%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU292+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 : n003.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 19.79s 3.32s
% Output : CNFRefutation 19.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 17 unt; 0 def)
% Number of atoms : 125 ( 39 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 121 ( 40 ~; 39 |; 23 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 65 ( 2 sgn 28 !; 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(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(t23_funct_1,axiom,
! [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(t21_funct_2,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
file('theBenchmark.p',t21_funct_2) ).
fof(t21_funct_2_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[t21_funct_2]) ).
cnf(c_56,plain,
( relation_of2(A,B,C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_57,plain,
( ~ relation_of2(A,B,C)
| relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
fof(nnf_55,plain,
? [A,B,C,D] :
( ? [E] :
( apply(relation_composition(D,E),C) != apply(E,apply(D,C))
& empty_set != B
& in(C,A)
& function(E)
& relation(E) )
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(fof_nnf,[status(thm)],[t21_funct_2_neg]) ).
fof(sk_t21_funct_2_neg,plain,
( apply(relation_composition(sK0,sK3),sK4) != apply(sK3,apply(sK0,sK4))
& empty_set != sK2
& in(sK4,sK1)
& function(sK3)
& relation(sK3)
& 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,sK4]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK4),skolemize(D,sK0),skolemize(E,sK3)],[nnf_55]) ).
cnf(c_58,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t21_funct_2_neg]) ).
cnf(c_60,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_66,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_68,plain,
( ~ relation_of2(A,B,C)
| element(A,powerset(cartesian_product2(B,C))) ),
inference(resolve,[status(thm)],[c_60,c_57]) ).
cnf(c_75,negated_conjecture,
relation_of2(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_56,c_58]) ).
cnf(c_80,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_87,negated_conjecture,
relation_dom(sK0) = relation_dom_as_subset(sK1,sK2,sK0),
inference(resolve,[status(thm)],[c_80,c_75]) ).
cnf(c_88,negated_conjecture,
relation_dom_as_subset(sK1,sK2,sK0) = relation_dom(sK0),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_142,negated_conjecture,
element(sK0,powerset(cartesian_product2(sK1,sK2))),
inference(resolve,[status(thm)],[c_75,c_68]) ).
cnf(c_156,negated_conjecture,
apply(relation_composition(sK0,sK3),sK4) != apply(sK3,apply(sK0,sK4)),
inference(split_conjunct,[status(thm)],[sk_t21_funct_2_neg]) ).
cnf(c_157,negated_conjecture,
empty_set != sK2,
inference(split_conjunct,[status(thm)],[sk_t21_funct_2_neg]) ).
cnf(c_158,negated_conjecture,
sK2 != empty_set,
inference(copy,[status(thm)],[c_157]) ).
cnf(c_159,negated_conjecture,
in(sK4,sK1),
inference(split_conjunct,[status(thm)],[sk_t21_funct_2_neg]) ).
cnf(c_160,negated_conjecture,
function(sK3),
inference(split_conjunct,[status(thm)],[sk_t21_funct_2_neg]) ).
cnf(c_161,negated_conjecture,
relation(sK3),
inference(split_conjunct,[status(thm)],[sk_t21_funct_2_neg]) ).
cnf(c_162,negated_conjecture,
quasi_total(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t21_funct_2_neg]) ).
cnf(c_163,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t21_funct_2_neg]) ).
cnf(c_170,plain,
( apply(relation_composition(A,B),C) = apply(B,apply(A,C))
| ~ in(C,relation_dom(A))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t23_funct_1]) ).
cnf(c_215,plain,
( relation(A)
| ~ element(A,powerset(cartesian_product2(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_231,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| empty_set = sK2 ),
inference(resolve,[status(thm)],[c_66,c_58]) ).
cnf(c_18559,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| empty_set = sK2 ),
inference(paramod,[status(thm)],[c_88,c_231]) ).
cnf(c_18560,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| sK2 = empty_set ),
inference(copy,[status(thm)],[c_18559]) ).
cnf(c_18561,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_158,c_18560]) ).
cnf(c_232,negated_conjecture,
relation_dom(sK0) = sK1,
inference(resolve,[status(thm)],[c_162,c_18561]) ).
cnf(c_440,plain,
relation(sK0),
inference(resolve,[status(thm)],[c_215,c_142]) ).
cnf(c_18562,plain,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,sK1)
| ~ function(A)
| ~ relation(A)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_232,c_170]) ).
cnf(c_18563,plain,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,sK1)
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_440,c_18562]) ).
cnf(c_451,negated_conjecture,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,sK1)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_163,c_18563]) ).
cnf(c_18564,negated_conjecture,
( apply(relation_composition(sK0,sK3),A) = apply(sK3,apply(sK0,A))
| ~ in(A,sK1)
| ~ function(sK3) ),
inference(resolve,[status(thm)],[c_451,c_161]) ).
cnf(c_18565,negated_conjecture,
( apply(relation_composition(sK0,sK3),A) = apply(sK3,apply(sK0,A))
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_18564,c_160]) ).
cnf(c_18566,negated_conjecture,
apply(relation_composition(sK0,sK3),sK4) = apply(sK3,apply(sK0,sK4)),
inference(resolve,[status(thm)],[c_18565,c_159]) ).
cnf(c_18558,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_156,c_18566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU292+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 09:08:38 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2518660 was started by sandbox on n003,
% 0.11/0.37 % Sat Sep 26 09:08:38 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 19.79/3.32
% 19.79/3.32 % SZS status Theorem for theBenchmark
% 19.79/3.32
% 19.79/3.32 % Proof 1 at 1.83 (+ 0.83) seconds.
% 19.79/3.32 % Length of proof is 33.
% 19.79/3.32 % Level of proof is 7.
% 19.79/3.32 % Maximum clause weight is 43.000.
% 19.79/3.32 % Given clauses 450.
% 19.79/3.32
% 19.79/3.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------