%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/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 : Thu Sep 24 08:57:08 AM UTC 2026
% Result : Theorem 120.26s 120.50s
% Output : Proof 120.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 28 unt; 0 def)
% Number of atoms : 37 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 13 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('theBenchmark.p',symmetric_difference_defn) ).
fof(idempotency_of_union,axiom,
! [B] : union(B,B) = B,
file('theBenchmark.p',idempotency_of_union) ).
fof(self_difference_is_empty_set,axiom,
! [B] : difference(B,B) = empty_set,
file('theBenchmark.p',self_difference_is_empty_set) ).
fof(prove_th93,conjecture,
! [B] : symmetric_difference(B,B) = empty_set,
file('theBenchmark.p',prove_th93) ).
fof(f_1_1,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(fof_nnf,[status(thm)],[symmetric_difference_defn]) ).
fof(f_1_2,plain,
! [U_1,U_0] : symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B] : union(B,B) = B,
inference(fof_nnf,[status(thm)],[idempotency_of_union]) ).
fof(f_2_2,plain,
! [U_2] : union(U_2,U_2) = U_2,
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
union(U_2,U_2) = U_2,
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [B] : difference(B,B) = empty_set,
inference(fof_nnf,[status(thm)],[self_difference_is_empty_set]) ).
fof(f_3_2,plain,
! [U_3] : difference(U_3,U_3) = empty_set,
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
difference(U_3,U_3) = empty_set,
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_12_1,negated_conjecture,
~ ! [B] : symmetric_difference(B,B) = empty_set,
inference(negate,[status(cth)],[prove_th93]) ).
fof(f_12_2,negated_conjecture,
? [B] : symmetric_difference(B,B) != empty_set,
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_41] : symmetric_difference(U_41,U_41) != empty_set,
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
symmetric_difference(sK5,sK5) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_41,sK5)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
symmetric_difference(sK5,sK5) != empty_set,
inference(definitional_conversion,[status(esa)],[f_12_4]) ).
cnf(f_12_6,negated_conjecture,
symmetric_difference(sK5,sK5) != empty_set,
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(t1,plain,
symmetric_difference(sK5,sK5) != empty_set,
inference(start,[status(thm),parent(0:0)],[f_12_6]) ).
cnf(t2,plain,
( union(difference(sK5,sK5),difference(sK5,sK5)) != empty_set
| symmetric_difference(sK5,sK5) != union(difference(sK5,sK5),difference(sK5,sK5))
| symmetric_difference(sK5,sK5) = empty_set ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
symmetric_difference(sK5,sK5) = union(difference(sK5,sK5),difference(sK5,sK5)),
inference(extension,[status(thm),parent(t2:2)],[f_1_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( difference(sK5,sK5) != empty_set
| union(difference(sK5,sK5),difference(sK5,sK5)) != difference(sK5,sK5)
| union(difference(sK5,sK5),difference(sK5,sK5)) = empty_set ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
union(difference(sK5,sK5),difference(sK5,sK5)) = difference(sK5,sK5),
inference(extension,[status(thm),parent(t6:2)],[f_2_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
difference(sK5,sK5) = empty_set,
inference(extension,[status(thm),parent(t6:3)],[f_3_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 19 22:44:08 UTC 2026
% 0.10/0.35 % CPUTime :
% 120.26/120.50 % SZS status Theorem for theBenchmark
% 120.26/120.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------