%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET596+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:36:33 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 33 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 4 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 20 ( 0 sgn 10 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_empty_set_is_empty_set,axiom,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('theBenchmark.p',subset_of_empty_set_is_empty_set) ).
fof(intersection_of_subset,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
file('theBenchmark.p',intersection_of_subset) ).
fof(prove_th55,conjecture,
! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,C) )
=> intersection(B,D) = empty_set ),
file('theBenchmark.p',prove_th55) ).
fof(prove_th55_neg,negated_conjecture,
~ ! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,C) )
=> intersection(B,D) = empty_set ),
inference(assume_negation,[status(cth)],[prove_th55]) ).
fof(nnf_11,plain,
? [B,C,D] :
( intersection(B,D) != empty_set
& intersection(C,D) = empty_set
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th55_neg]) ).
fof(sk_prove_th55_neg,plain,
( intersection(sK0,sK1) != empty_set
& intersection(sK2,sK1) = empty_set
& subset(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(B,sK0),skolemize(C,sK2),skolemize(D,sK1)],[nnf_11]) ).
cnf(c_15,negated_conjecture,
intersection(sK0,sK1) != empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_th55_neg]) ).
cnf(c_16,negated_conjecture,
intersection(sK2,sK1) = empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_th55_neg]) ).
cnf(c_17,negated_conjecture,
empty_set = intersection(sK2,sK1),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_18,negated_conjecture,
subset(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_th55_neg]) ).
cnf(c_36,plain,
( subset(intersection(A,C),intersection(B,C))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[intersection_of_subset]) ).
cnf(c_37,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(clausify,[status(thm)],[subset_of_empty_set_is_empty_set]) ).
cnf(c_79,plain,
( empty_set = A
| ~ subset(A,intersection(sK2,sK1)) ),
inference(paramod,[status(thm)],[c_17,c_37]) ).
cnf(c_38,plain,
( intersection(sK2,sK1) = A
| ~ subset(A,intersection(sK2,sK1)) ),
inference(paramod,[status(thm)],[c_17,c_79]) ).
cnf(c_80,negated_conjecture,
intersection(sK0,sK1) != intersection(sK2,sK1),
inference(paramod,[status(thm)],[c_17,c_15]) ).
cnf(c_39,negated_conjecture,
intersection(sK2,sK1) != intersection(sK0,sK1),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_76,plain,
subset(intersection(sK0,A),intersection(sK2,A)),
inference(resolve,[status(thm)],[c_36,c_18]) ).
cnf(c_81,negated_conjecture,
~ subset(intersection(sK0,sK1),intersection(sK2,sK1)),
inference(resolve,[status(thm)],[c_38,c_39]) ).
cnf(c_78,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_76,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET596+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:00:10 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2385965 was started by sandbox on n003,
% 0.13/0.36 % Sat Sep 26 08:00:10 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 13.
% 0.13/0.38 % Level of proof is 4.
% 0.13/0.38 % Maximum clause weight is 10.000.
% 0.13/0.38 % Given clauses 22.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------