%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU009+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:44:53 AM UTC 2026
% Result : Theorem 0.16s 6.01s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 11 unt; 0 def)
% Number of atoms : 166 ( 8 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 208 ( 88 ~; 88 |; 22 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_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(t34_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t40_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_composition(C,identity_relation(A))))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',t40_funct_1) ).
fof(t40_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_composition(C,identity_relation(A))))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
inference(assume_negation,[status(cth)],[t40_funct_1]) ).
cnf(c_44,plain,
relation(identity_relation(A)),
inference(clausify,[status(thm)],[dt_k6_relat_1]) ).
cnf(c_52,plain,
function(identity_relation(A)),
inference(clausify,[status(thm)],[fc2_funct_1]) ).
cnf(c_72,plain,
( 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_73,plain,
( in(apply(B,C),relation_dom(A))
| ~ 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_74,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_76,plain,
( relation_dom(A) = B
| identity_relation(B) != A
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t34_funct_1]) ).
fof(nnf_35,plain,
? [A,B,C] :
( ( ~ in(apply(C,B),A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_composition(C,identity_relation(A)))) )
& ( ( in(apply(C,B),A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_composition(C,identity_relation(A)))) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t40_funct_1_neg]) ).
fof(sk_t40_funct_1_neg_sk,plain,
( ( ~ in(apply(sK0,sK1),sK2)
| ~ in(sK1,relation_dom(sK0))
| ~ in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) )
& ( ( in(apply(sK0,sK1),sK2)
& in(sK1,relation_dom(sK0)) )
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) )
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1),skolemize(C,sK0)],[nnf_35]) ).
fof(sk_t40_funct_1_neg,plain,
( ( ~ in(apply(sK0,sK1),sK2)
| ~ in(sK1,relation_dom(sK0))
| ~ in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) )
& ( in(apply(sK0,sK1),sK2)
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) )
& ( in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) )
& function(sK0)
& relation(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t40_funct_1_neg_sk]) ).
cnf(c_85,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t40_funct_1_neg]) ).
cnf(c_86,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t40_funct_1_neg]) ).
cnf(c_87,negated_conjecture,
( in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) ),
inference(split_conjunct,[status(thm)],[sk_t40_funct_1_neg]) ).
cnf(c_88,negated_conjecture,
( in(apply(sK0,sK1),sK2)
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) ),
inference(split_conjunct,[status(thm)],[sk_t40_funct_1_neg]) ).
cnf(c_89,negated_conjecture,
( ~ in(apply(sK0,sK1),sK2)
| ~ in(sK1,relation_dom(sK0))
| ~ in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) ),
inference(split_conjunct,[status(thm)],[sk_t40_funct_1_neg]) ).
cnf(c_3682,plain,
( in(apply(B,C),relation_dom(identity_relation(A)))
| ~ in(C,relation_dom(relation_composition(B,identity_relation(A))))
| ~ function(B)
| ~ relation(B)
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_73,c_44]) ).
cnf(c_198,plain,
( in(apply(A,B),relation_dom(identity_relation(C)))
| ~ in(B,relation_dom(relation_composition(A,identity_relation(C))))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_52,c_3682]) ).
cnf(c_3683,plain,
( ~ in(apply(B,C),relation_dom(identity_relation(A)))
| ~ in(C,relation_dom(B))
| in(C,relation_dom(relation_composition(B,identity_relation(A))))
| ~ function(B)
| ~ relation(B)
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_74,c_44]) ).
cnf(c_212,plain,
( ~ in(apply(A,B),relation_dom(identity_relation(C)))
| ~ in(B,relation_dom(A))
| in(B,relation_dom(relation_composition(A,identity_relation(C))))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_52,c_3683]) ).
cnf(c_3684,plain,
( relation_dom(identity_relation(A)) = A
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(xxres,[status(thm)],[c_76]) ).
cnf(c_3685,plain,
( relation_dom(identity_relation(A)) = A
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_44,c_3684]) ).
cnf(c_231,plain,
relation_dom(identity_relation(A)) = A,
inference(resolve,[status(thm)],[c_52,c_3685]) ).
cnf(c_234,plain,
( ~ in(apply(A,B),C)
| ~ in(B,relation_dom(A))
| in(B,relation_dom(relation_composition(A,identity_relation(C))))
| ~ function(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_231,c_212]) ).
cnf(c_235,plain,
( in(apply(A,B),C)
| ~ in(B,relation_dom(relation_composition(A,identity_relation(C))))
| ~ function(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_231,c_198]) ).
cnf(c_3686,negated_conjecture,
( in(sK1,relation_dom(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ function(identity_relation(sK2))
| ~ relation(identity_relation(sK2))
| in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_87,c_72]) ).
cnf(c_3687,negated_conjecture,
( ~ function(sK0)
| ~ relation(sK0)
| ~ function(identity_relation(sK2))
| ~ relation(identity_relation(sK2))
| in(sK1,relation_dom(sK0)) ),
inference(copy,[status(thm)],[c_3686]) ).
cnf(c_3688,negated_conjecture,
( ~ function(sK0)
| ~ relation(sK0)
| ~ function(identity_relation(sK2))
| in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_44,c_3687]) ).
cnf(c_3689,negated_conjecture,
( ~ function(sK0)
| ~ relation(sK0)
| in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_52,c_3688]) ).
cnf(c_3690,negated_conjecture,
( ~ function(sK0)
| in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_85,c_3689]) ).
cnf(c_310,negated_conjecture,
in(sK1,relation_dom(sK0)),
inference(resolve,[status(thm)],[c_86,c_3690]) ).
cnf(c_311,negated_conjecture,
( ~ in(apply(sK0,sK1),sK2)
| ~ in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) ),
inference(resolve,[status(thm)],[c_310,c_89]) ).
cnf(c_3691,negated_conjecture,
( in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2))))
| ~ in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2))))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_234,c_88]) ).
cnf(c_3692,negated_conjecture,
( ~ in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2))))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_3691]) ).
cnf(c_3693,negated_conjecture,
( ~ in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2))))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_85,c_3692]) ).
cnf(c_3694,negated_conjecture,
( ~ in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))) ),
inference(resolve,[status(thm)],[c_86,c_3693]) ).
cnf(c_3354,negated_conjecture,
in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))),
inference(resolve,[status(thm)],[c_310,c_3694]) ).
cnf(c_3355,negated_conjecture,
~ in(apply(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_3354,c_311]) ).
cnf(c_3695,negated_conjecture,
( in(apply(sK0,A),B)
| ~ in(A,relation_dom(relation_composition(sK0,identity_relation(B))))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_235,c_85]) ).
cnf(c_3696,negated_conjecture,
( in(apply(sK0,A),B)
| ~ in(A,relation_dom(relation_composition(sK0,identity_relation(B)))) ),
inference(resolve,[status(thm)],[c_3695,c_86]) ).
cnf(c_3697,negated_conjecture,
~ in(sK1,relation_dom(relation_composition(sK0,identity_relation(sK2)))),
inference(resolve,[status(thm)],[c_3696,c_3355]) ).
cnf(c_3681,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3354,c_3697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU009+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n026.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 08:33:15 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 562654 was started by sandbox on n026,
% 0.11/5.39 % Sat Sep 26 08:33:15 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.40
% 0.16/5.40 % From the command line: assign(max_seconds, 300).
% 0.16/6.01
% 0.16/6.01 % SZS status Theorem for theBenchmark
% 0.16/6.01
% 0.16/6.01 % Proof 1 at 0.47 (+ 0.12) seconds.
% 0.16/6.01 % Length of proof is 26.
% 0.16/6.01 % Level of proof is 6.
% 0.16/6.01 % Maximum clause weight is 42.000.
% 0.16/6.01 % Given clauses 346.
% 0.16/6.01
% 0.16/6.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------