%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET872+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:37:11 AM UTC 2026
% Result : Theorem 1.51s 0.65s
% Output : CNFRefutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 57 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 19 |; 6 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 4 sgn 29 !; 3 ?)
% 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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t12_zfmisc_1,conjecture,
! [A,B] : subset(singleton(A),unordered_pair(A,B)),
file('theBenchmark.p',t12_zfmisc_1) ).
fof(t12_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] : subset(singleton(A),unordered_pair(A,B)),
inference(assume_negation,[status(cth)],[t12_zfmisc_1]) ).
cnf(c_11,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_12,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_17,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
fof(nnf_5,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_5]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_23,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_24,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_9,plain,
? [A,B] : ~ subset(singleton(A),unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[t12_zfmisc_1_neg]) ).
fof(sk_t12_zfmisc_1_neg,plain,
~ subset(singleton(sK1),unordered_pair(sK1,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_9]) ).
cnf(c_28,negated_conjecture,
~ subset(singleton(sK1),unordered_pair(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_t12_zfmisc_1_neg]) ).
cnf(c_35,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_12]) ).
cnf(c_48,plain,
( A != C
| in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_78,plain,
in(sK0(singleton(sK1),unordered_pair(sK1,sK2)),singleton(sK1)),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_79,negated_conjecture,
~ in(sK0(singleton(sK1),unordered_pair(sK1,sK2)),unordered_pair(sK1,sK2)),
inference(resolve,[status(thm)],[c_24,c_28]) ).
cnf(c_189,plain,
in(A,unordered_pair(B,A)),
inference(xxres,[status(thm)],[c_48]) ).
cnf(c_225,plain,
in(A,unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_11,c_189]) ).
cnf(c_936,plain,
sK0(singleton(sK1),unordered_pair(sK1,sK2)) = sK1,
inference(resolve,[status(thm)],[c_78,c_35]) ).
cnf(c_939,negated_conjecture,
~ in(sK1,unordered_pair(sK1,sK2)),
inference(paramod,[status(thm)],[c_936,c_79]) ).
cnf(c_938,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_225,c_939]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET872+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n007.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 08:21:24 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 3284597 was started by sandbox on n007,
% 0.10/0.38 % Sat Sep 26 08:21:24 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 1.51/0.65
% 1.51/0.65 % SZS status Theorem for theBenchmark
% 1.51/0.65
% 1.51/0.65 % Proof 1 at 0.18 (+ 0.07) seconds.
% 1.51/0.65 % Length of proof is 19.
% 1.51/0.65 % Level of proof is 5.
% 1.51/0.65 % Maximum clause weight is 25.000.
% 1.51/0.65 % Given clauses 97.
% 1.51/0.65
% 1.51/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------