%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET599+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 : n006.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 08:57:04 AM UTC 2026
% Result : Theorem 120.56s 120.80s
% Output : Proof 120.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 29 unt; 0 def)
% Number of atoms : 47 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 20 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 1 sgn 16 !; 5 ?)
% 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(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)),
file('theBenchmark.p',subset_of_union) ).
fof(prove_th58,conjecture,
! [B,C] : subset(difference(B,C),symmetric_difference(B,C)),
file('theBenchmark.p',prove_th58) ).
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,C] : subset(B,union(B,C)),
inference(fof_nnf,[status(thm)],[subset_of_union]) ).
fof(f_2_2,plain,
! [U_3,U_2] : subset(U_3,union(U_3,U_2)),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
subset(U_3,union(U_3,U_2)),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_9_1,negated_conjecture,
~ ! [B,C] : subset(difference(B,C),symmetric_difference(B,C)),
inference(negate,[status(cth)],[prove_th58]) ).
fof(f_9_2,negated_conjecture,
? [B,C] : ~ subset(difference(B,C),symmetric_difference(B,C)),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_39,U_38] : ~ subset(difference(U_39,U_38),symmetric_difference(U_39,U_38)),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_38] : ~ subset(difference(sK4,U_38),symmetric_difference(sK4,U_38)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_39,sK4)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
~ subset(difference(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_38,sK5)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
~ subset(difference(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(definitional_conversion,[status(esa)],[f_9_5]) ).
cnf(f_9_7,negated_conjecture,
~ subset(difference(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_5,axiom,
( difference(Eq_x_0,Eq_x_1) = difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ subset(difference(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(start,[status(thm),parent(0:0)],[f_9_7]) ).
cnf(t2,plain,
( union(difference(sK4,sK5),difference(sK5,sK4)) != symmetric_difference(sK4,sK5)
| ~ subset(difference(sK4,sK5),union(difference(sK4,sK5),difference(sK5,sK4)))
| difference(sK4,sK5) != difference(sK4,sK5)
| subset(difference(sK4,sK5),symmetric_difference(sK4,sK5)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_10]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sK5 != sK5
| sK4 != sK4
| difference(sK4,sK5) = difference(sK4,sK5) ),
inference(extension,[status(thm),parent(t2:2)],[equality_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sK4 = sK4,
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t4:3)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
subset(difference(sK4,sK5),union(difference(sK4,sK5),difference(sK5,sK4))),
inference(extension,[status(thm),parent(t2:3)],[f_2_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( symmetric_difference(sK4,sK5) != union(difference(sK4,sK5),difference(sK5,sK4))
| union(difference(sK4,sK5),difference(sK5,sK4)) = symmetric_difference(sK4,sK5) ),
inference(extension,[status(thm),parent(t2:4)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
symmetric_difference(sK4,sK5) = union(difference(sK4,sK5),difference(sK5,sK4)),
inference(extension,[status(thm),parent(t12:2)],[f_1_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET599+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 22:41:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 120.56/120.80 % SZS status Theorem for theBenchmark
% 120.56/120.80 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------