%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU215+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 : n006.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 08:45:26 AM UTC 2026
% Result : Theorem 0.84s 0.54s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 15 unt; 0 def)
% Number of atoms : 158 ( 30 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 184 ( 74 ~; 65 |; 26 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(fc1_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(t21_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('theBenchmark.p',t21_funct_1) ).
fof(t22_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('theBenchmark.p',t22_funct_1) ).
fof(t23_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_1) ).
fof(t23_funct_1_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
inference(assume_negation,[status(cth)],[t23_funct_1]) ).
cnf(c_50,plain,
( empty_set != C
| apply(A,B) = C
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_funct_1]) ).
cnf(c_53,plain,
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k5_relat_1]) ).
cnf(c_58,plain,
( function(relation_composition(A,B))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc1_funct_1]) ).
cnf(c_79,plain,
( ~ in(apply(B,C),relation_dom(A))
| ~ in(C,relation_dom(B))
| in(C,relation_dom(relation_composition(B,A)))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t21_funct_1]) ).
cnf(c_80,plain,
( apply(relation_composition(B,A),C) = apply(A,apply(B,C))
| ~ in(C,relation_dom(relation_composition(B,A)))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t22_funct_1]) ).
fof(nnf_39,plain,
? [A,B] :
( ? [C] :
( apply(relation_composition(B,C),A) != apply(C,apply(B,A))
& in(A,relation_dom(B))
& function(C)
& relation(C) )
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t23_funct_1_neg]) ).
fof(sk_t23_funct_1_neg,plain,
( apply(relation_composition(sK0,sK1),sK2) != apply(sK1,apply(sK0,sK2))
& in(sK2,relation_dom(sK0))
& function(sK1)
& relation(sK1)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK2),skolemize(B,sK0),skolemize(C,sK1)],[nnf_39]) ).
cnf(c_84,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_85,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_86,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_87,negated_conjecture,
function(sK1),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_88,negated_conjecture,
in(sK2,relation_dom(sK0)),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_89,negated_conjecture,
apply(relation_composition(sK0,sK1),sK2) != apply(sK1,apply(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_1594,negated_conjecture,
( relation(relation_composition(sK0,A))
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_53,c_84]) ).
cnf(c_227,negated_conjecture,
relation(relation_composition(sK0,sK1)),
inference(resolve,[status(thm)],[c_1594,c_86]) ).
cnf(c_1595,negated_conjecture,
( function(relation_composition(sK0,A))
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_58,c_84]) ).
cnf(c_1596,negated_conjecture,
( function(relation_composition(sK0,A))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_1595,c_85]) ).
cnf(c_1597,negated_conjecture,
( function(relation_composition(sK0,sK1))
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_1596,c_86]) ).
cnf(c_240,negated_conjecture,
function(relation_composition(sK0,sK1)),
inference(resolve,[status(thm)],[c_1597,c_87]) ).
cnf(c_1598,negated_conjecture,
( apply(relation_composition(A,sK1),B) = apply(sK1,apply(A,B))
| ~ in(B,relation_dom(relation_composition(A,sK1)))
| ~ function(A)
| ~ relation(A)
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_80,c_86]) ).
cnf(c_1599,negated_conjecture,
( apply(relation_composition(A,sK1),B) = apply(sK1,apply(A,B))
| ~ in(B,relation_dom(relation_composition(A,sK1)))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_1598,c_87]) ).
cnf(c_1600,negated_conjecture,
( apply(relation_composition(sK0,sK1),A) = apply(sK1,apply(sK0,A))
| ~ in(A,relation_dom(relation_composition(sK0,sK1)))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_1599,c_84]) ).
cnf(c_1601,negated_conjecture,
( apply(relation_composition(sK0,sK1),A) = apply(sK1,apply(sK0,A))
| ~ in(A,relation_dom(relation_composition(sK0,sK1))) ),
inference(resolve,[status(thm)],[c_1600,c_85]) ).
cnf(c_247,negated_conjecture,
~ in(sK2,relation_dom(relation_composition(sK0,sK1))),
inference(resolve,[status(thm)],[c_1601,c_89]) ).
cnf(c_1602,negated_conjecture,
( ~ in(apply(A,B),relation_dom(sK1))
| ~ in(B,relation_dom(A))
| in(B,relation_dom(relation_composition(A,sK1)))
| ~ function(A)
| ~ relation(A)
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_79,c_86]) ).
cnf(c_1603,negated_conjecture,
( ~ in(apply(A,B),relation_dom(sK1))
| ~ in(B,relation_dom(A))
| in(B,relation_dom(relation_composition(A,sK1)))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_1602,c_87]) ).
cnf(c_1604,negated_conjecture,
( ~ in(apply(sK0,A),relation_dom(sK1))
| ~ in(A,relation_dom(sK0))
| in(A,relation_dom(relation_composition(sK0,sK1)))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_1603,c_84]) ).
cnf(c_1605,negated_conjecture,
( ~ in(apply(sK0,A),relation_dom(sK1))
| ~ in(A,relation_dom(sK0))
| in(A,relation_dom(relation_composition(sK0,sK1))) ),
inference(resolve,[status(thm)],[c_1604,c_85]) ).
cnf(c_1606,negated_conjecture,
( ~ in(apply(sK0,sK2),relation_dom(sK1))
| ~ in(sK2,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_1605,c_247]) ).
cnf(c_373,negated_conjecture,
~ in(apply(sK0,sK2),relation_dom(sK1)),
inference(resolve,[status(thm)],[c_1606,c_88]) ).
cnf(c_1607,negated_conjecture,
( empty_set != B
| apply(sK1,A) = B
| in(A,relation_dom(sK1))
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_50,c_86]) ).
cnf(c_1608,negated_conjecture,
( empty_set != B
| apply(sK1,A) = B
| in(A,relation_dom(sK1)) ),
inference(resolve,[status(thm)],[c_1607,c_87]) ).
cnf(c_1609,negated_conjecture,
( empty_set != A
| apply(sK1,apply(sK0,sK2)) = A ),
inference(resolve,[status(thm)],[c_1608,c_373]) ).
cnf(c_1610,negated_conjecture,
apply(sK1,apply(sK0,sK2)) != apply(relation_composition(sK0,sK1),sK2),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_1611,negated_conjecture,
empty_set != apply(relation_composition(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_1609,c_1610]) ).
cnf(c_378,negated_conjecture,
apply(relation_composition(sK0,sK1),sK2) != empty_set,
inference(copy,[status(thm)],[c_1611]) ).
cnf(c_1612,plain,
( empty_set != B
| apply(relation_composition(sK0,sK1),A) = B
| in(A,relation_dom(relation_composition(sK0,sK1)))
| ~ function(relation_composition(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_50,c_227]) ).
cnf(c_1613,plain,
( empty_set != A
| apply(relation_composition(sK0,sK1),sK2) = A
| ~ function(relation_composition(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_1612,c_247]) ).
cnf(c_1614,plain,
( empty_set != empty_set
| ~ function(relation_composition(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_1613,c_378]) ).
cnf(c_1615,plain,
~ function(relation_composition(sK0,sK1)),
inference(xxres,[status(thm)],[c_1614]) ).
cnf(c_1593,plain,
$false,
inference(resolve,[status(thm)],[c_240,c_1615]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU215+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:50:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 858272 was started by sandbox on n006,
% 0.09/0.37 % Sat Sep 26 08:50:58 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.84/0.54
% 0.84/0.54 % SZS status Theorem for theBenchmark
% 0.84/0.54
% 0.84/0.54 % Proof 1 at 0.11 (+ 0.04) seconds.
% 0.84/0.54 % Length of proof is 23.
% 0.84/0.54 % Level of proof is 5.
% 0.84/0.54 % Maximum clause weight is 45.000.
% 0.84/0.54 % Given clauses 140.
% 0.84/0.54
% 0.84/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------