%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET173+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 : n006.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 08:35:58 AM UTC 2026
% Result : Theorem 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 75 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 29 ~; 26 |; 8 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 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 : 69 ( 5 sgn 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_defn) ).
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_absorbtion_for_intersection,conjecture,
! [B,C] : intersection(B,union(B,C)) = B,
file('theBenchmark.p',prove_absorbtion_for_intersection) ).
fof(prove_absorbtion_for_intersection_neg,negated_conjecture,
~ ! [B,C] : intersection(B,union(B,C)) = B,
inference(assume_negation,[status(cth)],[prove_absorbtion_for_intersection]) ).
cnf(c_12,plain,
( ~ member(A,C)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_14,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_15,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_18,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
cnf(c_19,plain,
union(A,B) = union(B,A),
inference(clausify,[status(thm)],[commutativity_of_union]) ).
cnf(c_20,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
fof(nnf_6,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(sk_subset_defn_sk,plain,
! [B,C] :
( ( ( ~ member(sK0(B,C),C)
& member(sK0(B,C),B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(B,C))],[nnf_6]) ).
fof(sk_subset_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subset_defn_sk]) ).
cnf(c_22,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_23,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
fof(nnf_9,plain,
? [B,C] : intersection(B,union(B,C)) != B,
inference(fof_nnf,[status(thm)],[prove_absorbtion_for_intersection_neg]) ).
fof(sk_prove_absorbtion_for_intersection_neg,plain,
intersection(sK1,union(sK1,sK2)) != sK1,
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1),skolemize(C,sK2)],[nnf_9]) ).
cnf(c_29,negated_conjecture,
intersection(sK1,union(sK1,sK2)) != sK1,
inference(split_conjunct,[status(thm)],[sk_prove_absorbtion_for_intersection_neg]) ).
cnf(c_37,plain,
( ~ member(sK0(A,B),C)
| member(sK0(A,B),intersection(C,A))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_22,c_15]) ).
cnf(c_39,plain,
( member(sK0(intersection(A,B),C),B)
| subset(intersection(A,B),C) ),
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_41,plain,
( member(sK0(A,B),union(C,A))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_22,c_12]) ).
cnf(c_91,plain,
intersection(sK1,union(sK2,sK1)) != sK1,
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_102,plain,
intersection(union(sK2,sK1),sK1) != sK1,
inference(paramod,[status(thm)],[c_20,c_91]) ).
cnf(c_525,plain,
( subset(intersection(A,B),B)
| subset(intersection(A,B),B) ),
inference(resolve,[status(thm)],[c_39,c_23]) ).
cnf(c_254,plain,
subset(intersection(A,B),B),
inference(copy,[status(thm)],[c_525]) ).
cnf(c_526,plain,
( ~ subset(intersection(union(sK2,sK1),sK1),sK1)
| ~ subset(sK1,intersection(union(sK2,sK1),sK1)) ),
inference(resolve,[status(thm)],[c_18,c_102]) ).
cnf(c_266,plain,
~ subset(sK1,intersection(union(sK2,sK1),sK1)),
inference(resolve,[status(thm)],[c_526,c_254]) ).
cnf(c_397,plain,
member(sK0(sK1,intersection(union(sK2,sK1),sK1)),union(A,sK1)),
inference(resolve,[status(thm)],[c_266,c_41]) ).
cnf(c_399,plain,
~ member(sK0(sK1,intersection(union(sK2,sK1),sK1)),intersection(union(sK2,sK1),sK1)),
inference(resolve,[status(thm)],[c_23,c_266]) ).
cnf(c_527,plain,
( ~ member(sK0(sK1,intersection(union(sK2,sK1),sK1)),A)
| member(sK0(sK1,intersection(union(sK2,sK1),sK1)),intersection(A,sK1)) ),
inference(resolve,[status(thm)],[c_37,c_266]) ).
cnf(c_528,plain,
~ member(sK0(sK1,intersection(union(sK2,sK1),sK1)),union(sK2,sK1)),
inference(resolve,[status(thm)],[c_527,c_399]) ).
cnf(c_524,plain,
$false,
inference(resolve,[status(thm)],[c_397,c_528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET173+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 07:16:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 660953 was started by sandbox on n006,
% 0.10/0.36 % Sat Sep 26 07:16:11 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.42
% 0.15/0.42 % SZS status Theorem for theBenchmark
% 0.15/0.42
% 0.15/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/0.42 % Length of proof is 26.
% 0.15/0.42 % Level of proof is 6.
% 0.15/0.42 % Maximum clause weight is 33.000.
% 0.15/0.42 % Given clauses 72.
% 0.15/0.42
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------