%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU245+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 : n003.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 08:45:34 AM UTC 2026
% Result : Theorem 1.98s 0.80s
% Output : CNFRefutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 95 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 97 ( 37 ~; 41 |; 12 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 8 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('theBenchmark.p',d6_wellord1) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(t16_wellord1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t16_wellord1_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
inference(assume_negation,[status(cth)],[t16_wellord1]) ).
fof(nnf_25,plain,
? [A,B,C] :
( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| ~ in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| in(A,relation_restriction(C,B)) )
& relation(C) ),
inference(fof_nnf,[status(thm)],[t16_wellord1_neg]) ).
fof(sk_t16_wellord1_neg_sk,plain,
( ( ~ in(sK0,cartesian_product2(sK2,sK2))
| ~ in(sK0,sK1)
| ~ in(sK0,relation_restriction(sK1,sK2)) )
& ( ( in(sK0,cartesian_product2(sK2,sK2))
& in(sK0,sK1) )
| in(sK0,relation_restriction(sK1,sK2)) )
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK1)],[nnf_25]) ).
fof(sk_t16_wellord1_neg,plain,
( ( ~ in(sK0,cartesian_product2(sK2,sK2))
| ~ in(sK0,sK1)
| ~ in(sK0,relation_restriction(sK1,sK2)) )
& ( in(sK0,cartesian_product2(sK2,sK2))
| in(sK0,relation_restriction(sK1,sK2)) )
& ( in(sK0,sK1)
| in(sK0,relation_restriction(sK1,sK2)) )
& relation(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_t16_wellord1_neg_sk]) ).
cnf(c_35,negated_conjecture,
( ~ in(sK0,cartesian_product2(sK2,sK2))
| ~ in(sK0,sK1)
| ~ in(sK0,relation_restriction(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t16_wellord1_neg]) ).
cnf(c_36,negated_conjecture,
( in(sK0,cartesian_product2(sK2,sK2))
| in(sK0,relation_restriction(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t16_wellord1_neg]) ).
cnf(c_37,negated_conjecture,
( in(sK0,sK1)
| in(sK0,relation_restriction(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t16_wellord1_neg]) ).
cnf(c_38,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t16_wellord1_neg]) ).
cnf(c_42,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_43,plain,
( in(D,B)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_44,plain,
( in(D,A)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_45,plain,
( relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[d6_wellord1]) ).
cnf(c_46,plain,
( set_intersection2(A,cartesian_product2(B,B)) = relation_restriction(A,B)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_51,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_75,plain,
( in(sK0,relation_restriction(sK1,sK2))
| ~ in(sK0,A)
| in(sK0,B)
| set_intersection2(cartesian_product2(sK2,sK2),A) != B ),
inference(resolve,[status(thm)],[c_42,c_36]) ).
cnf(c_654,negated_conjecture,
( in(sK0,sK1)
| in(sK0,A)
| set_intersection2(A,B) != relation_restriction(sK1,sK2) ),
inference(resolve,[status(thm)],[c_44,c_37]) ).
cnf(c_115,negated_conjecture,
( in(sK0,sK1)
| in(sK0,A)
| relation_restriction(sK1,sK2) != set_intersection2(A,B) ),
inference(copy,[status(thm)],[c_654]) ).
cnf(c_122,plain,
( in(sK0,sK1)
| relation_restriction(sK1,sK2) != set_intersection2(sK1,A) ),
inference(factor,[status(thm)],[c_115]) ).
cnf(c_124,plain,
set_intersection2(sK1,cartesian_product2(A,A)) = relation_restriction(sK1,A),
inference(resolve,[status(thm)],[c_46,c_38]) ).
cnf(c_655,plain,
( in(sK0,sK1)
| set_intersection2(sK1,A) != relation_restriction(sK1,sK2) ),
inference(copy,[status(thm)],[c_122]) ).
cnf(c_495,plain,
in(sK0,sK1),
inference(resolve,[status(thm)],[c_124,c_655]) ).
cnf(c_509,negated_conjecture,
( ~ in(sK0,cartesian_product2(sK2,sK2))
| ~ in(sK0,relation_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_495,c_35]) ).
cnf(c_656,plain,
( in(sK0,relation_restriction(sK1,sK2))
| in(sK0,A)
| set_intersection2(cartesian_product2(sK2,sK2),sK1) != A ),
inference(resolve,[status(thm)],[c_495,c_75]) ).
cnf(c_657,plain,
( in(sK0,relation_restriction(sK1,sK2))
| in(sK0,A)
| set_intersection2(sK1,cartesian_product2(sK2,sK2)) != A ),
inference(paramod,[status(thm)],[c_51,c_656]) ).
cnf(c_510,plain,
( in(sK0,relation_restriction(sK1,sK2))
| in(sK0,A)
| relation_restriction(sK1,sK2) != A ),
inference(paramod,[status(thm)],[c_124,c_657]) ).
cnf(c_658,plain,
( in(sK0,relation_restriction(sK1,sK2))
| relation_restriction(sK1,sK2) != relation_restriction(sK1,sK2) ),
inference(factor,[status(thm)],[c_510]) ).
cnf(c_536,plain,
in(sK0,relation_restriction(sK1,sK2)),
inference(copy,[status(thm)],[c_658]) ).
cnf(c_538,negated_conjecture,
~ in(sK0,cartesian_product2(sK2,sK2)),
inference(resolve,[status(thm)],[c_536,c_509]) ).
cnf(c_659,plain,
( in(sK0,B)
| set_intersection2(A,B) != relation_restriction(sK1,sK2) ),
inference(resolve,[status(thm)],[c_43,c_536]) ).
cnf(c_652,negated_conjecture,
set_intersection2(A,cartesian_product2(sK2,sK2)) != relation_restriction(sK1,sK2),
inference(resolve,[status(thm)],[c_659,c_538]) ).
cnf(c_653,plain,
$false,
inference(resolve,[status(thm)],[c_652,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU245+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n003.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 08:59:38 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2503473 was started by sandbox on n003,
% 0.09/0.35 % Sat Sep 26 08:59:38 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 1.98/0.80
% 1.98/0.80 % Assigning unary symbol f1 kb_weight 0 and highest precedence (18).
% 1.98/0.80
% 1.98/0.80 % SZS status Theorem for theBenchmark
% 1.98/0.80
% 1.98/0.80 % Proof 1 at 0.14 (+ 0.05) seconds.
% 1.98/0.80 % Length of proof is 25.
% 1.98/0.80 % Level of proof is 9.
% 1.98/0.80 % Maximum clause weight is 33.000.
% 1.98/0.80 % Given clauses 170.
% 1.98/0.80
% 1.98/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------