%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU221+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 : n013.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 08:45:28 AM UTC 2026
% Result : Theorem 45.44s 6.28s
% Output : CNFRefutation 45.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 16 unt; 0 def)
% Number of atoms : 225 ( 51 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 271 ( 106 ~; 113 |; 36 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 25 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(t54_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t57_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t62_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t62_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
inference(assume_negation,[status(cth)],[t62_funct_1]) ).
fof(nnf_5,plain,
! [A] :
( ( ( ? [B,C] :
( C != B
& apply(A,C) = apply(A,B)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(sk_d8_funct_1_sk,plain,
! [A] :
( ( ( ( sK1(A) != sK0(A)
& apply(A,sK1(A)) = apply(A,sK0(A))
& in(sK1(A),relation_dom(A))
& in(sK0(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0(A)),skolemize(C,sK1(A))],[nnf_5]) ).
fof(sk_d8_funct_1,plain,
( ! [VAR_0] :
( sK1(VAR_0) != sK0(VAR_0)
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( apply(VAR_0,sK1(VAR_0)) = apply(VAR_0,sK0(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK1(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK0(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| apply(VAR_0,VAR_2) != apply(VAR_0,VAR_1)
| ~ in(VAR_2,relation_dom(VAR_0))
| ~ in(VAR_1,relation_dom(VAR_0))
| ~ one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d8_funct_1_sk]) ).
cnf(c_50,plain,
( in(sK0(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_51,plain,
( in(sK1(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_52,plain,
( apply(A,sK1(A)) = apply(A,sK0(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_53,plain,
( sK1(A) != sK0(A)
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_54,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_55,plain,
( function(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_94,plain,
( relation_rng(A) = relation_dom(B)
| function_inverse(A) != B
| ~ function(B)
| ~ relation(B)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t54_funct_1]) ).
cnf(c_104,plain,
( apply(A,apply(function_inverse(A),B)) = B
| ~ in(B,relation_rng(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t57_funct_1]) ).
fof(nnf_40,plain,
? [A] :
( ~ one_to_one(function_inverse(A))
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t62_funct_1_neg]) ).
fof(sk_t62_funct_1_neg,plain,
( ~ one_to_one(function_inverse(sK2))
& one_to_one(sK2)
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_40]) ).
cnf(c_110,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t62_funct_1_neg]) ).
cnf(c_111,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t62_funct_1_neg]) ).
cnf(c_112,negated_conjecture,
one_to_one(sK2),
inference(split_conjunct,[status(thm)],[sk_t62_funct_1_neg]) ).
cnf(c_113,negated_conjecture,
~ one_to_one(function_inverse(sK2)),
inference(split_conjunct,[status(thm)],[sk_t62_funct_1_neg]) ).
cnf(c_10321,plain,
( relation_rng(A) = relation_dom(function_inverse(A))
| ~ function(function_inverse(A))
| ~ relation(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(xxres,[status(thm)],[c_94]) ).
cnf(c_306,plain,
( relation_dom(function_inverse(A)) = relation_rng(A)
| ~ function(function_inverse(A))
| ~ relation(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_10321]) ).
cnf(c_10322,negated_conjecture,
( function(function_inverse(sK2))
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_110,c_55]) ).
cnf(c_539,negated_conjecture,
function(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_111,c_10322]) ).
cnf(c_10323,negated_conjecture,
( relation(function_inverse(sK2))
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_110,c_54]) ).
cnf(c_540,negated_conjecture,
relation(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_111,c_10323]) ).
cnf(c_10324,plain,
( sK1(function_inverse(sK2)) != sK0(function_inverse(sK2))
| one_to_one(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_539,c_53]) ).
cnf(c_10325,plain,
( sK1(function_inverse(sK2)) != sK0(function_inverse(sK2))
| one_to_one(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_540,c_10324]) ).
cnf(c_822,negated_conjecture,
sK1(function_inverse(sK2)) != sK0(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_113,c_10325]) ).
cnf(c_10326,plain,
( apply(function_inverse(sK2),sK1(function_inverse(sK2))) = apply(function_inverse(sK2),sK0(function_inverse(sK2)))
| one_to_one(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_539,c_52]) ).
cnf(c_10327,plain,
( apply(function_inverse(sK2),sK1(function_inverse(sK2))) = apply(function_inverse(sK2),sK0(function_inverse(sK2)))
| one_to_one(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_540,c_10326]) ).
cnf(c_823,negated_conjecture,
apply(function_inverse(sK2),sK1(function_inverse(sK2))) = apply(function_inverse(sK2),sK0(function_inverse(sK2))),
inference(resolve,[status(thm)],[c_113,c_10327]) ).
cnf(c_10328,plain,
( in(sK1(function_inverse(sK2)),relation_dom(function_inverse(sK2)))
| one_to_one(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_539,c_51]) ).
cnf(c_10329,plain,
( in(sK1(function_inverse(sK2)),relation_dom(function_inverse(sK2)))
| one_to_one(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_540,c_10328]) ).
cnf(c_824,negated_conjecture,
in(sK1(function_inverse(sK2)),relation_dom(function_inverse(sK2))),
inference(resolve,[status(thm)],[c_113,c_10329]) ).
cnf(c_10330,plain,
( in(sK0(function_inverse(sK2)),relation_dom(function_inverse(sK2)))
| one_to_one(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_539,c_50]) ).
cnf(c_10331,plain,
( in(sK0(function_inverse(sK2)),relation_dom(function_inverse(sK2)))
| one_to_one(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_540,c_10330]) ).
cnf(c_825,negated_conjecture,
in(sK0(function_inverse(sK2)),relation_dom(function_inverse(sK2))),
inference(resolve,[status(thm)],[c_113,c_10331]) ).
cnf(c_10332,negated_conjecture,
( relation_dom(function_inverse(sK2)) = relation_rng(sK2)
| ~ function(function_inverse(sK2))
| ~ relation(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_306,c_110]) ).
cnf(c_10333,negated_conjecture,
( relation_dom(function_inverse(sK2)) = relation_rng(sK2)
| ~ function(function_inverse(sK2))
| ~ relation(function_inverse(sK2))
| ~ one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_111,c_10332]) ).
cnf(c_10334,negated_conjecture,
( relation_dom(function_inverse(sK2)) = relation_rng(sK2)
| ~ function(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_112,c_10333]) ).
cnf(c_10335,negated_conjecture,
( relation_dom(function_inverse(sK2)) = relation_rng(sK2)
| ~ function(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_540,c_10334]) ).
cnf(c_7578,negated_conjecture,
relation_dom(function_inverse(sK2)) = relation_rng(sK2),
inference(resolve,[status(thm)],[c_539,c_10335]) ).
cnf(c_7612,negated_conjecture,
in(sK0(function_inverse(sK2)),relation_rng(sK2)),
inference(paramod,[status(thm)],[c_7578,c_825]) ).
cnf(c_7613,negated_conjecture,
in(sK1(function_inverse(sK2)),relation_rng(sK2)),
inference(paramod,[status(thm)],[c_7578,c_824]) ).
cnf(c_10336,plain,
( apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_7612,c_104]) ).
cnf(c_10337,negated_conjecture,
( apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_110,c_10336]) ).
cnf(c_10338,negated_conjecture,
( apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_111,c_10337]) ).
cnf(c_10303,negated_conjecture,
apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK0(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_112,c_10338]) ).
cnf(c_10339,plain,
( apply(sK2,apply(function_inverse(sK2),sK1(function_inverse(sK2)))) = sK1(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_7613,c_104]) ).
cnf(c_10340,plain,
( apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK1(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(paramod,[status(thm)],[c_823,c_10339]) ).
cnf(c_10341,plain,
( sK0(function_inverse(sK2)) = sK1(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(paramod,[status(thm)],[c_10303,c_10340]) ).
cnf(c_10342,plain,
( sK1(function_inverse(sK2)) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(copy,[status(thm)],[c_10341]) ).
cnf(c_10343,negated_conjecture,
( sK1(function_inverse(sK2)) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_110,c_10342]) ).
cnf(c_10344,negated_conjecture,
( sK1(function_inverse(sK2)) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_111,c_10343]) ).
cnf(c_10345,negated_conjecture,
sK1(function_inverse(sK2)) = sK0(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_112,c_10344]) ).
cnf(c_10320,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_822,c_10345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:52:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 2375776 was started by sandbox2 on n013,
% 0.14/0.37 % Sat Sep 26 08:52:21 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 45.44/6.28
% 45.44/6.28 % given #500 (W,wt=20): 2304 relation(function_inverse(relation_composition(c9,c1))). [back_unit_del(2121),unit_del(a,2293)].
% 45.44/6.28
% 45.44/6.28 % SZS status Theorem for theBenchmark
% 45.44/6.28
% 45.44/6.28 % Proof 1 at 5.39 (+ 0.46) seconds.
% 45.44/6.28 % Length of proof is 29.
% 45.44/6.28 % Level of proof is 6.
% 45.44/6.28 % Maximum clause weight is 40.000.
% 45.44/6.28 % Given clauses 707.
% 45.44/6.28
% 45.44/6.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------