%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET027+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 08:35:24 AM UTC 2026
% Result : Theorem 0.17s 5.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 52 ( 20 ~; 16 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_transitivity_of_subset,conjecture,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('theBenchmark.p',prove_transitivity_of_subset) ).
fof(prove_transitivity_of_subset_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
inference(assume_negation,[status(cth)],[prove_transitivity_of_subset]) ).
fof(nnf_1,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_1]) ).
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_4,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_5,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_6,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
fof(nnf_3,plain,
? [B,C,D] :
( ~ subset(B,D)
& subset(C,D)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_transitivity_of_subset_neg]) ).
fof(sk_prove_transitivity_of_subset_neg,plain,
( ~ subset(sK1,sK3)
& subset(sK2,sK3)
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_3]) ).
cnf(c_8,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_transitivity_of_subset_neg]) ).
cnf(c_9,negated_conjecture,
subset(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_prove_transitivity_of_subset_neg]) ).
cnf(c_10,negated_conjecture,
~ subset(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_prove_transitivity_of_subset_neg]) ).
cnf(c_11,negated_conjecture,
member(sK0(sK1,sK3),sK1),
inference(resolve,[status(thm)],[c_10,c_4]) ).
cnf(c_12,negated_conjecture,
~ member(sK0(sK1,sK3),sK3),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_13,negated_conjecture,
( member(A,sK3)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_14,negated_conjecture,
( member(A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_17,negated_conjecture,
~ member(sK0(sK1,sK3),sK2),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_19,negated_conjecture,
member(sK0(sK1,sK3),sK2),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_18,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET027+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n006.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Sat Sep 26 06:54:31 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.45 % Process 607514 was started by sandbox on n006,
% 0.17/5.45 % Sat Sep 26 06:54:31 2026
% 0.17/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.45
% 0.17/5.45 % From the command line: assign(max_seconds, 300).
% 0.17/5.46
% 0.17/5.46 % SZS status Theorem for theBenchmark
% 0.17/5.46
% 0.17/5.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/5.46 % Length of proof is 14.
% 0.17/5.46 % Level of proof is 4.
% 0.17/5.46 % Maximum clause weight is 6.000.
% 0.17/5.46 % Given clauses 4.
% 0.17/5.46
% 0.17/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------