%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 06:49:51 AM UTC 2026
% Result : Theorem 0.14s 5.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 68 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 33 ~; 21 |; 11 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_closure3,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('theBenchmark.p',d3_closure3) ).
fof(fraenkel_a_2_0_closure3,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('theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(t8_closure3,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('theBenchmark.p',t8_closure3) ).
fof(t8_closure3_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(assume_negation,[status(cth)],[t8_closure3]) ).
cnf(c_32,plain,
( a_2_0_closure3(A,B) != C
| k1_closure3(A,B) = C
| ~ m1_pboole(B,A)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[d3_closure3]) ).
cnf(c_37,plain,
( k1_funct_1(B,D) = k1_xboole_0
| D != C
| ~ m1_subset_1(D,A)
| r2_hidden(C,a_2_0_closure3(A,B))
| ~ m1_pboole(B,A)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[fraenkel_a_2_0_closure3]) ).
fof(nnf_28,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(fof_nnf,[status(thm)],[t8_closure3_neg]) ).
fof(sk_t8_closure3_neg,plain,
( k1_funct_1(sK0,sK2) != k1_xboole_0
& ~ r2_hidden(sK2,k1_closure3(sK1,sK0))
& m1_subset_1(sK2,sK1)
& m1_pboole(sK0,sK1)
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2)],[nnf_28]) ).
cnf(c_38,negated_conjecture,
m1_pboole(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t8_closure3_neg]) ).
cnf(c_62,negated_conjecture,
~ v1_xboole_0(sK1),
inference(split_conjunct,[status(thm)],[sk_t8_closure3_neg]) ).
cnf(c_63,negated_conjecture,
m1_subset_1(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t8_closure3_neg]) ).
cnf(c_64,negated_conjecture,
~ r2_hidden(sK2,k1_closure3(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_t8_closure3_neg]) ).
cnf(c_65,negated_conjecture,
k1_funct_1(sK0,sK2) != k1_xboole_0,
inference(split_conjunct,[status(thm)],[sk_t8_closure3_neg]) ).
cnf(c_72,negated_conjecture,
( k1_funct_1(sK0,B) = k1_xboole_0
| B != A
| ~ m1_subset_1(B,sK1)
| r2_hidden(A,a_2_0_closure3(sK1,sK0))
| v1_xboole_0(sK1) ),
inference(resolve,[status(thm)],[c_38,c_37]) ).
cnf(c_73,negated_conjecture,
( k1_funct_1(sK0,B) = k1_xboole_0
| B != A
| ~ m1_subset_1(B,sK1)
| r2_hidden(A,a_2_0_closure3(sK1,sK0)) ),
inference(resolve,[status(thm)],[c_62,c_72]) ).
cnf(c_80,negated_conjecture,
( a_2_0_closure3(sK1,sK0) != A
| k1_closure3(sK1,sK0) = A
| v1_xboole_0(sK1) ),
inference(resolve,[status(thm)],[c_38,c_32]) ).
cnf(c_81,negated_conjecture,
( a_2_0_closure3(sK1,sK0) != A
| k1_closure3(sK1,sK0) = A ),
inference(resolve,[status(thm)],[c_62,c_80]) ).
cnf(c_117,plain,
k1_closure3(sK1,sK0) = a_2_0_closure3(sK1,sK0),
inference(xxres,[status(thm)],[c_81]) ).
cnf(c_118,negated_conjecture,
~ r2_hidden(sK2,a_2_0_closure3(sK1,sK0)),
inference(paramod,[status(thm)],[c_117,c_64]) ).
cnf(c_139,negated_conjecture,
( k1_funct_1(sK0,A) = k1_xboole_0
| A != sK2
| ~ m1_subset_1(A,sK1) ),
inference(resolve,[status(thm)],[c_73,c_118]) ).
cnf(c_140,plain,
( k1_funct_1(sK0,sK2) = k1_xboole_0
| ~ m1_subset_1(sK2,sK1) ),
inference(xxres,[status(thm)],[c_139]) ).
cnf(c_141,negated_conjecture,
~ m1_subset_1(sK2,sK1),
inference(resolve,[status(thm)],[c_140,c_65]) ).
cnf(c_138,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.40 % Computer : n007.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.40 % DateTime : Sat Sep 26 21:34:29 UTC 2026
% 0.14/5.40 % CPUTime :
% 0.14/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/5.41 % Process 507060 was started by sandbox on n007,
% 0.14/5.41 % Sat Sep 26 21:34:29 2026
% 0.14/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.42
% 0.14/5.42 % From the command line: assign(max_seconds, 300).
% 0.14/5.44
% 0.14/5.44 % SZS status Theorem for theBenchmark
% 0.14/5.44
% 0.14/5.44 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/5.44 % Length of proof is 17.
% 0.14/5.44 % Level of proof is 6.
% 0.14/5.44 % Maximum clause weight is 26.000.
% 0.14/5.44 % Given clauses 44.
% 0.14/5.44
% 0.14/5.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------