%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU215+3 : 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 : n017.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 0.13s 5.97s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 22 unt; 0 def)
% Number of atoms : 202 ( 42 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 221 ( 85 ~; 87 |; 29 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 20 !; 7 ?)
% 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(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
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(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
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_51,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_54,plain,
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k5_relat_1]) ).
cnf(c_60,plain,
( function(relation_composition(A,B))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc1_funct_1]) ).
fof(nnf_21,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(sk_rc1_relat_1,plain,
( relation(sK0)
& empty(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_21]) ).
cnf(c_73,plain,
empty(sK0),
inference(split_conjunct,[status(thm)],[sk_rc1_relat_1]) ).
fof(nnf_23,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(sk_rc1_xboole_0,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_23]) ).
cnf(c_77,plain,
empty(sK1),
inference(split_conjunct,[status(thm)],[sk_rc1_xboole_0]) ).
cnf(c_87,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_88,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]) ).
cnf(c_92,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
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(sK2,sK3),sK4) != apply(sK3,apply(sK2,sK4))
& in(sK4,relation_dom(sK2))
& function(sK3)
& relation(sK3)
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(A,sK4),skolemize(B,sK2),skolemize(C,sK3)],[nnf_39]) ).
cnf(c_95,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_96,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_97,negated_conjecture,
relation(sK3),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_98,negated_conjecture,
function(sK3),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_99,negated_conjecture,
in(sK4,relation_dom(sK2)),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_100,negated_conjecture,
apply(relation_composition(sK2,sK3),sK4) != apply(sK3,apply(sK2,sK4)),
inference(split_conjunct,[status(thm)],[sk_t23_funct_1_neg]) ).
cnf(c_4064,plain,
( empty_set = apply(A,B)
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(xxres,[status(thm)],[c_50]) ).
cnf(c_110,plain,
( apply(A,B) = empty_set
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_4064]) ).
cnf(c_271,plain,
empty_set = sK1,
inference(resolve,[status(thm)],[c_92,c_77]) ).
cnf(c_4065,plain,
empty_set = sK0,
inference(resolve,[status(thm)],[c_92,c_73]) ).
cnf(c_272,plain,
sK1 = sK0,
inference(paramod,[status(thm)],[c_271,c_4065]) ).
cnf(c_4066,plain,
( apply(A,B) = sK1
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_271,c_110]) ).
cnf(c_284,plain,
( apply(A,B) = sK0
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_272,c_4066]) ).
cnf(c_4067,plain,
( sK1 != C
| apply(A,B) = C
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_271,c_51]) ).
cnf(c_286,plain,
( sK0 != C
| apply(A,B) = C
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_272,c_4067]) ).
cnf(c_4068,negated_conjecture,
( function(relation_composition(sK2,A))
| ~ function(A)
| ~ relation(A)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_95,c_60]) ).
cnf(c_301,negated_conjecture,
( function(relation_composition(sK2,A))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_96,c_4068]) ).
cnf(c_305,plain,
( relation(relation_composition(sK2,A))
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_95,c_54]) ).
cnf(c_4069,negated_conjecture,
( apply(relation_composition(A,sK3),B) = apply(sK3,apply(A,B))
| ~ in(B,relation_dom(relation_composition(A,sK3)))
| ~ function(A)
| ~ relation(A)
| ~ function(sK3) ),
inference(resolve,[status(thm)],[c_88,c_97]) ).
cnf(c_4070,negated_conjecture,
( apply(relation_composition(A,sK3),B) = apply(sK3,apply(A,B))
| ~ in(B,relation_dom(relation_composition(A,sK3)))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_4069,c_98]) ).
cnf(c_4071,negated_conjecture,
( apply(relation_composition(sK2,sK3),A) = apply(sK3,apply(sK2,A))
| ~ in(A,relation_dom(relation_composition(sK2,sK3)))
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_4070,c_95]) ).
cnf(c_4072,negated_conjecture,
( apply(relation_composition(sK2,sK3),A) = apply(sK3,apply(sK2,A))
| ~ in(A,relation_dom(relation_composition(sK2,sK3))) ),
inference(resolve,[status(thm)],[c_4071,c_96]) ).
cnf(c_330,negated_conjecture,
~ in(sK4,relation_dom(relation_composition(sK2,sK3))),
inference(resolve,[status(thm)],[c_4072,c_100]) ).
cnf(c_4073,negated_conjecture,
( ~ in(apply(A,B),relation_dom(sK3))
| ~ in(B,relation_dom(A))
| in(B,relation_dom(relation_composition(A,sK3)))
| ~ function(A)
| ~ relation(A)
| ~ function(sK3) ),
inference(resolve,[status(thm)],[c_87,c_97]) ).
cnf(c_4074,negated_conjecture,
( ~ in(apply(A,B),relation_dom(sK3))
| ~ in(B,relation_dom(A))
| in(B,relation_dom(relation_composition(A,sK3)))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_4073,c_98]) ).
cnf(c_4075,negated_conjecture,
( ~ in(apply(sK2,A),relation_dom(sK3))
| ~ in(A,relation_dom(sK2))
| in(A,relation_dom(relation_composition(sK2,sK3)))
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_4074,c_95]) ).
cnf(c_4076,negated_conjecture,
( ~ in(apply(sK2,A),relation_dom(sK3))
| ~ in(A,relation_dom(sK2))
| in(A,relation_dom(relation_composition(sK2,sK3))) ),
inference(resolve,[status(thm)],[c_4075,c_96]) ).
cnf(c_4077,negated_conjecture,
( ~ in(apply(sK2,sK4),relation_dom(sK3))
| ~ in(sK4,relation_dom(sK2)) ),
inference(resolve,[status(thm)],[c_4076,c_330]) ).
cnf(c_1768,negated_conjecture,
~ in(apply(sK2,sK4),relation_dom(sK3)),
inference(resolve,[status(thm)],[c_4077,c_99]) ).
cnf(c_2619,plain,
relation(relation_composition(sK2,sK3)),
inference(resolve,[status(thm)],[c_305,c_97]) ).
cnf(c_4078,negated_conjecture,
( function(relation_composition(sK2,sK3))
| ~ function(sK3) ),
inference(resolve,[status(thm)],[c_301,c_97]) ).
cnf(c_3404,negated_conjecture,
function(relation_composition(sK2,sK3)),
inference(resolve,[status(thm)],[c_98,c_4078]) ).
cnf(c_4079,negated_conjecture,
( apply(sK3,A) = sK0
| in(A,relation_dom(sK3))
| ~ function(sK3) ),
inference(resolve,[status(thm)],[c_284,c_97]) ).
cnf(c_4000,negated_conjecture,
( apply(sK3,A) = sK0
| in(A,relation_dom(sK3)) ),
inference(resolve,[status(thm)],[c_98,c_4079]) ).
cnf(c_4080,plain,
( sK0 != B
| apply(relation_composition(sK2,sK3),A) = B
| in(A,relation_dom(relation_composition(sK2,sK3)))
| ~ function(relation_composition(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_286,c_2619]) ).
cnf(c_4081,plain,
( sK0 != B
| apply(relation_composition(sK2,sK3),A) = B
| in(A,relation_dom(relation_composition(sK2,sK3))) ),
inference(resolve,[status(thm)],[c_4080,c_3404]) ).
cnf(c_4082,plain,
( sK0 != A
| apply(relation_composition(sK2,sK3),sK4) = A ),
inference(resolve,[status(thm)],[c_4081,c_330]) ).
cnf(c_4083,negated_conjecture,
sK0 != apply(sK3,apply(sK2,sK4)),
inference(resolve,[status(thm)],[c_4082,c_100]) ).
cnf(c_4029,negated_conjecture,
apply(sK3,apply(sK2,sK4)) != sK0,
inference(copy,[status(thm)],[c_4083]) ).
cnf(c_4084,plain,
apply(sK3,apply(sK2,sK4)) = sK0,
inference(resolve,[status(thm)],[c_4000,c_1768]) ).
cnf(c_4063,plain,
$false,
inference(resolve,[status(thm)],[c_4029,c_4084]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU215+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n017.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 08:47:25 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 306720 was started by sandbox2 on n017,
% 0.09/5.37 % Sat Sep 26 08:47:25 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.13/5.97
% 0.13/5.97 % SZS status Theorem for theBenchmark
% 0.13/5.97
% 0.13/5.97 % Proof 1 at 0.46 (+ 0.10) seconds.
% 0.13/5.97 % Length of proof is 38.
% 0.13/5.97 % Level of proof is 6.
% 0.13/5.97 % Maximum clause weight is 45.000.
% 0.13/5.97 % Given clauses 408.
% 0.13/5.97
% 0.13/5.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------