%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU290+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 : 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 08:45:42 AM UTC 2026
% Result : Theorem 0.12s 5.66s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 114 ( 38 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 111 ( 39 ~; 38 |; 17 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 68 ( 2 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(d1_funct_2,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( B = empty_set
=> ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set ) )
& ( ( B = empty_set
=> A = empty_set )
=> ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) ) ) ),
file('theBenchmark.p',d1_funct_2) ).
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(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('theBenchmark.p',redefinition_k4_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(t6_funct_2,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( in(C,A)
=> ( in(apply(D,C),relation_rng(D))
| B = empty_set ) ) ),
file('theBenchmark.p',t6_funct_2) ).
fof(t6_funct_2_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( in(C,A)
=> ( in(apply(D,C),relation_rng(D))
| B = empty_set ) ) ),
inference(assume_negation,[status(cth)],[t6_funct_2]) ).
cnf(c_59,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_54,plain,
? [A,B,C,D] :
( ~ in(apply(D,C),relation_rng(D))
& empty_set != B
& in(C,A)
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(fof_nnf,[status(thm)],[t6_funct_2_neg]) ).
fof(sk_t6_funct_2_neg,plain,
( ~ in(apply(sK0,sK3),relation_rng(sK0))
& empty_set != sK2
& in(sK3,sK1)
& relation_of2_as_subset(sK0,sK1,sK2)
& quasi_total(sK0,sK1,sK2)
& function(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3),skolemize(D,sK0)],[nnf_54]) ).
cnf(c_70,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t6_funct_2_neg]) ).
cnf(c_72,plain,
( element(A,powerset(cartesian_product2(B,C)))
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[dt_m2_relset_1]) ).
cnf(c_78,plain,
( relation_dom_as_subset(B,C,A) = B
| ~ quasi_total(A,B,C)
| empty_set = C
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[d1_funct_2]) ).
cnf(c_79,plain,
( relation_of2(A,B,C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_80,plain,
( ~ relation_of2(A,B,C)
| relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_81,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t6_funct_2_neg]) ).
cnf(c_83,negated_conjecture,
relation_of2(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_81,c_79]) ).
cnf(c_89,plain,
( element(A,powerset(cartesian_product2(B,C)))
| ~ relation_of2(A,B,C) ),
inference(resolve,[status(thm)],[c_80,c_72]) ).
cnf(c_91,plain,
( relation_dom(A) = relation_dom_as_subset(B,C,A)
| ~ relation_of2(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_k4_relset_1]) ).
cnf(c_138,negated_conjecture,
relation_dom(sK0) = relation_dom_as_subset(sK1,sK2,sK0),
inference(resolve,[status(thm)],[c_91,c_83]) ).
cnf(c_139,negated_conjecture,
relation_dom_as_subset(sK1,sK2,sK0) = relation_dom(sK0),
inference(copy,[status(thm)],[c_138]) ).
cnf(c_142,negated_conjecture,
element(sK0,powerset(cartesian_product2(sK1,sK2))),
inference(resolve,[status(thm)],[c_89,c_83]) ).
cnf(c_149,plain,
( relation(A)
| ~ element(A,powerset(cartesian_product2(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_189,negated_conjecture,
quasi_total(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t6_funct_2_neg]) ).
cnf(c_190,negated_conjecture,
in(sK3,sK1),
inference(split_conjunct,[status(thm)],[sk_t6_funct_2_neg]) ).
cnf(c_191,negated_conjecture,
empty_set != sK2,
inference(split_conjunct,[status(thm)],[sk_t6_funct_2_neg]) ).
cnf(c_192,negated_conjecture,
sK2 != empty_set,
inference(copy,[status(thm)],[c_191]) ).
cnf(c_193,negated_conjecture,
~ in(apply(sK0,sK3),relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t6_funct_2_neg]) ).
cnf(c_289,negated_conjecture,
( apply(sK0,C) != B
| ~ in(C,relation_dom(sK0))
| in(B,A)
| relation_rng(sK0) != A
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_70,c_59]) ).
cnf(c_309,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| empty_set = sK2 ),
inference(resolve,[status(thm)],[c_81,c_78]) ).
cnf(c_2040,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| empty_set = sK2 ),
inference(paramod,[status(thm)],[c_139,c_309]) ).
cnf(c_2041,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| sK2 = empty_set ),
inference(copy,[status(thm)],[c_2040]) ).
cnf(c_2042,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_192,c_2041]) ).
cnf(c_310,negated_conjecture,
relation_dom(sK0) = sK1,
inference(resolve,[status(thm)],[c_189,c_2042]) ).
cnf(c_338,negated_conjecture,
( apply(sK0,C) != B
| ~ in(C,sK1)
| in(B,A)
| relation_rng(sK0) != A
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_310,c_289]) ).
cnf(c_346,plain,
relation(sK0),
inference(resolve,[status(thm)],[c_149,c_142]) ).
cnf(c_351,negated_conjecture,
( apply(sK0,C) != B
| ~ in(C,sK1)
| in(B,A)
| relation_rng(sK0) != A ),
inference(resolve,[status(thm)],[c_346,c_338]) ).
cnf(c_1370,plain,
( apply(sK0,B) != A
| ~ in(B,sK1)
| in(A,relation_rng(sK0)) ),
inference(xxres,[status(thm)],[c_351]) ).
cnf(c_2035,plain,
( apply(sK0,sK3) != A
| in(A,relation_rng(sK0)) ),
inference(resolve,[status(thm)],[c_1370,c_190]) ).
cnf(c_2043,plain,
in(apply(sK0,sK3),relation_rng(sK0)),
inference(xxres,[status(thm)],[c_2035]) ).
cnf(c_2039,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_193,c_2043]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU290+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/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
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 09:01:24 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 328998 was started by sandbox on n017,
% 0.09/5.38 % Sat Sep 26 09:01:24 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 0.12/5.66
% 0.12/5.66 % SZS status Theorem for theBenchmark
% 0.12/5.66
% 0.12/5.66 % Proof 1 at 0.19 (+ 0.05) seconds.
% 0.12/5.66 % Length of proof is 35.
% 0.12/5.66 % Level of proof is 10.
% 0.12/5.66 % Maximum clause weight is 28.000.
% 0.12/5.66 % Given clauses 305.
% 0.12/5.66
% 0.12/5.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------