%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:46:12 AM UTC 2026
% Result : Theorem 9.60s 1.68s
% Output : CNFRefutation 9.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 21 unt; 0 def)
% Number of atoms : 146 ( 12 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 144 ( 59 ~; 55 |; 28 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 9 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = k2_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,B)
| r2_hidden(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : k2_xboole_0(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(t39_xboole_1,axiom,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t1_latsum_1,conjecture,
! [A,B,C,D] :
~ ( ~ ( r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,D) )
& ~ ( r2_hidden(B,D)
& r2_hidden(A,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(B,D)
& r2_hidden(A,D) )
& ~ ( r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,k4_xboole_0(C,D)) )
& r2_hidden(B,k2_xboole_0(C,D))
& r2_hidden(A,k2_xboole_0(C,D)) ),
file('theBenchmark.p',t1_latsum_1) ).
fof(t1_latsum_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
~ ( ~ ( r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,D) )
& ~ ( r2_hidden(B,D)
& r2_hidden(A,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(B,D)
& r2_hidden(A,D) )
& ~ ( r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,k4_xboole_0(C,D)) )
& r2_hidden(B,k2_xboole_0(C,D))
& r2_hidden(A,k2_xboole_0(C,D)) ),
inference(assume_negation,[status(cth)],[t1_latsum_1]) ).
fof(nnf_23,plain,
? [A,B,C,D] :
( ( ~ r2_hidden(B,k4_xboole_0(C,D))
| ~ r2_hidden(A,D) )
& ( ~ r2_hidden(B,D)
| ~ r2_hidden(A,k4_xboole_0(C,D)) )
& ( ~ r2_hidden(B,D)
| ~ r2_hidden(A,D) )
& ( ~ r2_hidden(B,k4_xboole_0(C,D))
| ~ r2_hidden(A,k4_xboole_0(C,D)) )
& r2_hidden(B,k2_xboole_0(C,D))
& r2_hidden(A,k2_xboole_0(C,D)) ),
inference(fof_nnf,[status(thm)],[t1_latsum_1_neg]) ).
fof(sk_t1_latsum_1_neg,plain,
( ( ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1))
| ~ r2_hidden(sK0,sK1) )
& ( ~ r2_hidden(sK2,sK1)
| ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1)) )
& ( ~ r2_hidden(sK2,sK1)
| ~ r2_hidden(sK0,sK1) )
& ( ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1))
| ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1)) )
& r2_hidden(sK2,k2_xboole_0(sK3,sK1))
& r2_hidden(sK0,k2_xboole_0(sK3,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK3),skolemize(D,sK1)],[nnf_23]) ).
cnf(c_28,negated_conjecture,
( ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1))
| ~ r2_hidden(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t1_latsum_1_neg]) ).
cnf(c_29,negated_conjecture,
( ~ r2_hidden(sK2,sK1)
| ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t1_latsum_1_neg]) ).
cnf(c_30,negated_conjecture,
( ~ r2_hidden(sK2,sK1)
| ~ r2_hidden(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t1_latsum_1_neg]) ).
cnf(c_31,negated_conjecture,
( ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1))
| ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t1_latsum_1_neg]) ).
cnf(c_32,negated_conjecture,
r2_hidden(sK2,k2_xboole_0(sK3,sK1)),
inference(split_conjunct,[status(thm)],[sk_t1_latsum_1_neg]) ).
cnf(c_33,negated_conjecture,
r2_hidden(sK0,k2_xboole_0(sK3,sK1)),
inference(split_conjunct,[status(thm)],[sk_t1_latsum_1_neg]) ).
cnf(c_39,plain,
k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(clausify,[status(thm)],[t39_xboole_1]) ).
cnf(c_43,plain,
k2_xboole_0(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_50,plain,
( ~ r2_hidden(D,B)
| r2_hidden(D,C)
| k2_xboole_0(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_51,plain,
( ~ r2_hidden(D,A)
| r2_hidden(D,C)
| k2_xboole_0(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_52,plain,
( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C)
| k2_xboole_0(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_53,plain,
k2_xboole_0(A,B) = k2_xboole_0(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_2302,plain,
A = k2_xboole_0(A,A),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_2303,plain,
( ~ r2_hidden(A,C)
| r2_hidden(A,k2_xboole_0(k2_xboole_0(B,C),k2_xboole_0(B,C))) ),
inference(resolve,[status(thm)],[c_50,c_2302]) ).
cnf(c_74,plain,
( ~ r2_hidden(A,C)
| r2_hidden(A,k2_xboole_0(B,C)) ),
inference(paramod,[status(thm)],[c_43,c_2303]) ).
cnf(c_94,plain,
( ~ r2_hidden(A,B)
| r2_hidden(A,k2_xboole_0(B,C)) ),
inference(resolve,[status(thm)],[c_51,c_39]) ).
cnf(c_114,plain,
( r2_hidden(A,k4_xboole_0(C,B))
| r2_hidden(A,B)
| ~ r2_hidden(A,k2_xboole_0(B,C)) ),
inference(resolve,[status(thm)],[c_52,c_39]) ).
cnf(c_2304,plain,
A = k2_xboole_0(A,A),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_2305,plain,
( r2_hidden(A,C)
| r2_hidden(A,B)
| ~ r2_hidden(A,k2_xboole_0(k2_xboole_0(B,C),k2_xboole_0(B,C))) ),
inference(resolve,[status(thm)],[c_52,c_2304]) ).
cnf(c_115,plain,
( r2_hidden(A,C)
| r2_hidden(A,B)
| ~ r2_hidden(A,k2_xboole_0(B,C)) ),
inference(paramod,[status(thm)],[c_43,c_2305]) ).
cnf(c_535,plain,
( r2_hidden(sK0,sK1)
| r2_hidden(sK0,sK3) ),
inference(resolve,[status(thm)],[c_115,c_33]) ).
cnf(c_536,plain,
( r2_hidden(sK2,sK1)
| r2_hidden(sK2,sK3) ),
inference(resolve,[status(thm)],[c_115,c_32]) ).
cnf(c_573,plain,
( ~ r2_hidden(sK2,sK1)
| r2_hidden(sK0,sK3) ),
inference(resolve,[status(thm)],[c_535,c_30]) ).
cnf(c_574,plain,
( ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1))
| r2_hidden(sK0,sK3) ),
inference(resolve,[status(thm)],[c_535,c_28]) ).
cnf(c_588,plain,
( ~ r2_hidden(sK0,sK1)
| r2_hidden(sK2,sK3) ),
inference(resolve,[status(thm)],[c_536,c_30]) ).
cnf(c_589,plain,
( ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1))
| r2_hidden(sK2,sK3) ),
inference(resolve,[status(thm)],[c_536,c_29]) ).
cnf(c_646,plain,
( r2_hidden(sK2,sK3)
| r2_hidden(sK0,sK3) ),
inference(resolve,[status(thm)],[c_573,c_536]) ).
cnf(c_648,plain,
( r2_hidden(sK2,k2_xboole_0(A,sK3))
| r2_hidden(sK0,sK3) ),
inference(resolve,[status(thm)],[c_646,c_74]) ).
cnf(c_1364,plain,
( r2_hidden(sK0,sK3)
| r2_hidden(sK2,k4_xboole_0(sK3,A))
| r2_hidden(sK2,A) ),
inference(resolve,[status(thm)],[c_114,c_648]) ).
cnf(c_2306,plain,
( r2_hidden(sK0,sK3)
| r2_hidden(sK0,sK3)
| r2_hidden(sK2,sK1) ),
inference(resolve,[status(thm)],[c_1364,c_574]) ).
cnf(c_1548,plain,
( r2_hidden(sK0,sK3)
| r2_hidden(sK2,sK1) ),
inference(copy,[status(thm)],[c_2306]) ).
cnf(c_2307,plain,
( r2_hidden(sK0,sK3)
| r2_hidden(sK0,sK3) ),
inference(resolve,[status(thm)],[c_1548,c_573]) ).
cnf(c_1562,plain,
r2_hidden(sK0,sK3),
inference(copy,[status(thm)],[c_2307]) ).
cnf(c_1564,plain,
r2_hidden(sK0,k2_xboole_0(A,sK3)),
inference(resolve,[status(thm)],[c_1562,c_74]) ).
cnf(c_1621,plain,
( r2_hidden(sK0,k4_xboole_0(sK3,A))
| r2_hidden(sK0,A) ),
inference(resolve,[status(thm)],[c_1564,c_114]) ).
cnf(c_1676,plain,
( r2_hidden(sK2,sK3)
| r2_hidden(sK0,sK1) ),
inference(resolve,[status(thm)],[c_1621,c_589]) ).
cnf(c_1685,plain,
( ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1))
| r2_hidden(sK0,sK1) ),
inference(resolve,[status(thm)],[c_1621,c_31]) ).
cnf(c_1686,plain,
( ~ r2_hidden(sK2,sK1)
| r2_hidden(sK0,sK1) ),
inference(resolve,[status(thm)],[c_1621,c_29]) ).
cnf(c_1693,plain,
( r2_hidden(sK2,k2_xboole_0(A,sK3))
| r2_hidden(sK0,sK1) ),
inference(resolve,[status(thm)],[c_1676,c_74]) ).
cnf(c_1793,plain,
( r2_hidden(sK2,k4_xboole_0(sK3,A))
| r2_hidden(sK2,A)
| r2_hidden(sK0,sK1) ),
inference(resolve,[status(thm)],[c_1693,c_114]) ).
cnf(c_2308,plain,
( r2_hidden(sK0,sK1)
| r2_hidden(sK2,sK1)
| r2_hidden(sK0,sK1) ),
inference(resolve,[status(thm)],[c_1793,c_1685]) ).
cnf(c_2109,plain,
( r2_hidden(sK2,sK1)
| r2_hidden(sK0,sK1) ),
inference(copy,[status(thm)],[c_2308]) ).
cnf(c_2309,plain,
( r2_hidden(sK0,sK1)
| r2_hidden(sK0,sK1) ),
inference(resolve,[status(thm)],[c_2109,c_1686]) ).
cnf(c_2123,plain,
r2_hidden(sK0,sK1),
inference(copy,[status(thm)],[c_2309]) ).
cnf(c_2124,plain,
r2_hidden(sK2,sK3),
inference(resolve,[status(thm)],[c_2123,c_588]) ).
cnf(c_2125,negated_conjecture,
~ r2_hidden(sK2,sK1),
inference(resolve,[status(thm)],[c_2123,c_30]) ).
cnf(c_2126,negated_conjecture,
~ r2_hidden(sK2,k4_xboole_0(sK3,sK1)),
inference(resolve,[status(thm)],[c_2123,c_28]) ).
cnf(c_2176,plain,
r2_hidden(sK2,k2_xboole_0(sK3,A)),
inference(resolve,[status(thm)],[c_2124,c_94]) ).
cnf(c_2310,negated_conjecture,
( r2_hidden(sK2,A)
| ~ r2_hidden(sK2,k2_xboole_0(sK1,A)) ),
inference(resolve,[status(thm)],[c_115,c_2125]) ).
cnf(c_2311,negated_conjecture,
~ r2_hidden(sK2,k2_xboole_0(sK1,k4_xboole_0(sK3,sK1))),
inference(resolve,[status(thm)],[c_2310,c_2126]) ).
cnf(c_2312,negated_conjecture,
~ r2_hidden(sK2,k2_xboole_0(sK1,sK3)),
inference(paramod,[status(thm)],[c_39,c_2311]) ).
cnf(c_2313,negated_conjecture,
~ r2_hidden(sK2,k2_xboole_0(sK3,sK1)),
inference(paramod,[status(thm)],[c_53,c_2312]) ).
cnf(c_2301,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2176,c_2313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 09:27:36 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 1384909 was started by sandbox2 on n004,
% 0.09/0.37 % Sat Sep 26 09:27:36 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).
% 9.60/1.68
% 9.60/1.68 % Assigning unary symbol f2 kb_weight 0 and highest precedence (14).
% 9.60/1.68
% 9.60/1.68 % SZS status Theorem for theBenchmark
% 9.60/1.68
% 9.60/1.68 % Proof 1 at 0.84 (+ 0.39) seconds.
% 9.60/1.68 % Length of proof is 46.
% 9.60/1.68 % Level of proof is 19.
% 9.60/1.68 % Maximum clause weight is 24.000.
% 9.60/1.68 % Given clauses 367.
% 9.60/1.68
% 9.60/1.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------