%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:44:58 AM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 59 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 19 ~; 11 |; 13 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(t121_funct_1,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( one_to_one(C)
=> relation_image(C,set_intersection2(A,B)) = set_intersection2(relation_image(C,A),relation_image(C,B)) ) ),
file('theBenchmark.p',t121_funct_1) ).
fof(t149_relat_1,axiom,
! [A] :
( relation(A)
=> relation_image(A,empty_set) = empty_set ),
file('theBenchmark.p',t149_relat_1) ).
fof(t125_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( one_to_one(C)
& disjoint(A,B) )
=> disjoint(relation_image(C,A),relation_image(C,B)) ) ),
file('theBenchmark.p',t125_funct_1) ).
fof(t125_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( one_to_one(C)
& disjoint(A,B) )
=> disjoint(relation_image(C,A),relation_image(C,B)) ) ),
inference(assume_negation,[status(cth)],[t125_funct_1]) ).
cnf(c_42,plain,
( relation_image(A,set_intersection2(B,C)) = set_intersection2(relation_image(A,B),relation_image(A,C))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t121_funct_1]) ).
fof(nnf_36,plain,
? [A,B,C] :
( ~ disjoint(relation_image(C,A),relation_image(C,B))
& one_to_one(C)
& disjoint(A,B)
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t125_funct_1_neg]) ).
fof(sk_t125_funct_1_neg,plain,
( ~ disjoint(relation_image(sK0,sK1),relation_image(sK0,sK2))
& one_to_one(sK0)
& disjoint(sK1,sK2)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK0)],[nnf_36]) ).
cnf(c_43,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t125_funct_1_neg]) ).
cnf(c_48,negated_conjecture,
( relation_image(sK0,set_intersection2(A,B)) = set_intersection2(relation_image(sK0,A),relation_image(sK0,B))
| ~ one_to_one(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_43,c_42]) ).
cnf(c_49,negated_conjecture,
( set_intersection2(relation_image(sK0,A),relation_image(sK0,B)) = relation_image(sK0,set_intersection2(A,B))
| ~ one_to_one(sK0)
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_60,negated_conjecture,
~ disjoint(relation_image(sK0,sK1),relation_image(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_t125_funct_1_neg]) ).
cnf(c_61,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t125_funct_1_neg]) ).
cnf(c_62,negated_conjecture,
disjoint(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t125_funct_1_neg]) ).
cnf(c_63,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t125_funct_1_neg]) ).
cnf(c_72,plain,
( relation_image(A,empty_set) = empty_set
| ~ relation(A) ),
inference(clausify,[status(thm)],[t149_relat_1]) ).
cnf(c_96,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_97,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_162,negated_conjecture,
( set_intersection2(relation_image(sK0,A),relation_image(sK0,B)) = relation_image(sK0,set_intersection2(A,B))
| ~ one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_63,c_49]) ).
cnf(c_101,negated_conjecture,
set_intersection2(relation_image(sK0,A),relation_image(sK0,B)) = relation_image(sK0,set_intersection2(A,B)),
inference(resolve,[status(thm)],[c_61,c_162]) ).
cnf(c_107,plain,
relation_image(sK0,empty_set) = empty_set,
inference(resolve,[status(thm)],[c_72,c_63]) ).
cnf(c_163,negated_conjecture,
set_intersection2(relation_image(sK0,sK1),relation_image(sK0,sK2)) != empty_set,
inference(resolve,[status(thm)],[c_96,c_60]) ).
cnf(c_158,negated_conjecture,
relation_image(sK0,set_intersection2(sK1,sK2)) != empty_set,
inference(paramod,[status(thm)],[c_101,c_163]) ).
cnf(c_160,plain,
set_intersection2(sK1,sK2) = empty_set,
inference(resolve,[status(thm)],[c_97,c_62]) ).
cnf(c_164,negated_conjecture,
relation_image(sK0,empty_set) != empty_set,
inference(paramod,[status(thm)],[c_160,c_158]) ).
cnf(c_165,negated_conjecture,
empty_set != empty_set,
inference(paramod,[status(thm)],[c_107,c_164]) ).
cnf(c_161,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n002.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 08:35:35 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 1267297 was started by sandbox2 on n002,
% 0.15/0.43 % Sat Sep 26 08:35:35 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.45
% 0.15/0.45 % From the command line: assign(max_seconds, 300).
% 0.15/0.47
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47
% 0.15/0.47 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.47 % Length of proof is 20.
% 0.15/0.47 % Level of proof is 6.
% 0.15/0.47 % Maximum clause weight is 32.000.
% 0.15/0.47 % Given clauses 39.
% 0.15/0.47
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------