%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU187+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 : n001.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 08:45:21 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 18 unt; 0 def)
% Number of atoms : 168 ( 42 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 198 ( 80 ~; 88 |; 21 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-3 aty)
% Number of variables : 108 ( 4 sgn 63 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t60_relat_1,conjecture,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_relat_1_neg,negated_conjecture,
~ ( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(assume_negation,[status(cth)],[t60_relat_1]) ).
cnf(c_33,plain,
( relation(A)
| ~ empty(A) ),
inference(clausify,[status(thm)],[cc1_relat_1]) ).
fof(nnf_4,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) )
& ( ? [X3] : in(ordered_pair(C,X3),A)
| in(C,B) ) )
| relation_dom(A) = B )
& ( ! [X0] :
( ( ! [X2] : ~ in(ordered_pair(X0,X2),A)
| in(X0,B) )
& ( ? [X1] : in(ordered_pair(X0,X1),A)
| ~ in(X0,B) ) )
| relation_dom(A) != B ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_1]) ).
fof(sk_d4_relat_1_sk,plain,
! [A] :
( ! [B] :
( ( ( ( ! [D] : ~ in(ordered_pair(sK0(A,B),D),A)
| ~ in(sK0(A,B),B) )
& ( in(ordered_pair(sK0(A,B),sK1(A,B)),A)
| in(sK0(A,B),B) ) )
| relation_dom(A) = B )
& ( ! [X0] :
( ( ! [X2] : ~ in(ordered_pair(X0,X2),A)
| in(X0,B) )
& ( in(ordered_pair(X0,sK4(A,B,X0)),A)
| ~ in(X0,B) ) )
| relation_dom(A) != B ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK0,sK1]),skolemize(X1,sK4(A,B,X0)),skolemize(C,sK0(A,B)),skolemize(X3,sK1(A,B))],[nnf_4]) ).
fof(sk_d4_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(ordered_pair(sK0(VAR_0,VAR_1),VAR_2),VAR_0)
| ~ in(sK0(VAR_0,VAR_1),VAR_1)
| relation_dom(VAR_0) = VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(ordered_pair(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1)),VAR_0)
| in(sK0(VAR_0,VAR_1),VAR_1)
| relation_dom(VAR_0) = VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(ordered_pair(VAR_2,VAR_3),VAR_0)
| in(VAR_2,VAR_1)
| relation_dom(VAR_0) != VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(ordered_pair(VAR_2,sK4(VAR_0,VAR_1,VAR_2)),VAR_0)
| ~ in(VAR_2,VAR_1)
| relation_dom(VAR_0) != VAR_1
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_relat_1_sk]) ).
cnf(c_35,plain,
( in(ordered_pair(sK0(A,B),sK1(A,B)),A)
| in(sK0(A,B),B)
| relation_dom(A) = B
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d4_relat_1]) ).
fof(nnf_5,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) )
& ( ? [X3] : in(ordered_pair(X3,C),A)
| in(C,B) ) )
| relation_rng(A) = B )
& ( ! [X0] :
( ( ! [X2] : ~ in(ordered_pair(X2,X0),A)
| in(X0,B) )
& ( ? [X1] : in(ordered_pair(X1,X0),A)
| ~ in(X0,B) ) )
| relation_rng(A) != B ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_relat_1]) ).
fof(sk_d5_relat_1_sk,plain,
! [A] :
( ! [B] :
( ( ( ( ! [D] : ~ in(ordered_pair(D,sK5(A,B)),A)
| ~ in(sK5(A,B),B) )
& ( in(ordered_pair(sK6(A,B),sK5(A,B)),A)
| in(sK5(A,B),B) ) )
| relation_rng(A) = B )
& ( ! [X0] :
( ( ! [X2] : ~ in(ordered_pair(X2,X0),A)
| in(X0,B) )
& ( in(ordered_pair(sK2(A,B,X0),X0),A)
| ~ in(X0,B) ) )
| relation_rng(A) != B ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK5,sK6]),skolemize(X1,sK2(A,B,X0)),skolemize(C,sK5(A,B)),skolemize(X3,sK6(A,B))],[nnf_5]) ).
fof(sk_d5_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(ordered_pair(VAR_2,sK5(VAR_0,VAR_1)),VAR_0)
| ~ in(sK5(VAR_0,VAR_1),VAR_1)
| relation_rng(VAR_0) = VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(ordered_pair(sK6(VAR_0,VAR_1),sK5(VAR_0,VAR_1)),VAR_0)
| in(sK5(VAR_0,VAR_1),VAR_1)
| relation_rng(VAR_0) = VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(ordered_pair(VAR_3,VAR_2),VAR_0)
| in(VAR_2,VAR_1)
| relation_rng(VAR_0) != VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(ordered_pair(sK2(VAR_0,VAR_1,VAR_2),VAR_2),VAR_0)
| ~ in(VAR_2,VAR_1)
| relation_rng(VAR_0) != VAR_1
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d5_relat_1_sk]) ).
cnf(c_37,plain,
( in(ordered_pair(sK2(A,B,C),C),A)
| ~ in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d5_relat_1]) ).
cnf(c_47,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
fof(nnf_14,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(sk_existence_m1_subset_1,plain,
! [A] : element(sK3(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(B,sK3(A))],[nnf_14]) ).
cnf(c_48,plain,
element(sK3(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
cnf(c_49,plain,
( in(sK3(A),A)
| empty(A) ),
inference(resolve,[status(thm)],[c_48,c_47]) ).
cnf(c_51,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_52,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
cnf(c_53,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_64,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
cnf(c_65,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_67,negated_conjecture,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(clausify,[status(thm)],[t60_relat_1_neg]) ).
cnf(c_70,plain,
( ~ empty(A)
| in(ordered_pair(sK0(A,B),sK1(A,B)),A)
| in(sK0(A,B),B)
| relation_dom(A) = B ),
inference(resolve,[status(thm)],[c_35,c_33]) ).
cnf(c_71,plain,
( ~ empty(A)
| in(unordered_pair(unordered_pair(sK0(A,B),sK1(A,B)),singleton(sK0(A,B))),A)
| in(sK0(A,B),B)
| relation_dom(A) = B ),
inference(paramod,[status(thm)],[c_52,c_70]) ).
cnf(c_72,plain,
( ~ empty(A)
| in(ordered_pair(sK2(A,B,C),C),A)
| ~ in(C,B)
| relation_rng(A) != B ),
inference(resolve,[status(thm)],[c_37,c_33]) ).
cnf(c_200,plain,
( ~ empty(A)
| in(unordered_pair(unordered_pair(sK2(A,B,C),C),singleton(sK2(A,B,C))),A)
| ~ in(C,B)
| relation_rng(A) != B ),
inference(paramod,[status(thm)],[c_52,c_72]) ).
cnf(c_73,plain,
( ~ empty(A)
| in(unordered_pair(unordered_pair(C,sK2(A,B,C)),singleton(sK2(A,B,C))),A)
| ~ in(C,B)
| relation_rng(A) != B ),
inference(paramod,[status(thm)],[c_51,c_200]) ).
cnf(c_136,plain,
~ in(A,empty_set),
inference(resolve,[status(thm)],[c_65,c_53]) ).
cnf(c_201,plain,
( ~ empty(B)
| in(unordered_pair(unordered_pair(A,sK2(B,relation_rng(B),A)),singleton(sK2(B,relation_rng(B),A))),B)
| ~ in(A,relation_rng(B)) ),
inference(xxres,[status(thm)],[c_73]) ).
cnf(c_202,plain,
( ~ empty(empty_set)
| ~ in(A,relation_rng(empty_set)) ),
inference(resolve,[status(thm)],[c_201,c_136]) ).
cnf(c_183,plain,
~ in(A,relation_rng(empty_set)),
inference(resolve,[status(thm)],[c_202,c_53]) ).
cnf(c_187,plain,
empty(relation_rng(empty_set)),
inference(resolve,[status(thm)],[c_183,c_49]) ).
cnf(c_203,plain,
empty_set = relation_rng(empty_set),
inference(resolve,[status(thm)],[c_187,c_64]) ).
cnf(c_191,plain,
relation_rng(empty_set) = empty_set,
inference(copy,[status(thm)],[c_203]) ).
cnf(c_204,negated_conjecture,
( empty_set != empty_set
| relation_dom(empty_set) != empty_set ),
inference(paramod,[status(thm)],[c_191,c_67]) ).
cnf(c_194,negated_conjecture,
relation_dom(empty_set) != empty_set,
inference(copy,[status(thm)],[c_204]) ).
cnf(c_205,negated_conjecture,
( ~ empty(empty_set)
| in(unordered_pair(unordered_pair(sK0(empty_set,empty_set),sK1(empty_set,empty_set)),singleton(sK0(empty_set,empty_set))),empty_set)
| in(sK0(empty_set,empty_set),empty_set) ),
inference(resolve,[status(thm)],[c_71,c_194]) ).
cnf(c_206,negated_conjecture,
( ~ empty(empty_set)
| in(unordered_pair(unordered_pair(sK0(empty_set,empty_set),sK1(empty_set,empty_set)),singleton(sK0(empty_set,empty_set))),empty_set) ),
inference(resolve,[status(thm)],[c_205,c_136]) ).
cnf(c_207,negated_conjecture,
~ empty(empty_set),
inference(resolve,[status(thm)],[c_206,c_136]) ).
cnf(c_199,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_53,c_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:52:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1412742 was started by sandbox on n001,
% 0.13/0.36 % Sat Sep 26 08:52:28 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.40
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.40 % Length of proof is 32.
% 0.13/0.40 % Level of proof is 8.
% 0.13/0.40 % Maximum clause weight is 25.000.
% 0.13/0.40 % Given clauses 44.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------