%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET175+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 71 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 63 ( 25 ~; 25 |; 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 : 63 ( 6 sgn 30 !; 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(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_absorbtion_for_union,conjecture,
! [B,C] : union(B,intersection(B,C)) = B,
file('theBenchmark.p',prove_absorbtion_for_union) ).
fof(prove_absorbtion_for_union_neg,negated_conjecture,
~ ! [B,C] : union(B,intersection(B,C)) = B,
inference(assume_negation,[status(cth)],[prove_absorbtion_for_union]) ).
cnf(c_10,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_12,plain,
( ~ member(A,C)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_13,plain,
( 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]) ).
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] : union(B,intersection(B,C)) != B,
inference(fof_nnf,[status(thm)],[prove_absorbtion_for_union_neg]) ).
fof(sk_prove_absorbtion_for_union_neg,plain,
union(sK1,intersection(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,
union(sK1,intersection(sK1,sK2)) != sK1,
inference(split_conjunct,[status(thm)],[sk_prove_absorbtion_for_union_neg]) ).
cnf(c_41,plain,
( member(sK0(A,B),union(C,A))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_22,c_12]) ).
cnf(c_43,plain,
( member(sK0(union(A,B),C),B)
| member(sK0(union(A,B),C),A)
| subset(union(A,B),C) ),
inference(resolve,[status(thm)],[c_22,c_10]) ).
cnf(c_276,plain,
( subset(A,union(B,A))
| subset(A,union(B,A)) ),
inference(resolve,[status(thm)],[c_41,c_23]) ).
cnf(c_118,plain,
subset(A,union(B,A)),
inference(copy,[status(thm)],[c_276]) ).
cnf(c_126,plain,
subset(A,union(A,B)),
inference(paramod,[status(thm)],[c_19,c_118]) ).
cnf(c_277,negated_conjecture,
sK1 != union(sK1,intersection(sK1,sK2)),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_278,negated_conjecture,
( ~ subset(sK1,union(sK1,intersection(sK1,sK2)))
| ~ subset(union(sK1,intersection(sK1,sK2)),sK1) ),
inference(resolve,[status(thm)],[c_18,c_277]) ).
cnf(c_129,negated_conjecture,
~ subset(union(sK1,intersection(sK1,sK2)),sK1),
inference(resolve,[status(thm)],[c_278,c_126]) ).
cnf(c_184,plain,
~ member(sK0(union(sK1,intersection(sK1,sK2)),sK1),sK1),
inference(resolve,[status(thm)],[c_23,c_129]) ).
cnf(c_258,plain,
~ member(sK0(union(sK1,intersection(sK1,sK2)),sK1),intersection(sK1,A)),
inference(resolve,[status(thm)],[c_13,c_184]) ).
cnf(c_279,plain,
( member(sK0(union(sK1,intersection(sK1,sK2)),sK1),intersection(sK1,sK2))
| member(sK0(union(sK1,intersection(sK1,sK2)),sK1),sK1) ),
inference(resolve,[status(thm)],[c_43,c_129]) ).
cnf(c_280,plain,
member(sK0(union(sK1,intersection(sK1,sK2)),sK1),intersection(sK1,sK2)),
inference(resolve,[status(thm)],[c_184,c_279]) ).
cnf(c_275,plain,
$false,
inference(resolve,[status(thm)],[c_258,c_280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET175+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n015.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 07:19:59 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3422627 was started by sandbox2 on n015,
% 0.19/0.45 % Sat Sep 26 07:19:59 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.51
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51
% 0.19/0.51 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.19/0.51 % Length of proof is 22.
% 0.19/0.51 % Level of proof is 8.
% 0.19/0.51 % Maximum clause weight is 34.000.
% 0.19/0.51 % Given clauses 61.
% 0.19/0.51
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------