%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU186+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 : 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 08:45:21 AM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 18 unt; 0 def)
% Number of atoms : 77 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 75 ( 34 ~; 22 |; 13 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 3 sgn 37 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_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(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t56_relat_1,conjecture,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t56_relat_1_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
inference(assume_negation,[status(cth)],[t56_relat_1]) ).
fof(nnf_4,plain,
! [A] :
( ( ? [B] :
( ! [C,D] : ordered_pair(C,D) != B
& in(B,A) )
| relation(A) )
& ( ! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
| ~ in(X0,A) )
| ~ relation(A) ) ),
inference(fof_nnf,[status(thm)],[d1_relat_1]) ).
fof(sk_d1_relat_1_sk,plain,
! [A] :
( ( ( ! [C,D] : ordered_pair(C,D) != sK4(A)
& in(sK4(A),A) )
| relation(A) )
& ( ! [X0] :
( ordered_pair(sK0(A,X0),sK1(A,X0)) = X0
| ~ in(X0,A) )
| ~ relation(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK4]),skolemize(X1,sK0(A,X0)),skolemize(X2,sK1(A,X0)),skolemize(B,sK4(A))],[nnf_4]) ).
fof(sk_d1_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ordered_pair(VAR_1,VAR_2) != sK4(VAR_0)
| relation(VAR_0) )
& ! [VAR_0] :
( in(sK4(VAR_0),VAR_0)
| relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( ordered_pair(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1)) = VAR_1
| ~ in(VAR_1,VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_relat_1_sk]) ).
cnf(c_26,plain,
( ordered_pair(sK0(A,B),sK1(A,B)) = B
| ~ in(B,A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_relat_1]) ).
fof(nnf_25,plain,
? [A] :
( empty_set != A
& ! [B,C] : ~ in(ordered_pair(B,C),A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t56_relat_1_neg]) ).
fof(sk_t56_relat_1_neg,plain,
( empty_set != sK2
& ! [B,C] : ~ in(ordered_pair(B,C),sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_25]) ).
cnf(c_33,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t56_relat_1_neg]) ).
cnf(c_35,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
fof(nnf_11,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_11]) ).
cnf(c_36,plain,
element(sK3(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
cnf(c_37,plain,
( in(sK3(A),A)
| empty(A) ),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_40,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_41,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_52,plain,
( ~ empty(B)
| B = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t8_boole]) ).
cnf(c_53,negated_conjecture,
~ in(ordered_pair(A,B),sK2),
inference(split_conjunct,[status(thm)],[sk_t56_relat_1_neg]) ).
cnf(c_54,negated_conjecture,
~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK2),
inference(paramod,[status(thm)],[c_40,c_53]) ).
cnf(c_55,negated_conjecture,
empty_set != sK2,
inference(split_conjunct,[status(thm)],[sk_t56_relat_1_neg]) ).
cnf(c_56,negated_conjecture,
sK2 != empty_set,
inference(copy,[status(thm)],[c_55]) ).
cnf(c_67,negated_conjecture,
( ordered_pair(sK0(sK2,A),sK1(sK2,A)) = A
| ~ in(A,sK2) ),
inference(resolve,[status(thm)],[c_33,c_26]) ).
cnf(c_68,negated_conjecture,
( unordered_pair(unordered_pair(sK0(sK2,A),sK1(sK2,A)),singleton(sK0(sK2,A))) = A
| ~ in(A,sK2) ),
inference(paramod,[status(thm)],[c_40,c_67]) ).
cnf(c_105,plain,
( ~ empty(A)
| A = empty_set ),
inference(resolve,[status(thm)],[c_52,c_41]) ).
cnf(c_76,negated_conjecture,
~ empty(sK2),
inference(resolve,[status(thm)],[c_105,c_56]) ).
cnf(c_106,negated_conjecture,
( empty(sK2)
| unordered_pair(unordered_pair(sK0(sK2,sK3(sK2)),sK1(sK2,sK3(sK2))),singleton(sK0(sK2,sK3(sK2)))) = sK3(sK2) ),
inference(resolve,[status(thm)],[c_68,c_37]) ).
cnf(c_80,negated_conjecture,
unordered_pair(unordered_pair(sK0(sK2,sK3(sK2)),sK1(sK2,sK3(sK2))),singleton(sK0(sK2,sK3(sK2)))) = sK3(sK2),
inference(resolve,[status(thm)],[c_76,c_106]) ).
cnf(c_91,plain,
~ in(sK3(sK2),sK2),
inference(paramod,[status(thm)],[c_80,c_54]) ).
cnf(c_107,plain,
empty(sK2),
inference(resolve,[status(thm)],[c_91,c_37]) ).
cnf(c_104,plain,
$false,
inference(resolve,[status(thm)],[c_76,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 08:48:38 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 2482678 was started by sandbox2 on n003,
% 0.12/0.38 % Sat Sep 26 08:48:38 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % SZS status Theorem for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.40 % Length of proof is 24.
% 0.12/0.40 % Level of proof is 6.
% 0.12/0.40 % Maximum clause weight is 18.000.
% 0.12/0.40 % Given clauses 41.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------