%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU142+2 : 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 : n012.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 200.86s 38.69s
% Output : CNFRefutation 200.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 81 ( 56 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 85 ( 31 ~; 41 |; 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 : 54 ( 3 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_65,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
fof(nnf_7,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_7]) ).
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_73,plain,
( sK0(A,B) = A
| in(sK0(A,B),B)
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_74,plain,
( sK0(A,B) != A
| ~ in(sK0(A,B),B)
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_77,plain,
( D = B
| D = A
| ~ in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_78,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
fof(nnf_62,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_62]) ).
cnf(c_158,negated_conjecture,
singleton(sK1) != unordered_pair(sK1,sK1),
inference(split_conjunct,[status(thm)],[sk_t69_enumset1_neg]) ).
cnf(c_13584,plain,
( A = B
| A = C
| ~ in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_77,c_65]) ).
cnf(c_217,plain,
( sK0(A,unordered_pair(B,C)) = A
| singleton(A) = unordered_pair(B,C)
| sK0(A,unordered_pair(B,C)) = B
| sK0(A,unordered_pair(B,C)) = C ),
inference(resolve,[status(thm)],[c_13584,c_73]) ).
cnf(c_13585,plain,
( A != B
| in(A,unordered_pair(B,C)) ),
inference(xxres,[status(thm)],[c_78]) ).
cnf(c_239,plain,
in(A,unordered_pair(A,B)),
inference(xxres,[status(thm)],[c_13585]) ).
cnf(c_13586,negated_conjecture,
( sK0(sK1,unordered_pair(sK1,sK1)) = sK1
| sK0(sK1,unordered_pair(sK1,sK1)) = sK1
| sK0(sK1,unordered_pair(sK1,sK1)) = sK1 ),
inference(resolve,[status(thm)],[c_217,c_158]) ).
cnf(c_13587,negated_conjecture,
( sK0(sK1,unordered_pair(sK1,sK1)) = sK1
| sK0(sK1,unordered_pair(sK1,sK1)) = sK1 ),
inference(copy,[status(thm)],[c_13586]) ).
cnf(c_4745,negated_conjecture,
sK0(sK1,unordered_pair(sK1,sK1)) = sK1,
inference(copy,[status(thm)],[c_13587]) ).
cnf(c_13588,plain,
( ~ in(sK0(sK1,unordered_pair(sK1,sK1)),unordered_pair(sK1,sK1))
| singleton(sK1) = unordered_pair(sK1,sK1) ),
inference(resolve,[status(thm)],[c_4745,c_74]) ).
cnf(c_13589,plain,
( ~ in(sK1,unordered_pair(sK1,sK1))
| singleton(sK1) = unordered_pair(sK1,sK1) ),
inference(paramod,[status(thm)],[c_4745,c_13588]) ).
cnf(c_13590,negated_conjecture,
~ in(sK1,unordered_pair(sK1,sK1)),
inference(resolve,[status(thm)],[c_158,c_13589]) ).
cnf(c_13583,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_239,c_13590]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU142+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/10.32 % Computer : n012.cluster.edu
% 0.04/10.32 % Model : x86_64 x86_64
% 0.04/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/10.32 % Memory : 8046.5625MB
% 0.04/10.32 % OS : Linux 6.8.0-71-generic
% 0.04/10.32 % CPULimit : 300
% 0.04/10.32 % WCLimit : 300
% 0.04/10.32 % DateTime : Sat Sep 26 08:39:48 UTC 2026
% 0.04/10.32 % CPUTime :
% 0.04/10.32 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/10.32 % Process 164807 was started by sandbox on n012,
% 0.04/10.32 % Sat Sep 26 08:39:48 2026
% 0.04/10.32 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/10.33
% 0.04/10.33 % From the command line: assign(max_seconds, 300).
% 200.86/38.69
% 200.86/38.69 % SZS status Theorem for theBenchmark
% 200.86/38.69
% 200.86/38.69 % Proof 1 at 3.24 (+ 0.93) seconds.
% 200.86/38.69 % Length of proof is 14.
% 200.86/38.69 % Level of proof is 4.
% 200.86/38.69 % Maximum clause weight is 27.000.
% 200.86/38.69 % Given clauses 224.
% 200.86/38.69
% 200.86/38.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------