%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET616+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 : n017.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 08:36:37 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 102 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 26 ~; 47 |; 7 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 3 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_equal,axiom,
! [B,C] :
( ! [D] :
( member(D,B)
<=> member(D,C) )
=> B = C ),
file('theBenchmark.p',member_equal) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_th90,conjecture,
! [B,C] :
( difference(B,C) = difference(C,B)
=> B = C ),
file('theBenchmark.p',prove_th90) ).
fof(prove_th90_neg,negated_conjecture,
~ ! [B,C] :
( difference(B,C) = difference(C,B)
=> B = C ),
inference(assume_negation,[status(cth)],[prove_th90]) ).
fof(nnf_1,plain,
! [B,C] :
( C = B
| ? [D] :
( ( ~ member(D,C)
| ~ member(D,B) )
& ( member(D,C)
| member(D,B) ) ) ),
inference(fof_nnf,[status(thm)],[member_equal]) ).
fof(sk_member_equal_sk,plain,
! [B,C] :
( C = B
| ( ( ~ member(sK0(B,C),C)
| ~ member(sK0(B,C),B) )
& ( member(sK0(B,C),C)
| member(sK0(B,C),B) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(B,C))],[nnf_1]) ).
fof(sk_member_equal,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ member(sK0(VAR_0,VAR_1),VAR_1)
| ~ member(sK0(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| member(sK0(VAR_0,VAR_1),VAR_1)
| member(sK0(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_member_equal_sk]) ).
cnf(c_8,plain,
( B = A
| member(sK0(A,B),B)
| member(sK0(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_member_equal]) ).
cnf(c_9,plain,
( B = A
| ~ member(sK0(A,B),B)
| ~ member(sK0(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_member_equal]) ).
cnf(c_10,plain,
( member(A,B)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_11,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_12,plain,
( member(A,C)
| ~ member(A,B)
| member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_14,plain,
( subset(A,B)
| A != B ),
inference(clausify,[status(thm)],[equal_defn]) ).
cnf(c_20,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset_defn]) ).
fof(nnf_7,plain,
? [B,C] :
( C != B
& difference(C,B) = difference(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th90_neg]) ).
fof(sk_prove_th90_neg,plain,
( sK1 != sK2
& difference(sK1,sK2) = difference(sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK2),skolemize(C,sK1)],[nnf_7]) ).
cnf(c_24,negated_conjecture,
difference(sK1,sK2) = difference(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th90_neg]) ).
cnf(c_25,negated_conjecture,
sK1 != sK2,
inference(split_conjunct,[status(thm)],[sk_prove_th90_neg]) ).
cnf(c_32,plain,
( B = A
| member(sK0(A,B),A)
| member(sK0(A,B),C)
| member(sK0(A,B),difference(B,C)) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_33,plain,
( B = A
| member(sK0(A,B),B)
| member(sK0(A,B),C)
| member(sK0(A,B),difference(A,C)) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_65,plain,
subset(difference(sK1,sK2),difference(sK2,sK1)),
inference(resolve,[status(thm)],[c_24,c_14]) ).
cnf(c_67,plain,
( member(A,sK1)
| ~ member(A,difference(sK2,sK1)) ),
inference(paramod,[status(thm)],[c_24,c_10]) ).
cnf(c_129,plain,
( member(A,difference(sK2,sK1))
| ~ member(A,difference(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_65,c_20]) ).
cnf(c_309,plain,
( member(sK0(A,sK2),sK1)
| sK2 = A
| member(sK0(A,sK2),A)
| member(sK0(A,sK2),sK1) ),
inference(resolve,[status(thm)],[c_32,c_67]) ).
cnf(c_212,plain,
( sK2 = A
| member(sK0(A,sK2),A)
| member(sK0(A,sK2),sK1) ),
inference(copy,[status(thm)],[c_309]) ).
cnf(c_310,plain,
( sK2 = sK1
| member(sK0(sK1,sK2),sK1) ),
inference(factor,[status(thm)],[c_212]) ).
cnf(c_311,plain,
( sK1 = sK2
| member(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_310]) ).
cnf(c_231,negated_conjecture,
member(sK0(sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_25,c_311]) ).
cnf(c_312,plain,
( member(sK0(sK1,A),difference(sK2,sK1))
| A = sK1
| member(sK0(sK1,A),A)
| member(sK0(sK1,A),sK2) ),
inference(resolve,[status(thm)],[c_33,c_129]) ).
cnf(c_259,plain,
( member(sK0(sK1,A),difference(sK2,sK1))
| sK1 = A
| member(sK0(sK1,A),A)
| member(sK0(sK1,A),sK2) ),
inference(copy,[status(thm)],[c_312]) ).
cnf(c_313,plain,
( member(sK0(sK1,sK2),difference(sK2,sK1))
| sK1 = sK2
| member(sK0(sK1,sK2),sK2) ),
inference(factor,[status(thm)],[c_259]) ).
cnf(c_276,negated_conjecture,
( member(sK0(sK1,sK2),difference(sK2,sK1))
| member(sK0(sK1,sK2),sK2) ),
inference(resolve,[status(thm)],[c_25,c_313]) ).
cnf(c_314,plain,
( sK2 = sK1
| ~ member(sK0(sK1,sK2),sK2) ),
inference(resolve,[status(thm)],[c_231,c_9]) ).
cnf(c_315,plain,
( sK1 = sK2
| ~ member(sK0(sK1,sK2),sK2) ),
inference(copy,[status(thm)],[c_314]) ).
cnf(c_306,negated_conjecture,
~ member(sK0(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_25,c_315]) ).
cnf(c_307,plain,
~ member(sK0(sK1,sK2),difference(A,sK1)),
inference(resolve,[status(thm)],[c_11,c_231]) ).
cnf(c_316,negated_conjecture,
member(sK0(sK1,sK2),difference(sK2,sK1)),
inference(resolve,[status(thm)],[c_306,c_276]) ).
cnf(c_308,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_307,c_316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 07:55:48 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 216066 was started by sandbox on n017,
% 0.10/0.36 % Sat Sep 26 07:55:48 2026
% 0.10/0.36 % 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).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.39 % Length of proof is 26.
% 0.14/0.39 % Level of proof is 6.
% 0.14/0.39 % Maximum clause weight is 30.000.
% 0.14/0.39 % Given clauses 41.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------