%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU105+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 16.95s 5.63s
% Output : CNFRefutation 16.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 26 unt; 0 def)
% Number of atoms : 153 ( 12 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 147 ( 52 ~; 59 |; 25 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 77 ( 1 sgn 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(commutativity_k5_xboole_0,axiom,
! [A,B] : symmetric_difference(A,B) = symmetric_difference(B,A),
file('theBenchmark.p',commutativity_k5_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(t100_xboole_1,axiom,
! [A,B] : set_difference(A,B) = symmetric_difference(A,set_intersection2(A,B)),
file('theBenchmark.p',t100_xboole_1) ).
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(t94_xboole_1,axiom,
! [A,B] : set_union2(A,B) = symmetric_difference(symmetric_difference(A,B),set_intersection2(A,B)),
file('theBenchmark.p',t94_xboole_1) ).
fof(t16_finsub_1,conjecture,
! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_intersection2(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
file('theBenchmark.p',t16_finsub_1) ).
fof(t16_finsub_1_neg,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_intersection2(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
inference(assume_negation,[status(cth)],[t16_finsub_1]) ).
fof(nnf_47,plain,
? [A] :
( ~ preboolean(A)
& ! [B] :
( ! [C] :
( ( in(set_intersection2(B,C),A)
& in(symmetric_difference(B,C),A) )
| ~ element(C,A) )
| ~ element(B,A) )
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t16_finsub_1_neg]) ).
fof(sk_t16_finsub_1_neg_sk,plain,
( ~ preboolean(sK0)
& ! [B] :
( ! [C] :
( ( in(set_intersection2(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_47]) ).
fof(sk_t16_finsub_1_neg,plain,
( ~ preboolean(sK0)
& ! [VAR_0,VAR_1] :
( in(set_intersection2(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_t16_finsub_1_neg_sk]) ).
cnf(c_55,negated_conjecture,
~ preboolean(sK0),
inference(split_conjunct,[status(thm)],[sk_t16_finsub_1_neg]) ).
cnf(c_56,negated_conjecture,
( in(set_intersection2(A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t16_finsub_1_neg]) ).
cnf(c_57,negated_conjecture,
( in(symmetric_difference(A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t16_finsub_1_neg]) ).
cnf(c_59,plain,
symmetric_difference(symmetric_difference(A,B),set_intersection2(A,B)) = set_union2(A,B),
inference(clausify,[status(thm)],[t94_xboole_1]) ).
cnf(c_70,plain,
( element(A,B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t1_subset]) ).
fof(nnf_32,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_32]) ).
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_72,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_73,plain,
( in(sK2(A),A)
| preboolean(A) ),
inference(split_conjunct,[status(thm)],[sk_t10_finsub_1]) ).
cnf(c_74,plain,
( in(sK1(A),A)
| preboolean(A) ),
inference(split_conjunct,[status(thm)],[sk_t10_finsub_1]) ).
cnf(c_77,plain,
set_difference(A,B) = symmetric_difference(A,set_intersection2(A,B)),
inference(clausify,[status(thm)],[t100_xboole_1]) ).
cnf(c_78,plain,
symmetric_difference(A,set_intersection2(A,B)) = set_difference(A,B),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_98,plain,
set_intersection2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k3_xboole_0]) ).
cnf(c_112,plain,
symmetric_difference(A,B) = symmetric_difference(B,A),
inference(clausify,[status(thm)],[commutativity_k5_xboole_0]) ).
cnf(c_113,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_13804,plain,
( in(set_intersection2(A,A),sK0)
| ~ element(A,sK0) ),
inference(factor,[status(thm)],[c_56]) ).
cnf(c_118,plain,
( in(A,sK0)
| ~ element(A,sK0) ),
inference(paramod,[status(thm)],[c_98,c_13804]) ).
cnf(c_122,plain,
symmetric_difference(set_intersection2(A,B),symmetric_difference(A,B)) = set_union2(A,B),
inference(paramod,[status(thm)],[c_112,c_59]) ).
cnf(c_125,plain,
( element(sK2(A),A)
| preboolean(A) ),
inference(resolve,[status(thm)],[c_73,c_70]) ).
cnf(c_129,plain,
( element(sK1(A),A)
| preboolean(A) ),
inference(resolve,[status(thm)],[c_74,c_70]) ).
cnf(c_13805,plain,
( in(sK1(sK0),sK0)
| preboolean(sK0) ),
inference(resolve,[status(thm)],[c_129,c_118]) ).
cnf(c_617,negated_conjecture,
in(sK1(sK0),sK0),
inference(resolve,[status(thm)],[c_55,c_13805]) ).
cnf(c_13806,negated_conjecture,
( preboolean(sK0)
| in(symmetric_difference(sK2(sK0),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_57,c_125]) ).
cnf(c_13807,negated_conjecture,
( preboolean(sK0)
| preboolean(sK0)
| in(symmetric_difference(sK2(sK0),sK1(sK0)),sK0) ),
inference(resolve,[status(thm)],[c_13806,c_129]) ).
cnf(c_13808,negated_conjecture,
( preboolean(sK0)
| preboolean(sK0)
| in(symmetric_difference(sK1(sK0),sK2(sK0)),sK0) ),
inference(paramod,[status(thm)],[c_112,c_13807]) ).
cnf(c_13809,negated_conjecture,
( preboolean(sK0)
| in(symmetric_difference(sK1(sK0),sK2(sK0)),sK0) ),
inference(copy,[status(thm)],[c_13808]) ).
cnf(c_636,negated_conjecture,
in(symmetric_difference(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_55,c_13809]) ).
cnf(c_13810,negated_conjecture,
( preboolean(sK0)
| in(set_intersection2(sK2(sK0),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_56,c_125]) ).
cnf(c_13811,negated_conjecture,
( preboolean(sK0)
| preboolean(sK0)
| in(set_intersection2(sK2(sK0),sK1(sK0)),sK0) ),
inference(resolve,[status(thm)],[c_13810,c_129]) ).
cnf(c_13812,negated_conjecture,
( preboolean(sK0)
| preboolean(sK0)
| in(set_intersection2(sK1(sK0),sK2(sK0)),sK0) ),
inference(paramod,[status(thm)],[c_113,c_13811]) ).
cnf(c_13813,negated_conjecture,
( preboolean(sK0)
| in(set_intersection2(sK1(sK0),sK2(sK0)),sK0) ),
inference(copy,[status(thm)],[c_13812]) ).
cnf(c_638,negated_conjecture,
in(set_intersection2(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_55,c_13813]) ).
cnf(c_676,plain,
element(sK1(sK0),sK0),
inference(resolve,[status(thm)],[c_617,c_70]) ).
cnf(c_13676,plain,
element(symmetric_difference(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_636,c_70]) ).
cnf(c_13682,plain,
element(set_intersection2(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_638,c_70]) ).
cnf(c_13814,negated_conjecture,
( in(symmetric_difference(symmetric_difference(sK1(sK0),sK2(sK0)),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_57,c_13676]) ).
cnf(c_13815,negated_conjecture,
in(symmetric_difference(symmetric_difference(sK1(sK0),sK2(sK0)),set_intersection2(sK1(sK0),sK2(sK0))),sK0),
inference(resolve,[status(thm)],[c_13814,c_13682]) ).
cnf(c_13816,negated_conjecture,
in(symmetric_difference(set_intersection2(sK1(sK0),sK2(sK0)),symmetric_difference(sK1(sK0),sK2(sK0))),sK0),
inference(paramod,[status(thm)],[c_112,c_13815]) ).
cnf(c_13758,negated_conjecture,
in(set_union2(sK1(sK0),sK2(sK0)),sK0),
inference(paramod,[status(thm)],[c_122,c_13816]) ).
cnf(c_13817,negated_conjecture,
( in(symmetric_difference(sK1(sK0),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_57,c_676]) ).
cnf(c_13818,negated_conjecture,
in(symmetric_difference(sK1(sK0),set_intersection2(sK1(sK0),sK2(sK0))),sK0),
inference(resolve,[status(thm)],[c_13817,c_13682]) ).
cnf(c_13760,negated_conjecture,
in(set_difference(sK1(sK0),sK2(sK0)),sK0),
inference(paramod,[status(thm)],[c_78,c_13818]) ).
cnf(c_13819,negated_conjecture,
( ~ in(set_difference(sK1(sK0),sK2(sK0)),sK0)
| ~ in(set_union2(sK1(sK0),sK2(sK0)),sK0) ),
inference(resolve,[status(thm)],[c_72,c_55]) ).
cnf(c_13820,negated_conjecture,
~ in(set_difference(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_13819,c_13758]) ).
cnf(c_13803,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13760,c_13820]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU105+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.44 % Computer : n004.cluster.edu
% 0.08/0.44 % Model : x86_64 x86_64
% 0.08/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.44 % Memory : 8046.5625MB
% 0.08/0.44 % OS : Linux 6.8.0-71-generic
% 0.08/0.44 % CPULimit : 300
% 0.08/0.44 % WCLimit : 300
% 0.08/0.44 % DateTime : Sat Sep 26 08:36:06 UTC 2026
% 0.08/0.45 % CPUTime :
% 0.08/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.45 % Process 1259551 was started by sandbox on n004,
% 0.08/0.45 % Sat Sep 26 08:36:06 2026
% 0.08/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.46
% 0.08/0.46 % From the command line: assign(max_seconds, 300).
% 16.95/5.63
% 16.95/5.63 % given #500 (T,wt=22): 639 in(set_intersection2(f1(c5),f7(c5)),c5). [hyper(56,a,109,a,b,129,b),unit_del(b,55)].
% 16.95/5.63
% 16.95/5.63 % SZS status Theorem for theBenchmark
% 16.95/5.63
% 16.95/5.63 % Proof 1 at 1.80 (+ 0.60) seconds.
% 16.95/5.63 % Length of proof is 34.
% 16.95/5.63 % Level of proof is 6.
% 16.95/5.63 % Maximum clause weight is 31.000.
% 16.95/5.63 % Given clauses 545.
% 16.95/5.63
% 16.95/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------