%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET688+4 : 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 : n008.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 08:36:49 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 79 ( 33 ~; 20 |; 21 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',equal_set) ).
fof(thI04,conjecture,
! [A,B,C] :
( ( ~ equal_set(B,C)
& subset(B,C)
& ~ equal_set(A,B)
& subset(A,B) )
=> ~ equal_set(A,C) ),
file('theBenchmark.p',thI04) ).
fof(thI04_neg,negated_conjecture,
~ ! [A,B,C] :
( ( ~ equal_set(B,C)
& subset(B,C)
& ~ equal_set(A,B)
& subset(A,B) )
=> ~ equal_set(A,C) ),
inference(assume_negation,[status(cth)],[thI04]) ).
fof(nnf_1,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(sk_subset_sk,plain,
! [A,B] :
( ( ( ~ member(sK0(A,B),B)
& member(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(A,B))],[nnf_1]) ).
fof(sk_subset,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_sk]) ).
cnf(c_13,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_14,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_15,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_17,plain,
( subset(B,A)
| ~ equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
cnf(c_18,plain,
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
fof(nnf_12,plain,
? [A,B,C] :
( equal_set(A,C)
& ~ equal_set(B,C)
& subset(B,C)
& ~ equal_set(A,B)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[thI04_neg]) ).
fof(sk_thI04_neg,plain,
( equal_set(sK1,sK3)
& ~ equal_set(sK2,sK3)
& subset(sK2,sK3)
& ~ equal_set(sK1,sK2)
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_12]) ).
cnf(c_42,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_thI04_neg]) ).
cnf(c_43,negated_conjecture,
~ equal_set(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_thI04_neg]) ).
cnf(c_44,negated_conjecture,
subset(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_thI04_neg]) ).
cnf(c_46,negated_conjecture,
equal_set(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_thI04_neg]) ).
cnf(c_875,negated_conjecture,
( ~ subset(sK2,sK1)
| equal_set(sK1,sK2) ),
inference(resolve,[status(thm)],[c_42,c_18]) ).
cnf(c_123,negated_conjecture,
~ subset(sK2,sK1),
inference(resolve,[status(thm)],[c_43,c_875]) ).
cnf(c_128,plain,
( member(A,sK3)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_44,c_13]) ).
cnf(c_129,plain,
subset(sK3,sK1),
inference(resolve,[status(thm)],[c_46,c_17]) ).
cnf(c_139,plain,
member(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_123,c_14]) ).
cnf(c_142,plain,
~ member(sK0(sK2,sK1),sK1),
inference(resolve,[status(thm)],[c_15,c_123]) ).
cnf(c_152,plain,
( member(A,sK1)
| ~ member(A,sK3) ),
inference(resolve,[status(thm)],[c_129,c_13]) ).
cnf(c_793,plain,
~ member(sK0(sK2,sK1),sK3),
inference(resolve,[status(thm)],[c_152,c_142]) ).
cnf(c_876,plain,
member(sK0(sK2,sK1),sK3),
inference(resolve,[status(thm)],[c_139,c_128]) ).
cnf(c_874,plain,
$false,
inference(resolve,[status(thm)],[c_793,c_876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET688+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.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 08:06:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3165818 was started by sandbox on n008,
% 0.08/0.36 % Sat Sep 26 08:06:09 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.41 % Length of proof is 20.
% 0.14/0.41 % Level of proof is 5.
% 0.14/0.41 % Maximum clause weight is 18.000.
% 0.14/0.41 % Given clauses 100.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------