%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU142+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 : n008.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 08:45:09 AM UTC 2026
% Result : Theorem 5.66s 12.10s
% Output : CNFRefutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 80 ( 53 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 84 ( 32 ~; 39 |; 9 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 58 ( 4 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(t69_enumset1,conjecture,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t69_enumset1_neg,negated_conjecture,
~ ! [A] : unordered_pair(A,A) = singleton(A),
inference(assume_negation,[status(cth)],[t69_enumset1]) ).
cnf(c_10,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
fof(nnf_3,plain,
! [A,B] :
( ( ? [C] :
( ( C != A
| ~ in(C,B) )
& ( C = A
| in(C,B) ) )
| singleton(A) = B )
& ( ! [X0] :
( ( X0 != A
| in(X0,B) )
& ( X0 = A
| ~ in(X0,B) ) )
| singleton(A) != B ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(sk_d1_tarski_sk,plain,
! [A,B] :
( ( ( ( sK0(A,B) != A
| ~ in(sK0(A,B),B) )
& ( sK0(A,B) = A
| in(sK0(A,B),B) ) )
| singleton(A) = B )
& ( ! [X0] :
( ( X0 != A
| in(X0,B) )
& ( X0 = A
| ~ in(X0,B) ) )
| singleton(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_3]) ).
fof(sk_d1_tarski,plain,
( ! [VAR_0,VAR_1] :
( sK0(VAR_0,VAR_1) != VAR_0
| ~ in(sK0(VAR_0,VAR_1),VAR_1)
| singleton(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( sK0(VAR_0,VAR_1) = VAR_0
| in(sK0(VAR_0,VAR_1),VAR_1)
| singleton(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 != VAR_0
| in(VAR_2,VAR_1)
| singleton(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_0
| ~ in(VAR_2,VAR_1)
| singleton(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_tarski_sk]) ).
cnf(c_13,plain,
( sK0(A,B) = A
| in(sK0(A,B),B)
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_14,plain,
( sK0(A,B) != A
| ~ in(sK0(A,B),B)
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_15,plain,
( D = B
| D = A
| ~ in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_16,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
fof(nnf_8,plain,
? [A] : singleton(A) != unordered_pair(A,A),
inference(fof_nnf,[status(thm)],[t69_enumset1_neg]) ).
fof(sk_t69_enumset1_neg,plain,
singleton(sK1) != unordered_pair(sK1,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_8]) ).
cnf(c_23,negated_conjecture,
singleton(sK1) != unordered_pair(sK1,sK1),
inference(split_conjunct,[status(thm)],[sk_t69_enumset1_neg]) ).
cnf(c_36,plain,
( A = B
| A = C
| ~ in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_38,plain,
( A = B
| ~ in(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_43,plain,
( A != C
| in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_174,plain,
( sK0(A,unordered_pair(B,B)) = A
| singleton(A) = unordered_pair(B,B)
| sK0(A,unordered_pair(B,B)) = B ),
inference(resolve,[status(thm)],[c_38,c_13]) ).
cnf(c_177,plain,
( singleton(A) = unordered_pair(A,A)
| sK0(A,unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_174]) ).
cnf(c_179,plain,
in(A,unordered_pair(B,A)),
inference(xxres,[status(thm)],[c_43]) ).
cnf(c_230,plain,
in(A,unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_10,c_179]) ).
cnf(c_1976,plain,
sK0(sK1,unordered_pair(sK1,sK1)) = sK1,
inference(resolve,[status(thm)],[c_177,c_23]) ).
cnf(c_1995,plain,
( ~ in(sK0(sK1,unordered_pair(sK1,sK1)),unordered_pair(sK1,sK1))
| singleton(sK1) = unordered_pair(sK1,sK1) ),
inference(resolve,[status(thm)],[c_1976,c_14]) ).
cnf(c_1996,plain,
( ~ in(sK1,unordered_pair(sK1,sK1))
| singleton(sK1) = unordered_pair(sK1,sK1) ),
inference(paramod,[status(thm)],[c_1976,c_1995]) ).
cnf(c_1997,negated_conjecture,
~ in(sK1,unordered_pair(sK1,sK1)),
inference(resolve,[status(thm)],[c_23,c_1996]) ).
cnf(c_1994,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_230,c_1997]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/11.29 % Computer : n008.cluster.edu
% 0.18/11.29 % Model : x86_64 x86_64
% 0.18/11.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/11.29 % Memory : 8046.5625MB
% 0.18/11.29 % OS : Linux 6.8.0-71-generic
% 0.18/11.29 % CPULimit : 300
% 0.18/11.29 % WCLimit : 300
% 0.18/11.29 % DateTime : Sat Sep 26 08:40:52 UTC 2026
% 0.18/11.29 % CPUTime :
% 0.18/11.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/11.29 % Process 3235263 was started by sandbox on n008,
% 0.18/11.29 % Sat Sep 26 08:40:52 2026
% 0.18/11.29 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.24/11.30
% 0.24/11.30 % From the command line: assign(max_seconds, 300).
% 5.66/12.10
% 5.66/12.10 % SZS status Theorem for theBenchmark
% 5.66/12.10
% 5.66/12.10 % Proof 1 at 0.55 (+ 0.23) seconds.
% 5.66/12.10 % Length of proof is 19.
% 5.66/12.10 % Level of proof is 7.
% 5.66/12.10 % Maximum clause weight is 35.000.
% 5.66/12.10 % Given clauses 108.
% 5.66/12.10
% 5.66/12.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------