%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET017+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:35:19 AM UTC 2026
% Result : Theorem 16.94s 2.91s
% Output : CNFRefutation 16.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 51 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 15 ~; 9 |; 11 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 5 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('theBenchmark.p',unordered_pair_defn) ).
fof(left_cancellation,conjecture,
! [X,Y,Z] :
( ( unordered_pair(X,Y) = unordered_pair(X,Z)
& member(Z,universal_class)
& member(Y,universal_class) )
=> Y = Z ),
file('theBenchmark.p',left_cancellation) ).
fof(left_cancellation_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( unordered_pair(X,Y) = unordered_pair(X,Z)
& member(Z,universal_class)
& member(Y,universal_class) )
=> Y = Z ),
inference(assume_negation,[status(cth)],[left_cancellation]) ).
fof(nnf_42,plain,
? [X,Y,Z] :
( Z != Y
& unordered_pair(X,Z) = unordered_pair(X,Y)
& member(Z,universal_class)
& member(Y,universal_class) ),
inference(fof_nnf,[status(thm)],[left_cancellation_neg]) ).
fof(sk_left_cancellation_neg,plain,
( sK0 != sK1
& unordered_pair(sK2,sK0) = unordered_pair(sK2,sK1)
& member(sK0,universal_class)
& member(sK1,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(X,sK2),skolemize(Y,sK1),skolemize(Z,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_left_cancellation_neg]) ).
cnf(c_65,negated_conjecture,
unordered_pair(sK2,sK0) = unordered_pair(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_left_cancellation_neg]) ).
cnf(c_66,negated_conjecture,
member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_left_cancellation_neg]) ).
cnf(c_67,negated_conjecture,
member(sK1,universal_class),
inference(split_conjunct,[status(thm)],[sk_left_cancellation_neg]) ).
cnf(c_132,plain,
( A != C
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_134,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_325,plain,
( sK1 != B
| member(sK1,unordered_pair(A,B)) ),
inference(resolve,[status(thm)],[c_132,c_67]) ).
cnf(c_326,plain,
( sK0 != B
| member(sK0,unordered_pair(A,B)) ),
inference(resolve,[status(thm)],[c_132,c_66]) ).
cnf(c_9157,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_64]) ).
cnf(c_9158,negated_conjecture,
( sK1 = A
| ~ member(sK1,unordered_pair(sK0,A)) ),
inference(resolve,[status(thm)],[c_134,c_9157]) ).
cnf(c_9159,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_64]) ).
cnf(c_344,negated_conjecture,
~ member(sK1,unordered_pair(sK0,sK0)),
inference(resolve,[status(thm)],[c_9158,c_9159]) ).
cnf(c_7218,plain,
member(sK1,unordered_pair(A,sK1)),
inference(xxres,[status(thm)],[c_325]) ).
cnf(c_7378,plain,
member(sK0,unordered_pair(A,sK0)),
inference(xxres,[status(thm)],[c_326]) ).
cnf(c_7408,plain,
member(sK0,unordered_pair(sK2,sK1)),
inference(paramod,[status(thm)],[c_65,c_7378]) ).
cnf(c_9160,plain,
( sK0 = sK1
| sK0 = sK2 ),
inference(resolve,[status(thm)],[c_7408,c_134]) ).
cnf(c_7418,negated_conjecture,
sK0 = sK2,
inference(resolve,[status(thm)],[c_64,c_9160]) ).
cnf(c_9161,negated_conjecture,
~ member(sK1,unordered_pair(sK2,sK0)),
inference(paramod,[status(thm)],[c_7418,c_344]) ).
cnf(c_7935,negated_conjecture,
~ member(sK1,unordered_pair(sK2,sK2)),
inference(paramod,[status(thm)],[c_7418,c_9161]) ).
cnf(c_9162,negated_conjecture,
unordered_pair(sK2,sK2) = unordered_pair(sK2,sK1),
inference(paramod,[status(thm)],[c_7418,c_65]) ).
cnf(c_7954,negated_conjecture,
unordered_pair(sK2,sK1) = unordered_pair(sK2,sK2),
inference(copy,[status(thm)],[c_9162]) ).
cnf(c_9163,plain,
member(sK1,unordered_pair(sK2,sK2)),
inference(paramod,[status(thm)],[c_7954,c_7218]) ).
cnf(c_9156,plain,
$false,
inference(resolve,[status(thm)],[c_7935,c_9163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET017+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 06:51:03 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2425230 was started by sandbox on n014,
% 0.17/0.43 % Sat Sep 26 06:51:03 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 16.94/2.91
% 16.94/2.91 % given #500 (F,wt=16): 1914 -member(f4(c1,universal_class),complement(universal_class)). [resolve(932,a,114,b)].
% 16.94/2.91
% 16.94/2.91 % SZS status Theorem for theBenchmark
% 16.94/2.91
% 16.94/2.91 % Proof 1 at 1.82 (+ 0.58) seconds.
% 16.94/2.91 % Length of proof is 18.
% 16.94/2.91 % Level of proof is 7.
% 16.94/2.91 % Maximum clause weight is 21.000.
% 16.94/2.91 % Given clauses 712.
% 16.94/2.91
% 16.94/2.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------