%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 : Fri Sep 25 02:51:58 PM UTC 2026
% Result : Theorem 28.04s 3.99s
% Output : Proof 28.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 15 unt; 0 def)
% Number of atoms : 118 ( 15 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 141 ( 58 ~; 41 |; 40 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 32 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f18_nnf,plain,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c31,plain,
k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f3,axiom,
! [A,B,C] :
( C = k2_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,B)
| r2_hidden(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f3_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( r2_hidden(D,B)
| r2_hidden(D,A) )
& ~ r2_hidden(D,C) )
| ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A)
& r2_hidden(D,C) ) )
| C = k2_xboole_0(A,B) )
& ( ! [D] :
( ( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| r2_hidden(D,C) )
& ( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C != k2_xboole_0(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B,D] :
( ( ( ( r2_hidden(sk4(A,B,C),B)
| r2_hidden(sk4(A,B,C),A) )
& ~ r2_hidden(sk4(A,B,C),C) )
| ( ~ r2_hidden(sk4(A,B,C),B)
& ~ r2_hidden(sk4(A,B,C),A)
& r2_hidden(sk4(A,B,C),C) )
| C = k2_xboole_0(A,B) )
& ( ( ( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| r2_hidden(D,C) )
& ( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C != k2_xboole_0(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f3_nnf]) ).
cnf(c8,plain,
( r2_hidden(X3,X1)
| r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2)
| X2 != k2_xboole_0(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p56,plain,
( r2_hidden(X3,k4_xboole_0(X2,X1))
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| X0 != k2_xboole_0(X1,X2) ),
inference(superposition,[status(thm)],[c31,c8]) ).
fof(f2,axiom,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c7,plain,
k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p166,plain,
( r2_hidden(X0,k4_xboole_0(X1,X2))
| r2_hidden(X0,X2)
| ~ r2_hidden(X0,k2_xboole_0(X1,X2)) ),
inference(resolution,[status(thm)],[p56,c7]) ).
fof(f0,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(f0_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(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,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(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( ( ~ r2_hidden(sk1,k4_xboole_0(sk2,sk3))
| ~ r2_hidden(sk0,sk3) )
& ( ~ r2_hidden(sk1,sk3)
| ~ r2_hidden(sk0,k4_xboole_0(sk2,sk3)) )
& ( ~ r2_hidden(sk1,sk3)
| ~ r2_hidden(sk0,sk3) )
& ( ~ r2_hidden(sk1,k4_xboole_0(sk2,sk3))
| ~ r2_hidden(sk0,k4_xboole_0(sk2,sk3)) )
& r2_hidden(sk1,k2_xboole_0(sk2,sk3))
& r2_hidden(sk0,k2_xboole_0(sk2,sk3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f0_nnf]) ).
cnf(c0,plain,
r2_hidden(sk0,k2_xboole_0(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p732,plain,
( r2_hidden(sk0,k4_xboole_0(sk2,sk3))
| r2_hidden(sk0,sk3) ),
inference(resolution,[status(thm)],[p166,c0]) ).
cnf(c2,plain,
( ~ r2_hidden(sk1,k4_xboole_0(sk2,sk3))
| ~ r2_hidden(sk0,k4_xboole_0(sk2,sk3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p776,plain,
( ~ r2_hidden(sk1,k4_xboole_0(sk2,sk3))
| r2_hidden(sk0,sk3) ),
inference(resolution,[status(thm)],[p732,c2]) ).
cnf(c1,plain,
r2_hidden(sk1,k2_xboole_0(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p733,plain,
( r2_hidden(sk1,k4_xboole_0(sk2,sk3))
| r2_hidden(sk1,sk3) ),
inference(resolution,[status(thm)],[p166,c1]) ).
cnf(p931,plain,
( r2_hidden(sk1,sk3)
| r2_hidden(sk0,sk3) ),
inference(resolution,[status(thm)],[p776,p733]) ).
cnf(c4,plain,
( ~ r2_hidden(sk1,sk3)
| ~ r2_hidden(sk0,k4_xboole_0(sk2,sk3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p775,plain,
( ~ r2_hidden(sk1,sk3)
| r2_hidden(sk0,sk3) ),
inference(resolution,[status(thm)],[p732,c4]) ).
cnf(p937,plain,
( r2_hidden(sk0,sk3)
| r2_hidden(sk0,sk3) ),
inference(resolution,[status(thm)],[p931,p775]) ).
cnf(p938,plain,
r2_hidden(sk0,sk3),
inference(factoring,[status(thm)],[p937]) ).
cnf(c5,plain,
( ~ r2_hidden(sk1,k4_xboole_0(sk2,sk3))
| ~ r2_hidden(sk0,sk3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p940,plain,
~ r2_hidden(sk1,k4_xboole_0(sk2,sk3)),
inference(resolution,[status(thm)],[p938,c5]) ).
cnf(p952,plain,
r2_hidden(sk1,sk3),
inference(resolution,[status(thm)],[p940,p733]) ).
cnf(c3,plain,
( ~ r2_hidden(sk1,sk3)
| ~ r2_hidden(sk0,sk3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p939,plain,
~ r2_hidden(sk1,sk3),
inference(resolution,[status(thm)],[p938,c3]) ).
cnf(p957,plain,
$false,
inference(resolution,[status(thm)],[p952,p939]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Thu Sep 24 14:01:45 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 28.04/3.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.04/3.99 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------