%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU291+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.64s 0.51s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 13 unt; 0 def)
% Number of atoms : 169 ( 89 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 172 ( 66 ~; 70 |; 21 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t16_relset_1,axiom,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
file('theBenchmark.p',t16_relset_1) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t9_funct_2,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( subset(B,C)
=> ( ( relation_of2_as_subset(D,A,C)
& quasi_total(D,A,C)
& function(D) )
| ( A != empty_set
& B = empty_set ) ) ) ),
file('theBenchmark.p',t9_funct_2) ).
fof(t9_funct_2_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( subset(B,C)
=> ( ( relation_of2_as_subset(D,A,C)
& quasi_total(D,A,C)
& function(D) )
| ( A != empty_set
& B = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[t9_funct_2]) ).
cnf(c_73,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_74,plain,
( relation_of2(A,B,C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_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_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_80,plain,
( relation_dom_as_subset(B,C,A) = B
| ~ quasi_total(A,B,C)
| empty_set != B
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[d1_funct_2]) ).
cnf(c_81,plain,
( relation_dom_as_subset(B,C,A) != B
| quasi_total(A,B,C)
| empty_set != B
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[d1_funct_2]) ).
cnf(c_110,plain,
( relation_of2_as_subset(A,B,D)
| ~ subset(C,D)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[t16_relset_1]) ).
cnf(c_115,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(clausify,[status(thm)],[t3_xboole_1]) ).
fof(nnf_51,plain,
? [A,B,C,D] :
( ( ~ relation_of2_as_subset(D,A,C)
| ~ quasi_total(D,A,C)
| ~ function(D) )
& ( empty_set = A
| empty_set != B )
& subset(B,C)
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(fof_nnf,[status(thm)],[t9_funct_2_neg]) ).
fof(sk_t9_funct_2_neg,plain,
( ( ~ relation_of2_as_subset(sK0,sK1,sK3)
| ~ quasi_total(sK0,sK1,sK3)
| ~ function(sK0) )
& ( empty_set = sK1
| empty_set != sK2 )
& subset(sK2,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]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3),skolemize(D,sK0)],[nnf_51]) ).
cnf(c_121,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t9_funct_2_neg]) ).
cnf(c_122,negated_conjecture,
quasi_total(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t9_funct_2_neg]) ).
cnf(c_123,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t9_funct_2_neg]) ).
cnf(c_124,negated_conjecture,
subset(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t9_funct_2_neg]) ).
cnf(c_125,negated_conjecture,
( empty_set = sK1
| empty_set != sK2 ),
inference(split_conjunct,[status(thm)],[sk_t9_funct_2_neg]) ).
cnf(c_977,negated_conjecture,
( empty_set = sK1
| sK2 != empty_set ),
inference(copy,[status(thm)],[c_125]) ).
cnf(c_126,negated_conjecture,
( sK1 = empty_set
| sK2 != empty_set ),
inference(copy,[status(thm)],[c_977]) ).
cnf(c_127,negated_conjecture,
( ~ relation_of2_as_subset(sK0,sK1,sK3)
| ~ quasi_total(sK0,sK1,sK3)
| ~ function(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t9_funct_2_neg]) ).
cnf(c_128,negated_conjecture,
( ~ relation_of2_as_subset(sK0,sK1,sK3)
| ~ quasi_total(sK0,sK1,sK3) ),
inference(resolve,[status(thm)],[c_121,c_127]) ).
cnf(c_147,plain,
( relation_dom(A) = relation_dom_as_subset(B,C,A)
| ~ relation_of2_as_subset(A,B,C) ),
inference(resolve,[status(thm)],[c_74,c_73]) ).
cnf(c_148,plain,
( relation_dom_as_subset(B,C,A) = relation_dom(A)
| ~ relation_of2_as_subset(A,B,C) ),
inference(copy,[status(thm)],[c_147]) ).
cnf(c_978,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| empty_set != sK1
| ~ relation_of2_as_subset(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_122,c_80]) ).
cnf(c_979,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| sK1 != empty_set
| ~ relation_of2_as_subset(sK0,sK1,sK2) ),
inference(copy,[status(thm)],[c_978]) ).
cnf(c_218,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| sK1 != empty_set ),
inference(resolve,[status(thm)],[c_123,c_979]) ).
cnf(c_980,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| empty_set = sK2
| ~ relation_of2_as_subset(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_122,c_78]) ).
cnf(c_981,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| sK2 = empty_set
| ~ relation_of2_as_subset(sK0,sK1,sK2) ),
inference(copy,[status(thm)],[c_980]) ).
cnf(c_219,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| sK2 = empty_set ),
inference(resolve,[status(thm)],[c_123,c_981]) ).
cnf(c_982,negated_conjecture,
( relation_of2_as_subset(sK0,sK1,A)
| ~ subset(sK2,A) ),
inference(resolve,[status(thm)],[c_110,c_123]) ).
cnf(c_223,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK3),
inference(resolve,[status(thm)],[c_982,c_124]) ).
cnf(c_225,negated_conjecture,
~ quasi_total(sK0,sK1,sK3),
inference(resolve,[status(thm)],[c_223,c_128]) ).
cnf(c_236,plain,
relation_dom_as_subset(sK1,sK2,sK0) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_148,c_123]) ).
cnf(c_238,negated_conjecture,
( relation_dom(sK0) = sK1
| sK2 = empty_set ),
inference(paramod,[status(thm)],[c_236,c_219]) ).
cnf(c_239,negated_conjecture,
( relation_dom(sK0) = sK1
| sK1 != empty_set ),
inference(paramod,[status(thm)],[c_236,c_218]) ).
cnf(c_348,plain,
relation_dom_as_subset(sK1,sK3,sK0) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_223,c_148]) ).
cnf(c_983,plain,
( relation_dom_as_subset(sK1,sK3,sK0) != sK1
| quasi_total(sK0,sK1,sK3)
| empty_set != sK1 ),
inference(resolve,[status(thm)],[c_223,c_81]) ).
cnf(c_984,plain,
( relation_dom(sK0) != sK1
| quasi_total(sK0,sK1,sK3)
| empty_set != sK1 ),
inference(paramod,[status(thm)],[c_348,c_983]) ).
cnf(c_985,plain,
( relation_dom(sK0) != sK1
| quasi_total(sK0,sK1,sK3)
| sK1 != empty_set ),
inference(copy,[status(thm)],[c_984]) ).
cnf(c_352,negated_conjecture,
( relation_dom(sK0) != sK1
| sK1 != empty_set ),
inference(resolve,[status(thm)],[c_225,c_985]) ).
cnf(c_986,plain,
( relation_dom_as_subset(sK1,sK3,sK0) != sK1
| quasi_total(sK0,sK1,sK3)
| empty_set = sK3 ),
inference(resolve,[status(thm)],[c_223,c_79]) ).
cnf(c_987,plain,
( relation_dom(sK0) != sK1
| quasi_total(sK0,sK1,sK3)
| empty_set = sK3 ),
inference(paramod,[status(thm)],[c_348,c_986]) ).
cnf(c_988,plain,
( relation_dom(sK0) != sK1
| quasi_total(sK0,sK1,sK3)
| sK3 = empty_set ),
inference(copy,[status(thm)],[c_987]) ).
cnf(c_353,negated_conjecture,
( relation_dom(sK0) != sK1
| sK3 = empty_set ),
inference(resolve,[status(thm)],[c_225,c_988]) ).
cnf(c_928,plain,
( sK2 = empty_set
| sK3 = empty_set ),
inference(resolve,[status(thm)],[c_353,c_238]) ).
cnf(c_931,plain,
( subset(sK2,empty_set)
| sK2 = empty_set ),
inference(paramod,[status(thm)],[c_928,c_124]) ).
cnf(c_989,plain,
( empty_set = sK2
| sK2 = empty_set ),
inference(resolve,[status(thm)],[c_931,c_115]) ).
cnf(c_990,plain,
( sK2 = empty_set
| sK2 = empty_set ),
inference(copy,[status(thm)],[c_989]) ).
cnf(c_944,plain,
sK2 = empty_set,
inference(copy,[status(thm)],[c_990]) ).
cnf(c_991,negated_conjecture,
( sK1 = empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_944,c_126]) ).
cnf(c_956,negated_conjecture,
sK1 = empty_set,
inference(copy,[status(thm)],[c_991]) ).
cnf(c_992,negated_conjecture,
( relation_dom(sK0) != sK1
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_956,c_352]) ).
cnf(c_993,negated_conjecture,
( relation_dom(sK0) != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_956,c_992]) ).
cnf(c_972,negated_conjecture,
relation_dom(sK0) != empty_set,
inference(copy,[status(thm)],[c_993]) ).
cnf(c_994,negated_conjecture,
( relation_dom(sK0) = sK1
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_956,c_239]) ).
cnf(c_995,negated_conjecture,
( relation_dom(sK0) = empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_956,c_994]) ).
cnf(c_996,negated_conjecture,
relation_dom(sK0) = empty_set,
inference(copy,[status(thm)],[c_995]) ).
cnf(c_976,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_972,c_996]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU291+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 09:08:51 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 62468 was started by sandbox2 on n018,
% 0.10/0.38 % Sat Sep 26 09:08:51 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.64/0.51
% 0.64/0.51 % SZS status Theorem for theBenchmark
% 0.64/0.51
% 0.64/0.51 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.64/0.51 % Length of proof is 40.
% 0.64/0.51 % Level of proof is 11.
% 0.64/0.51 % Maximum clause weight is 27.000.
% 0.64/0.51 % Given clauses 169.
% 0.64/0.51
% 0.64/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------