%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG227+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 : n009.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 12:52:09 PM UTC 2026
% Result : Theorem 3.78s 1.08s
% Output : Proof 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 105 ( 37 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 120 ( 42 ~; 46 |; 19 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( C = k1_closure3(A,B)
<=> C = a_2_0_closure3(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
fof(f6_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C != a_2_0_closure3(A,B)
| C = k1_closure3(A,B) )
& ( C = a_2_0_closure3(A,B)
| C != k1_closure3(A,B) ) )
| ~ m1_pboole(B,A) )
| v1_xboole_0(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ( ( C != a_2_0_closure3(A,B)
| C = k1_closure3(A,B) )
& ( C = a_2_0_closure3(A,B)
| C != k1_closure3(A,B) ) )
| ~ m1_pboole(B,A)
| v1_xboole_0(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c12,plain,
( X2 = a_2_0_closure3(X0,X1)
| X2 != k1_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p75,plain,
( k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(equality_resolution,[status(thm)],[c12]) ).
fof(f0,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,k1_closure3(A,B))
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_closure3) ).
fof(f0_neg,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,k1_closure3(A,B))
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( k1_funct_1(B,C) != k1_xboole_0
& ~ r2_hidden(C,k1_closure3(A,B))
& m1_subset_1(C,A) )
& m1_pboole(B,A) )
& ~ v1_xboole_0(A) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( k1_funct_1(sk1,sk2) != k1_xboole_0
& ~ r2_hidden(sk2,k1_closure3(sk0,sk1))
& m1_subset_1(sk2,sk0)
& m1_pboole(sk1,sk0)
& ~ v1_xboole_0(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c1,plain,
m1_pboole(sk1,sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p88,plain,
( k1_closure3(sk0,sk1) = a_2_0_closure3(sk0,sk1)
| v1_xboole_0(sk0) ),
inference(resolution,[status(thm)],[p75,c1]) ).
fof(f15,axiom,
! [A,B,C] :
( ( m1_pboole(C,B)
& ~ v1_xboole_0(B) )
=> ( r2_hidden(A,a_2_0_closure3(B,C))
<=> ? [D] :
( k1_funct_1(C,D) != k1_xboole_0
& A = D
& m1_subset_1(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(f15_nnf,plain,
! [A,B,C] :
( ( ( ! [D] :
( k1_funct_1(C,D) = k1_xboole_0
| A != D
| ~ m1_subset_1(D,B) )
| r2_hidden(A,a_2_0_closure3(B,C)) )
& ( ? [D] :
( k1_funct_1(C,D) != k1_xboole_0
& A = D
& m1_subset_1(D,B) )
| ~ r2_hidden(A,a_2_0_closure3(B,C)) ) )
| ~ m1_pboole(C,B)
| v1_xboole_0(B) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [B,C,A,D] :
( ( ( k1_funct_1(C,D) = k1_xboole_0
| A != D
| ~ m1_subset_1(D,B)
| r2_hidden(A,a_2_0_closure3(B,C)) )
& ( ( k1_funct_1(C,sk5(A,B,C)) != k1_xboole_0
& A = sk5(A,B,C)
& m1_subset_1(sk5(A,B,C),B) )
| ~ r2_hidden(A,a_2_0_closure3(B,C)) ) )
| ~ m1_pboole(C,B)
| v1_xboole_0(B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f15_nnf]) ).
cnf(c26,plain,
( k1_funct_1(X2,X3) = k1_xboole_0
| X0 != X3
| ~ m1_subset_1(X3,X1)
| r2_hidden(X0,a_2_0_closure3(X1,X2))
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p96,plain,
( k1_funct_1(X1,X2) = k1_xboole_0
| ~ m1_subset_1(X2,X0)
| r2_hidden(X2,a_2_0_closure3(X0,X1))
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(equality_resolution,[status(thm)],[c26]) ).
cnf(p177,plain,
( k1_funct_1(sk1,X0) = k1_xboole_0
| ~ m1_subset_1(X0,sk0)
| r2_hidden(X0,a_2_0_closure3(sk0,sk1))
| v1_xboole_0(sk0) ),
inference(resolution,[status(thm)],[p96,c1]) ).
cnf(c2,plain,
m1_subset_1(sk2,sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p187,plain,
( k1_funct_1(sk1,sk2) = k1_xboole_0
| r2_hidden(sk2,a_2_0_closure3(sk0,sk1))
| v1_xboole_0(sk0) ),
inference(resolution,[status(thm)],[p177,c2]) ).
cnf(p200,plain,
( k1_funct_1(sk1,sk2) = k1_xboole_0
| r2_hidden(sk2,k1_closure3(sk0,sk1))
| v1_xboole_0(sk0)
| v1_xboole_0(sk0) ),
inference(superposition,[status(thm)],[p88,p187]) ).
cnf(p251,plain,
( k1_funct_1(sk1,sk2) = k1_xboole_0
| r2_hidden(sk2,k1_closure3(sk0,sk1))
| v1_xboole_0(sk0) ),
inference(factoring,[status(thm)],[p200]) ).
cnf(c3,plain,
~ r2_hidden(sk2,k1_closure3(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p252,plain,
( k1_funct_1(sk1,sk2) = k1_xboole_0
| v1_xboole_0(sk0) ),
inference(resolution,[status(thm)],[p251,c3]) ).
cnf(c4,plain,
k1_funct_1(sk1,sk2) != k1_xboole_0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p253,plain,
v1_xboole_0(sk0),
inference(resolution,[status(thm)],[p252,c4]) ).
cnf(c0,plain,
~ v1_xboole_0(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p257,plain,
$false,
inference(resolution,[status(thm)],[p253,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 05:11:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.78/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.78/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------