%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU072+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 : 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 08:44:59 AM UTC 2026
% Result : Theorem 0.16s 5.68s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 23 unt; 0 def)
% Number of atoms : 211 ( 76 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 224 ( 85 ~; 97 |; 26 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 1 sgn 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d5_funct_1) ).
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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t117_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ),
file('theBenchmark.p',t117_funct_1) ).
fof(t142_funct_1,axiom,
! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
file('theBenchmark.p',t142_funct_1) ).
fof(t39_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t6_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t153_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
=> one_to_one(A) ) ),
file('theBenchmark.p',t153_funct_1) ).
fof(t153_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
=> one_to_one(A) ) ),
inference(assume_negation,[status(cth)],[t153_funct_1]) ).
cnf(c_44,plain,
( apply(A,D) != C
| ~ in(D,relation_dom(A))
| in(C,B)
| relation_rng(A) != B
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_funct_1]) ).
fof(nnf_6,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) )
& ( ! [X3,X0] :
( X0 = X3
| apply(A,X0) != apply(A,X3)
| ~ in(X0,relation_dom(A))
| ~ in(X3,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) )
& ( ! [X3,X0] :
( X0 = X3
| apply(A,X0) != apply(A,X3)
| ~ in(X0,relation_dom(A))
| ~ in(X3,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_6]) ).
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_49,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_50,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_51,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_52,plain,
( sK1(A) != sK0(A)
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_56,plain,
( relation_image(A,singleton(B)) = singleton(apply(A,B))
| ~ in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t117_funct_1]) ).
fof(nnf_39,plain,
? [A] :
( ~ one_to_one(A)
& ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t153_funct_1_neg]) ).
fof(sk_t153_funct_1_neg,plain,
( ~ one_to_one(sK2)
& ! [B] : subset(relation_inverse_image(sK2,relation_image(sK2,B)),B)
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_39]) ).
cnf(c_57,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t153_funct_1_neg]) ).
cnf(c_87,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_88,plain,
( relation_inverse_image(A,singleton(B)) != empty_set
| ~ in(B,relation_rng(A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t142_funct_1]) ).
cnf(c_92,plain,
( singleton(B) = A
| empty_set = A
| ~ subset(A,singleton(B)) ),
inference(clausify,[status(thm)],[t39_zfmisc_1]) ).
cnf(c_100,plain,
( B = A
| ~ subset(singleton(A),singleton(B)) ),
inference(clausify,[status(thm)],[t6_zfmisc_1]) ).
cnf(c_103,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t153_funct_1_neg]) ).
cnf(c_104,negated_conjecture,
subset(relation_inverse_image(sK2,relation_image(sK2,A)),A),
inference(split_conjunct,[status(thm)],[sk_t153_funct_1_neg]) ).
cnf(c_105,negated_conjecture,
~ one_to_one(sK2),
inference(split_conjunct,[status(thm)],[sk_t153_funct_1_neg]) ).
cnf(c_182,negated_conjecture,
( relation_image(sK2,singleton(A)) = singleton(apply(sK2,A))
| ~ in(A,relation_dom(sK2))
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_56]) ).
cnf(c_1161,negated_conjecture,
( singleton(apply(sK2,A)) = relation_image(sK2,singleton(A))
| ~ in(A,relation_dom(sK2))
| ~ relation(sK2) ),
inference(copy,[status(thm)],[c_182]) ).
cnf(c_183,negated_conjecture,
( singleton(apply(sK2,A)) = relation_image(sK2,singleton(A))
| ~ in(A,relation_dom(sK2)) ),
inference(resolve,[status(thm)],[c_103,c_1161]) ).
cnf(c_184,negated_conjecture,
( sK1(sK2) != sK0(sK2)
| one_to_one(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_52]) ).
cnf(c_1162,negated_conjecture,
( sK1(sK2) != sK0(sK2)
| one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_103,c_184]) ).
cnf(c_185,negated_conjecture,
sK1(sK2) != sK0(sK2),
inference(resolve,[status(thm)],[c_105,c_1162]) ).
cnf(c_186,negated_conjecture,
( apply(sK2,sK1(sK2)) = apply(sK2,sK0(sK2))
| one_to_one(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_51]) ).
cnf(c_1163,negated_conjecture,
( apply(sK2,sK1(sK2)) = apply(sK2,sK0(sK2))
| one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_103,c_186]) ).
cnf(c_187,negated_conjecture,
apply(sK2,sK1(sK2)) = apply(sK2,sK0(sK2)),
inference(resolve,[status(thm)],[c_105,c_1163]) ).
cnf(c_188,negated_conjecture,
( in(sK1(sK2),relation_dom(sK2))
| one_to_one(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_50]) ).
cnf(c_1164,negated_conjecture,
( in(sK1(sK2),relation_dom(sK2))
| one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_103,c_188]) ).
cnf(c_189,negated_conjecture,
in(sK1(sK2),relation_dom(sK2)),
inference(resolve,[status(thm)],[c_105,c_1164]) ).
cnf(c_190,negated_conjecture,
( in(sK0(sK2),relation_dom(sK2))
| one_to_one(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_49]) ).
cnf(c_1165,negated_conjecture,
( in(sK0(sK2),relation_dom(sK2))
| one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_103,c_190]) ).
cnf(c_191,negated_conjecture,
in(sK0(sK2),relation_dom(sK2)),
inference(resolve,[status(thm)],[c_105,c_1165]) ).
cnf(c_198,negated_conjecture,
( apply(sK2,C) != B
| ~ in(C,relation_dom(sK2))
| in(B,A)
| relation_rng(sK2) != A
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_44]) ).
cnf(c_199,negated_conjecture,
( apply(sK2,C) != B
| ~ in(C,relation_dom(sK2))
| in(B,A)
| relation_rng(sK2) != A ),
inference(resolve,[status(thm)],[c_103,c_198]) ).
cnf(c_1166,negated_conjecture,
( singleton(A) = relation_inverse_image(sK2,relation_image(sK2,singleton(A)))
| empty_set = relation_inverse_image(sK2,relation_image(sK2,singleton(A))) ),
inference(resolve,[status(thm)],[c_104,c_92]) ).
cnf(c_1167,negated_conjecture,
( singleton(A) = relation_inverse_image(sK2,relation_image(sK2,singleton(A)))
| relation_inverse_image(sK2,relation_image(sK2,singleton(A))) = empty_set ),
inference(copy,[status(thm)],[c_1166]) ).
cnf(c_276,negated_conjecture,
( relation_inverse_image(sK2,relation_image(sK2,singleton(A))) = singleton(A)
| relation_inverse_image(sK2,relation_image(sK2,singleton(A))) = empty_set ),
inference(copy,[status(thm)],[c_1167]) ).
cnf(c_1168,negated_conjecture,
singleton(apply(sK2,sK1(sK2))) = relation_image(sK2,singleton(sK1(sK2))),
inference(resolve,[status(thm)],[c_189,c_183]) ).
cnf(c_1169,negated_conjecture,
singleton(apply(sK2,sK0(sK2))) = relation_image(sK2,singleton(sK1(sK2))),
inference(paramod,[status(thm)],[c_187,c_1168]) ).
cnf(c_378,negated_conjecture,
relation_image(sK2,singleton(sK1(sK2))) = singleton(apply(sK2,sK0(sK2))),
inference(copy,[status(thm)],[c_1169]) ).
cnf(c_390,plain,
singleton(apply(sK2,sK0(sK2))) = relation_image(sK2,singleton(sK0(sK2))),
inference(resolve,[status(thm)],[c_191,c_183]) ).
cnf(c_399,negated_conjecture,
relation_image(sK2,singleton(sK1(sK2))) = relation_image(sK2,singleton(sK0(sK2))),
inference(paramod,[status(thm)],[c_390,c_378]) ).
cnf(c_441,plain,
( apply(sK2,sK0(sK2)) != B
| in(B,A)
| relation_rng(sK2) != A ),
inference(resolve,[status(thm)],[c_199,c_191]) ).
cnf(c_1170,plain,
( relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) = singleton(sK1(sK2))
| relation_inverse_image(sK2,relation_image(sK2,singleton(sK1(sK2)))) = empty_set ),
inference(paramod,[status(thm)],[c_399,c_276]) ).
cnf(c_1171,plain,
( relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) = singleton(sK1(sK2))
| relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) = empty_set ),
inference(paramod,[status(thm)],[c_399,c_1170]) ).
cnf(c_865,plain,
( singleton(sK1(sK2)) = relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2))))
| relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) = empty_set ),
inference(copy,[status(thm)],[c_1171]) ).
cnf(c_1111,plain,
( apply(sK2,sK0(sK2)) != A
| in(A,relation_rng(sK2)) ),
inference(xxres,[status(thm)],[c_441]) ).
cnf(c_1172,negated_conjecture,
apply(sK2,sK0(sK2)) = apply(sK2,sK1(sK2)),
inference(copy,[status(thm)],[c_187]) ).
cnf(c_1173,negated_conjecture,
in(apply(sK2,sK1(sK2)),relation_rng(sK2)),
inference(resolve,[status(thm)],[c_1111,c_1172]) ).
cnf(c_1113,negated_conjecture,
in(apply(sK2,sK0(sK2)),relation_rng(sK2)),
inference(paramod,[status(thm)],[c_187,c_1173]) ).
cnf(c_1174,plain,
( relation_inverse_image(sK2,singleton(apply(sK2,sK0(sK2)))) != empty_set
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_1113,c_88]) ).
cnf(c_1175,plain,
( relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) != empty_set
| ~ relation(sK2) ),
inference(paramod,[status(thm)],[c_390,c_1174]) ).
cnf(c_1125,negated_conjecture,
relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) != empty_set,
inference(resolve,[status(thm)],[c_103,c_1175]) ).
cnf(c_1132,plain,
singleton(sK1(sK2)) = relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))),
inference(resolve,[status(thm)],[c_1125,c_865]) ).
cnf(c_1154,plain,
( sK1(sK2) = A
| ~ subset(singleton(A),relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2))))) ),
inference(paramod,[status(thm)],[c_1132,c_100]) ).
cnf(c_1176,plain,
( singleton(sK1(sK2)) = singleton(sK0(sK2))
| relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) = empty_set ),
inference(paramod,[status(thm)],[c_276,c_1132]) ).
cnf(c_1177,plain,
( relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) = singleton(sK0(sK2))
| relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) = empty_set ),
inference(paramod,[status(thm)],[c_1132,c_1176]) ).
cnf(c_1156,plain,
relation_inverse_image(sK2,relation_image(sK2,singleton(sK0(sK2)))) = singleton(sK0(sK2)),
inference(resolve,[status(thm)],[c_1125,c_1177]) ).
cnf(c_1157,plain,
( sK1(sK2) = A
| ~ subset(singleton(A),singleton(sK0(sK2))) ),
inference(paramod,[status(thm)],[c_1156,c_1154]) ).
cnf(c_1178,plain,
sK1(sK2) = sK0(sK2),
inference(resolve,[status(thm)],[c_1157,c_87]) ).
cnf(c_1160,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_185,c_1178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n006.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Sat Sep 26 08:34:03 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.40 % Process 830341 was started by sandbox on n006,
% 0.16/5.40 % Sat Sep 26 08:34:03 2026
% 0.16/5.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.42
% 0.16/5.42 % From the command line: assign(max_seconds, 300).
% 0.16/5.68
% 0.16/5.68 % SZS status Theorem for theBenchmark
% 0.16/5.68
% 0.16/5.68 % Proof 1 at 0.19 (+ 0.05) seconds.
% 0.16/5.68 % Length of proof is 48.
% 0.16/5.68 % Level of proof is 11.
% 0.16/5.68 % Maximum clause weight is 20.000.
% 0.16/5.68 % Given clauses 290.
% 0.16/5.68
% 0.16/5.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------