%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU106+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 : 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 08:45:02 AM UTC 2026
% Result : Theorem 25.16s 3.68s
% Output : CNFRefutation 25.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 27 unt; 0 def)
% Number of atoms : 154 ( 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_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_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_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_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(t95_xboole_1,axiom,
! [A,B] : set_intersection2(A,B) = symmetric_difference(symmetric_difference(A,B),set_union2(A,B)),
file('theBenchmark.p',t95_xboole_1) ).
fof(t17_finsub_1,conjecture,
! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_union2(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
file('theBenchmark.p',t17_finsub_1) ).
fof(t17_finsub_1_neg,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_union2(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
inference(assume_negation,[status(cth)],[t17_finsub_1]) ).
fof(nnf_47,plain,
? [A] :
( ~ preboolean(A)
& ! [B] :
( ! [C] :
( ( in(set_union2(B,C),A)
& in(symmetric_difference(B,C),A) )
| ~ element(C,A) )
| ~ element(B,A) )
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t17_finsub_1_neg]) ).
fof(sk_t17_finsub_1_neg_sk,plain,
( ~ preboolean(sK0)
& ! [B] :
( ! [C] :
( ( in(set_union2(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_t17_finsub_1_neg,plain,
( ~ preboolean(sK0)
& ! [VAR_0,VAR_1] :
( in(set_union2(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_t17_finsub_1_neg_sk]) ).
cnf(c_55,negated_conjecture,
~ preboolean(sK0),
inference(split_conjunct,[status(thm)],[sk_t17_finsub_1_neg]) ).
cnf(c_56,negated_conjecture,
( in(set_union2(A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t17_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_t17_finsub_1_neg]) ).
cnf(c_59,plain,
symmetric_difference(symmetric_difference(A,B),set_union2(A,B)) = set_intersection2(A,B),
inference(clausify,[status(thm)],[t95_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_99,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_112,plain,
symmetric_difference(A,B) = symmetric_difference(B,A),
inference(clausify,[status(thm)],[commutativity_k5_xboole_0]) ).
cnf(c_114,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_12705,plain,
( in(set_union2(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_99,c_12705]) ).
cnf(c_122,plain,
symmetric_difference(set_union2(A,B),symmetric_difference(A,B)) = set_intersection2(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_12706,plain,
( in(sK1(sK0),sK0)
| preboolean(sK0) ),
inference(resolve,[status(thm)],[c_129,c_118]) ).
cnf(c_569,negated_conjecture,
in(sK1(sK0),sK0),
inference(resolve,[status(thm)],[c_55,c_12706]) ).
cnf(c_12707,negated_conjecture,
( preboolean(sK0)
| in(symmetric_difference(sK2(sK0),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_57,c_125]) ).
cnf(c_12708,negated_conjecture,
( preboolean(sK0)
| preboolean(sK0)
| in(symmetric_difference(sK2(sK0),sK1(sK0)),sK0) ),
inference(resolve,[status(thm)],[c_12707,c_129]) ).
cnf(c_12709,negated_conjecture,
( preboolean(sK0)
| preboolean(sK0)
| in(symmetric_difference(sK1(sK0),sK2(sK0)),sK0) ),
inference(paramod,[status(thm)],[c_112,c_12708]) ).
cnf(c_12710,negated_conjecture,
( preboolean(sK0)
| in(symmetric_difference(sK1(sK0),sK2(sK0)),sK0) ),
inference(copy,[status(thm)],[c_12709]) ).
cnf(c_587,negated_conjecture,
in(symmetric_difference(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_55,c_12710]) ).
cnf(c_12711,negated_conjecture,
( preboolean(sK0)
| in(set_union2(sK2(sK0),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_56,c_125]) ).
cnf(c_12712,negated_conjecture,
( preboolean(sK0)
| preboolean(sK0)
| in(set_union2(sK2(sK0),sK1(sK0)),sK0) ),
inference(resolve,[status(thm)],[c_12711,c_129]) ).
cnf(c_12713,negated_conjecture,
( preboolean(sK0)
| preboolean(sK0)
| in(set_union2(sK1(sK0),sK2(sK0)),sK0) ),
inference(paramod,[status(thm)],[c_114,c_12712]) ).
cnf(c_12714,negated_conjecture,
( preboolean(sK0)
| in(set_union2(sK1(sK0),sK2(sK0)),sK0) ),
inference(copy,[status(thm)],[c_12713]) ).
cnf(c_589,negated_conjecture,
in(set_union2(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_55,c_12714]) ).
cnf(c_636,plain,
element(sK1(sK0),sK0),
inference(resolve,[status(thm)],[c_569,c_70]) ).
cnf(c_12406,plain,
element(symmetric_difference(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_587,c_70]) ).
cnf(c_12412,plain,
element(set_union2(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_589,c_70]) ).
cnf(c_12715,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_12414,negated_conjecture,
~ in(set_difference(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_12715,c_589]) ).
cnf(c_12716,negated_conjecture,
( in(symmetric_difference(symmetric_difference(sK1(sK0),sK2(sK0)),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_57,c_12406]) ).
cnf(c_12717,negated_conjecture,
in(symmetric_difference(symmetric_difference(sK1(sK0),sK2(sK0)),set_union2(sK1(sK0),sK2(sK0))),sK0),
inference(resolve,[status(thm)],[c_12716,c_12412]) ).
cnf(c_12718,negated_conjecture,
in(symmetric_difference(set_union2(sK1(sK0),sK2(sK0)),symmetric_difference(sK1(sK0),sK2(sK0))),sK0),
inference(paramod,[status(thm)],[c_112,c_12717]) ).
cnf(c_12626,negated_conjecture,
in(set_intersection2(sK1(sK0),sK2(sK0)),sK0),
inference(paramod,[status(thm)],[c_122,c_12718]) ).
cnf(c_12659,plain,
element(set_intersection2(sK1(sK0),sK2(sK0)),sK0),
inference(resolve,[status(thm)],[c_12626,c_70]) ).
cnf(c_12719,negated_conjecture,
( in(symmetric_difference(sK1(sK0),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_57,c_636]) ).
cnf(c_12720,negated_conjecture,
in(symmetric_difference(sK1(sK0),set_intersection2(sK1(sK0),sK2(sK0))),sK0),
inference(resolve,[status(thm)],[c_12719,c_12659]) ).
cnf(c_12721,negated_conjecture,
in(set_difference(sK1(sK0),sK2(sK0)),sK0),
inference(paramod,[status(thm)],[c_78,c_12720]) ).
cnf(c_12704,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_12414,c_12721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU106+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n017.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 08:31:33 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 279636 was started by sandbox on n017,
% 0.17/0.43 % Sat Sep 26 08:31:33 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 25.16/3.68
% 25.16/3.68 % given #500 (T,wt=22): 12580 in(set_intersection2(f1(c5),f8(c5)),c5). [hyper(57,a,8744,a,b,8747,a),rewrite([112(11),122(11)])].
% 25.16/3.68
% 25.16/3.68 % SZS status Theorem for theBenchmark
% 25.16/3.68
% 25.16/3.68 % Proof 1 at 2.28 (+ 0.92) seconds.
% 25.16/3.68 % Length of proof is 35.
% 25.16/3.68 % Level of proof is 7.
% 25.16/3.68 % Maximum clause weight is 31.000.
% 25.16/3.68 % Given clauses 511.
% 25.16/3.68
% 25.16/3.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------