%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU104+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:45:01 AM UTC 2026
% Result : Theorem 0.76s 0.52s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 125 ( 7 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 136 ( 51 ~; 49 |; 25 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 40 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d6_xboole_0,axiom,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
file('theBenchmark.p',d6_xboole_0) ).
fof(t10_finsub_1,axiom,
! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) ) ) ),
file('theBenchmark.p',t10_finsub_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t98_xboole_1,axiom,
! [A,B] : set_union2(A,B) = symmetric_difference(A,set_difference(B,A)),
file('theBenchmark.p',t98_xboole_1) ).
fof(t15_finsub_1,conjecture,
! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_difference(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
file('theBenchmark.p',t15_finsub_1) ).
fof(t15_finsub_1_neg,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_difference(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
inference(assume_negation,[status(cth)],[t15_finsub_1]) ).
fof(nnf_41,plain,
? [A] :
( ~ preboolean(A)
& ! [B] :
( ! [C] :
( ( in(set_difference(B,C),A)
& in(symmetric_difference(B,C),A) )
| ~ element(C,A) )
| ~ element(B,A) )
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t15_finsub_1_neg]) ).
fof(sk_t15_finsub_1_neg_sk,plain,
( ~ preboolean(sK0)
& ! [B] :
( ! [C] :
( ( in(set_difference(B,C),sK0)
& in(symmetric_difference(B,C),sK0) )
| ~ element(C,sK0) )
| ~ element(B,sK0) )
& ~ empty(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_41]) ).
fof(sk_t15_finsub_1_neg,plain,
( ~ preboolean(sK0)
& ! [VAR_0,VAR_1] :
( in(set_difference(VAR_0,VAR_1),sK0)
| ~ element(VAR_1,sK0)
| ~ element(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( in(symmetric_difference(VAR_0,VAR_1),sK0)
| ~ element(VAR_1,sK0)
| ~ element(VAR_0,sK0) )
& ~ empty(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t15_finsub_1_neg_sk]) ).
cnf(c_49,negated_conjecture,
~ preboolean(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_finsub_1_neg]) ).
cnf(c_50,negated_conjecture,
( in(set_difference(A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t15_finsub_1_neg]) ).
cnf(c_51,negated_conjecture,
( in(symmetric_difference(A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t15_finsub_1_neg]) ).
cnf(c_53,plain,
symmetric_difference(A,set_difference(B,A)) = set_union2(A,B),
inference(clausify,[status(thm)],[t98_xboole_1]) ).
cnf(c_63,plain,
( element(A,B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t1_subset]) ).
fof(nnf_27,plain,
! [A] :
( ( ? [B,C] :
( ( ~ in(set_difference(B,C),A)
| ~ in(set_union2(B,C),A) )
& in(C,A)
& in(B,A) )
| preboolean(A) )
& ( ! [X0,X1] :
( ( in(set_difference(X0,X1),A)
& in(set_union2(X0,X1),A) )
| ~ in(X1,A)
| ~ in(X0,A) )
| ~ preboolean(A) ) ),
inference(fof_nnf,[status(thm)],[t10_finsub_1]) ).
fof(sk_t10_finsub_1_sk,plain,
! [A] :
( ( ( ( ~ in(set_difference(sK1(A),sK2(A)),A)
| ~ in(set_union2(sK1(A),sK2(A)),A) )
& in(sK2(A),A)
& in(sK1(A),A) )
| preboolean(A) )
& ( ! [X0,X1] :
( ( in(set_difference(X0,X1),A)
& in(set_union2(X0,X1),A) )
| ~ in(X1,A)
| ~ in(X0,A) )
| ~ preboolean(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1(A)),skolemize(C,sK2(A))],[nnf_27]) ).
fof(sk_t10_finsub_1,plain,
( ! [VAR_0] :
( ~ in(set_difference(sK1(VAR_0),sK2(VAR_0)),VAR_0)
| ~ in(set_union2(sK1(VAR_0),sK2(VAR_0)),VAR_0)
| preboolean(VAR_0) )
& ! [VAR_0] :
( in(sK2(VAR_0),VAR_0)
| preboolean(VAR_0) )
& ! [VAR_0] :
( in(sK1(VAR_0),VAR_0)
| preboolean(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(set_difference(VAR_1,VAR_2),VAR_0)
| ~ in(VAR_2,VAR_0)
| ~ in(VAR_1,VAR_0)
| ~ preboolean(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(set_union2(VAR_1,VAR_2),VAR_0)
| ~ in(VAR_2,VAR_0)
| ~ in(VAR_1,VAR_0)
| ~ preboolean(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t10_finsub_1_sk]) ).
cnf(c_65,plain,
( ~ in(set_difference(sK1(A),sK2(A)),A)
| ~ in(set_union2(sK1(A),sK2(A)),A)
| preboolean(A) ),
inference(split_conjunct,[status(thm)],[sk_t10_finsub_1]) ).
cnf(c_66,plain,
( in(sK2(A),A)
| preboolean(A) ),
inference(split_conjunct,[status(thm)],[sk_t10_finsub_1]) ).
cnf(c_67,plain,
( in(sK1(A),A)
| preboolean(A) ),
inference(split_conjunct,[status(thm)],[sk_t10_finsub_1]) ).
cnf(c_98,plain,
symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
inference(clausify,[status(thm)],[d6_xboole_0]) ).
cnf(c_101,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_108,plain,
set_union2(set_difference(A,set_difference(B,A)),set_difference(set_difference(B,A),A)) = set_union2(A,B),
inference(paramod,[status(thm)],[c_98,c_53]) ).
cnf(c_109,negated_conjecture,
( in(set_union2(set_difference(A,B),set_difference(B,A)),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(paramod,[status(thm)],[c_98,c_51]) ).
cnf(c_112,plain,
( element(sK2(A),A)
| preboolean(A) ),
inference(resolve,[status(thm)],[c_66,c_63]) ).
cnf(c_116,plain,
( element(sK1(A),A)
| preboolean(A) ),
inference(resolve,[status(thm)],[c_67,c_63]) ).
cnf(c_2311,negated_conjecture,
( in(set_union2(set_difference(sK2(sK0),A),set_difference(A,sK2(sK0))),sK0)
| ~ element(A,sK0)
| preboolean(sK0) ),
inference(resolve,[status(thm)],[c_112,c_109]) ).
cnf(c_211,negated_conjecture,
( in(set_union2(set_difference(sK2(sK0),A),set_difference(A,sK2(sK0))),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_49,c_2311]) ).
cnf(c_2312,negated_conjecture,
( in(set_difference(A,sK2(sK0)),sK0)
| ~ element(A,sK0)
| preboolean(sK0) ),
inference(resolve,[status(thm)],[c_112,c_50]) ).
cnf(c_216,negated_conjecture,
( in(set_difference(A,sK2(sK0)),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_49,c_2312]) ).
cnf(c_2313,plain,
( preboolean(sK0)
| in(set_difference(sK1(sK0),sK2(sK0)),sK0) ),
inference(resolve,[status(thm)],[c_216,c_116]) ).
cnf(c_1542,negated_conjecture,
in(set_difference(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_49,c_2313]) ).
cnf(c_2314,plain,
( ~ in(set_union2(sK1(sK0),sK2(sK0)),sK0)
| preboolean(sK0) ),
inference(resolve,[status(thm)],[c_1542,c_65]) ).
cnf(c_2111,negated_conjecture,
~ in(set_union2(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_49,c_2314]) ).
cnf(c_2112,plain,
element(set_difference(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_1542,c_63]) ).
cnf(c_2315,plain,
in(set_union2(set_difference(sK2(sK0),set_difference(sK1(sK0),sK2(sK0))),set_difference(set_difference(sK1(sK0),sK2(sK0)),sK2(sK0))),sK0),
inference(resolve,[status(thm)],[c_2112,c_211]) ).
cnf(c_2316,plain,
in(set_union2(sK2(sK0),sK1(sK0)),sK0),
inference(paramod,[status(thm)],[c_108,c_2315]) ).
cnf(c_2317,plain,
in(set_union2(sK1(sK0),sK2(sK0)),sK0),
inference(paramod,[status(thm)],[c_101,c_2316]) ).
cnf(c_2310,plain,
$false,
inference(resolve,[status(thm)],[c_2111,c_2317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU104+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 08:35:36 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 2346901 was started by sandbox2 on n013,
% 0.08/0.34 % Sat Sep 26 08:35:36 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.76/0.52
% 0.76/0.52 % SZS status Theorem for theBenchmark
% 0.76/0.52
% 0.76/0.52 % Proof 1 at 0.11 (+ 0.05) seconds.
% 0.76/0.52 % Length of proof is 26.
% 0.76/0.52 % Level of proof is 6.
% 0.76/0.52 % Maximum clause weight is 45.000.
% 0.76/0.52 % Given clauses 403.
% 0.76/0.52
% 0.76/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------