture,
( ~ ordinal(sK5(A))
| ~ in(sK5(A),sK6)
| ~ in(sK5(A),A) ),
inference(split_conjunct,[status(thm)],[sk_s1_xboole_0__e6_22__wellord2_neg]) ).
cnf(c_64,plain,
( in(sK3(A,sK5(sK2(A))),A)
| sK1(A) = sK0(A)
| in(sK5(sK2(A)),sK6) ),
inference(resolve,[status(thm)],[c_36,c_13]) ).
cnf(c_66,plain,
( ~ ordinal(B)
| sK5(A) != B
| in(B,sK2(sK6))
| sK4(sK6) != sK1(sK6)
| in(sK5(A),A) ),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_68,plain,
( ~ ordinal(B)
| sK5(A) != B
| in(B,sK2(sK6))
| sK4(sK6) = sK0(sK6)
| in(sK5(A),A) ),
inference(resolve,[status(thm)],[c_36,c_27]) ).
cnf(c_70,plain,
( ~ ordinal(B)
| sK5(A) != B
| in(B,sK2(sK6))
| sK1(sK6) = sK0(sK6)
| in(sK5(A),A) ),
inference(resolve,[status(thm)],[c_36,c_19]) ).
cnf(c_411,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK5(sK2(sK6)) != sK5(sK2(sK6))
| sK4(sK6) != sK1(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(factor,[status(thm)],[c_66]) ).
cnf(c_72,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK4(sK6) != sK1(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(copy,[status(thm)],[c_411]) ).
cnf(c_412,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK5(sK2(sK6)) != sK5(sK2(sK6))
| sK4(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(factor,[status(thm)],[c_68]) ).
cnf(c_74,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK4(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(copy,[status(thm)],[c_412]) ).
cnf(c_413,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK5(sK2(sK6)) != sK5(sK2(sK6))
| sK1(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(factor,[status(thm)],[c_70]) ).
cnf(c_76,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK1(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(copy,[status(thm)],[c_413]) ).
cnf(c_414,negated_conjecture,
( ordinal(sK5(sK2(A)))
| sK4(A) != sK1(A)
| ordinal(sK5(sK2(A))) ),
inference(resolve,[status(thm)],[c_37,c_34]) ).
cnf(c_78,negated_conjecture,
( sK4(A) != sK1(A)
| ordinal(sK5(sK2(A))) ),
inference(copy,[status(thm)],[c_414]) ).
cnf(c_415,negated_conjecture,
( ordinal(sK5(sK2(A)))
| sK4(A) = sK0(A)
| ordinal(sK5(sK2(A))) ),
inference(resolve,[status(thm)],[c_37,c_26]) ).
cnf(c_82,negated_conjecture,
( sK4(A) = sK0(A)
| ordinal(sK5(sK2(A))) ),
inference(copy,[status(thm)],[c_415]) ).
cnf(c_416,negated_conjecture,
( ordinal(sK5(sK2(A)))
| sK1(A) = sK0(A)
| ordinal(sK5(sK2(A))) ),
inference(resolve,[status(thm)],[c_37,c_17]) ).
cnf(c_86,negated_conjecture,
( sK1(A) = sK0(A)
| ordinal(sK5(sK2(A))) ),
inference(copy,[status(thm)],[c_416]) ).
cnf(c_417,plain,
( sK4(sK6) = sK0(sK6)
| sK4(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(resolve,[status(thm)],[c_74,c_82]) ).
cnf(c_217,plain,
( sK4(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(copy,[status(thm)],[c_417]) ).
cnf(c_218,plain,
( ~ ordinal(sK5(sK2(sK6)))
| ~ in(sK5(sK2(sK6)),sK6)
| sK4(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_217,c_38]) ).
cnf(c_418,plain,
( sK3(sK6,sK5(sK2(sK6))) = sK5(sK2(sK6))
| sK4(sK6) = sK0(sK6)
| sK4(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_217,c_25]) ).
cnf(c_224,plain,
( sK3(sK6,sK5(sK2(sK6))) = sK5(sK2(sK6))
| sK4(sK6) = sK0(sK6) ),
inference(copy,[status(thm)],[c_418]) ).
cnf(c_419,plain,
( in(sK3(sK6,sK5(sK2(sK6))),sK6)
| sK4(sK6) = sK0(sK6)
| sK4(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_217,c_24]) ).
cnf(c_225,plain,
( in(sK3(sK6,sK5(sK2(sK6))),sK6)
| sK4(sK6) = sK0(sK6) ),
inference(copy,[status(thm)],[c_419]) ).
cnf(c_420,plain,
( in(sK5(sK2(sK6)),sK6)
| sK4(sK6) = sK0(sK6)
| sK4(sK6) = sK0(sK6) ),
inference(paramod,[status(thm)],[c_224,c_225]) ).
cnf(c_254,plain,
( in(sK5(sK2(sK6)),sK6)
| sK4(sK6) = sK0(sK6) ),
inference(copy,[status(thm)],[c_420]) ).
cnf(c_421,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK4(sK6) = sK0(sK6)
| sK4(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_254,c_218]) ).
cnf(c_256,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK4(sK6) = sK0(sK6) ),
inference(copy,[status(thm)],[c_421]) ).
cnf(c_422,plain,
( sK4(sK6) = sK0(sK6)
| sK4(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_256,c_82]) ).
cnf(c_270,plain,
sK4(sK6) = sK0(sK6),
inference(copy,[status(thm)],[c_422]) ).
cnf(c_423,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK0(sK6) != sK1(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(paramod,[status(thm)],[c_270,c_72]) ).
cnf(c_298,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK1(sK6) != sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(copy,[status(thm)],[c_423]) ).
cnf(c_424,plain,
( sK0(sK6) != sK1(sK6)
| ordinal(sK5(sK2(sK6))) ),
inference(paramod,[status(thm)],[c_270,c_78]) ).
cnf(c_304,plain,
( sK1(sK6) != sK0(sK6)
| ordinal(sK5(sK2(sK6))) ),
inference(copy,[status(thm)],[c_424]) ).
cnf(c_425,plain,
( sK1(sK6) = sK0(sK6)
| sK1(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(resolve,[status(thm)],[c_76,c_86]) ).
cnf(c_331,plain,
( sK1(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(copy,[status(thm)],[c_425]) ).
cnf(c_332,plain,
( ~ ordinal(sK5(sK2(sK6)))
| ~ in(sK5(sK2(sK6)),sK6)
| sK1(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_331,c_38]) ).
cnf(c_426,plain,
( sK3(sK6,sK5(sK2(sK6))) = sK5(sK2(sK6))
| sK1(sK6) = sK0(sK6)
| sK1(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_331,c_15]) ).
cnf(c_338,plain,
( sK3(sK6,sK5(sK2(sK6))) = sK5(sK2(sK6))
| sK1(sK6) = sK0(sK6) ),
inference(copy,[status(thm)],[c_426]) ).
cnf(c_427,plain,
( in(sK5(sK2(sK6)),sK6)
| sK1(sK6) = sK0(sK6)
| in(sK5(sK2(sK6)),sK6)
| sK1(sK6) = sK0(sK6) ),
inference(paramod,[status(thm)],[c_338,c_64]) ).
cnf(c_428,plain,
( in(sK5(sK2(sK6)),sK6)
| in(sK5(sK2(sK6)),sK6)
| sK1(sK6) = sK0(sK6) ),
inference(copy,[status(thm)],[c_427]) ).
cnf(c_365,plain,
( in(sK5(sK2(sK6)),sK6)
| sK1(sK6) = sK0(sK6) ),
inference(copy,[status(thm)],[c_428]) ).
cnf(c_429,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK1(sK6) = sK0(sK6)
| sK1(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_365,c_332]) ).
cnf(c_372,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK1(sK6) = sK0(sK6) ),
inference(copy,[status(thm)],[c_429]) ).
cnf(c_430,plain,
( sK1(sK6) = sK0(sK6)
| sK1(sK6) = sK0(sK6) ),
inference(resolve,[status(thm)],[c_372,c_86]) ).
cnf(c_377,plain,
sK1(sK6) = sK0(sK6),
inference(copy,[status(thm)],[c_430]) ).
cnf(c_431,plain,
( sK0(sK6) != sK0(sK6)
| ordinal(sK5(sK2(sK6))) ),
inference(paramod,[status(thm)],[c_377,c_304]) ).
cnf(c_386,plain,
ordinal(sK5(sK2(sK6))),
inference(copy,[status(thm)],[c_431]) ).
cnf(c_432,plain,
( ~ ordinal(sK5(sK2(sK6)))
| sK0(sK6) != sK0(sK6)
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(paramod,[status(thm)],[c_377,c_298]) ).
cnf(c_433,plain,
( ~ ordinal(sK5(sK2(sK6)))
| in(sK5(sK2(sK6)),sK2(sK6)) ),
inference(copy,[status(thm)],[c_432]) ).
cnf(c_390,plain,
in(sK5(sK2(sK6)),sK2(sK6)),
inference(resolve,[status(thm)],[c_386,c_433]) ).
cnf(c_434,negated_conjecture,
( ~ ordinal(sK5(sK2(sK6)))
| ~ in(sK5(sK2(sK6)),sK6) ),
inference(resolve,[status(thm)],[c_390,c_38]) ).
cnf(c_407,negated_conjecture,
~ in(sK5(sK2(sK6)),sK6),
inference(resolve,[status(thm)],[c_386,c_434]) ).
cnf(c_435,plain,
( sK3(sK6,sK5(sK2(sK6))) = sK5(sK2(sK6))
| sK4(sK6) != sK1(sK6) ),
inference(resolve,[status(thm)],[c_390,c_33]) ).
cnf(c_436,plain,
( sK3(sK6,sK5(sK2(sK6))) = sK5(sK2(sK6))
| sK0(sK6) != sK1(sK6) ),
inference(paramod,[status(thm)],[c_270,c_435]) ).
cnf(c_437,plain,
( sK3(sK6,sK5(sK2(sK6))) = sK5(sK2(sK6))
| sK0(sK6) != sK0(sK6) ),
inference(paramod,[status(thm)],[c_377,c_436]) ).
cnf(c_409,plain,
sK3(sK6,sK5(sK2(sK6))) = sK5(sK2(sK6)),
inference(copy,[status(thm)],[c_437]) ).
cnf(c_438,plain,
( in(sK3(sK6,sK5(sK2(sK6))),sK6)
| sK4(sK6) != sK1(sK6) ),
inference(resolve,[status(thm)],[c_390,c_32]) ).
cnf(c_439,plain,
( in(sK3(sK6,sK5(sK2(sK6))),sK6)
| sK0(sK6) != sK1(sK6) ),
inference(paramod,[status(thm)],[c_270,c_438]) ).
cnf(c_440,plain,
( in(sK3(sK6,sK5(sK2(sK6))),sK6)
| sK0(sK6) != sK0(sK6) ),
inference(paramod,[status(thm)],[c_377,c_439]) ).
cnf(c_441,plain,
( in(sK5(sK2(sK6)),sK6)
| sK0(sK6) != sK0(sK6) ),
inference(paramod,[status(thm)],[c_409,c_440]) ).
cnf(c_442,plain,
in(sK5(sK2(sK6)),sK6),
inference(copy,[status(thm)],[c_441]) ).
cnf(c_410,plain,
$false,
inference(resolve,[status(thm)],[c_407,c_442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU280+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n016.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 09:09:17 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 513255 was started by sandbox on n016,
% 0.18/0.44 % Sat Sep 26 09:09:17 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.53
% 0.18/0.53 % SZS status Theorem for theBenchmark
% 0.18/0.53
% 0.18/0.53 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.18/0.53 % Length of proof is 51.
% 0.18/0.53 % Level of proof is 13.
% 0.18/0.53 % Maximum clause weight is 19.000.
% 0.18/0.53 % Given clauses 109.
% 0.18/0.53
% 0.18/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------