%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU172+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:58:20 AM UTC 2026
% Result : Theorem 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 124 ( 18 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 142 ( 49 ~; 43 |; 45 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 1 sgn 48 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(t54_subset_1,conjecture,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(f_20_1,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[d5_subset_1]) ).
fof(f_20_2,plain,
! [U_23,U_22] :
( subset_complement(U_23,U_22) = set_difference(U_23,U_22)
| ~ element(U_22,powerset(U_23)) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( subset_complement(U_23,U_22) = set_difference(U_23,U_22)
| ~ element(U_22,powerset(U_23)) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,negated_conjecture,
~ ! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
inference(negate,[status(cth)],[t54_subset_1]) ).
fof(f_21_2,negated_conjecture,
? [A,B,C] :
( in(B,C)
& in(B,subset_complement(A,C))
& element(C,powerset(A)) ),
inference(fof_nnf,[status(thm)],[f_21_1]) ).
fof(f_21_3,negated_conjecture,
? [U_26,U_25,U_24] :
( in(U_25,U_24)
& in(U_25,subset_complement(U_26,U_24))
& element(U_24,powerset(U_26)) ),
inference(variable_rename,[status(thm)],[f_21_2]) ).
fof(f_21_4,negated_conjecture,
? [U_25,U_24] :
( in(U_25,U_24)
& in(U_25,subset_complement(sK6,U_24))
& element(U_24,powerset(sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_26,sK6)],[f_21_3]) ).
fof(f_21_5,negated_conjecture,
? [U_24] :
( in(sK7,U_24)
& in(sK7,subset_complement(sK6,U_24))
& element(U_24,powerset(sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_25,sK7)],[f_21_4]) ).
fof(f_21_6,negated_conjecture,
( in(sK7,sK8)
& in(sK7,subset_complement(sK6,sK8))
& element(sK8,powerset(sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_24,sK8)],[f_21_5]) ).
fof(f_21_7,negated_conjecture,
( in(sK7,sK8)
& in(sK7,subset_complement(sK6,sK8))
& element(sK8,powerset(sK6)) ),
inference(definitional_conversion,[status(esa)],[f_21_6]) ).
cnf(f_21_8,negated_conjecture,
element(sK8,powerset(sK6)),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_9,negated_conjecture,
in(sK7,subset_complement(sK6,sK8)),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_10,negated_conjecture,
in(sK7,sK8),
inference(clausify,[status(thm)],[f_21_7]) ).
fof(f_22_1,plain,
! [A,B,C] :
( ( C = set_difference(A,B)
| ? [D] :
( ( ~ in(D,C)
& ~ in(D,B)
& in(D,A) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| in(D,B)
| ~ in(D,A) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_22_2,plain,
! [U_31,U_30,U_29] :
( ( U_29 = set_difference(U_31,U_30)
| ? [U_28] :
( ( ~ in(U_28,U_29)
& ~ in(U_28,U_30)
& in(U_28,U_31) )
| ( ( in(U_28,U_30)
| ~ in(U_28,U_31) )
& in(U_28,U_29) ) ) )
& ( ! [U_27] :
( ( in(U_27,U_29)
| in(U_27,U_30)
| ~ in(U_27,U_31) )
& ( ( ~ in(U_27,U_30)
& in(U_27,U_31) )
| ~ in(U_27,U_29) ) )
| U_29 != set_difference(U_31,U_30) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_41,U_39,U_37] :
( U_37 = set_difference(U_41,U_39)
| ? [U_35] :
( ~ in(U_35,U_37)
& ~ in(U_35,U_39)
& in(U_35,U_41) )
| ? [U_34] :
( ( in(U_34,U_39)
| ~ in(U_34,U_41) )
& in(U_34,U_37) ) )
& ! [U_40,U_38,U_36] :
( ( ! [U_33] :
( in(U_33,U_36)
| in(U_33,U_38)
| ~ in(U_33,U_40) )
& ! [U_32] :
( ( ~ in(U_32,U_38)
& in(U_32,U_40) )
| ~ in(U_32,U_36) ) )
| U_36 != set_difference(U_40,U_38) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_41,U_39,U_37] :
( U_37 = set_difference(U_41,U_39)
| ? [U_35] :
( ~ in(U_35,U_37)
& ~ in(U_35,U_39)
& in(U_35,U_41) )
| ( ( in(sK9(U_41,U_39,U_37),U_39)
| ~ in(sK9(U_41,U_39,U_37),U_41) )
& in(sK9(U_41,U_39,U_37),U_37) ) )
& ! [U_40,U_38,U_36] :
( ( ! [U_33] :
( in(U_33,U_36)
| in(U_33,U_38)
| ~ in(U_33,U_40) )
& ! [U_32] :
( ( ~ in(U_32,U_38)
& in(U_32,U_40) )
| ~ in(U_32,U_36) ) )
| U_36 != set_difference(U_40,U_38) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_34,sK9(U_41,U_39,U_37))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_41,U_39,U_37] :
( U_37 = set_difference(U_41,U_39)
| ( ~ in(sK10(U_41,U_39,U_37),U_37)
& ~ in(sK10(U_41,U_39,U_37),U_39)
& in(sK10(U_41,U_39,U_37),U_41) )
| ( ( in(sK9(U_41,U_39,U_37),U_39)
| ~ in(sK9(U_41,U_39,U_37),U_41) )
& in(sK9(U_41,U_39,U_37),U_37) ) )
& ! [U_40,U_38,U_36] :
( ( ! [U_33] :
( in(U_33,U_36)
| in(U_33,U_38)
| ~ in(U_33,U_40) )
& ! [U_32] :
( ( ~ in(U_32,U_38)
& in(U_32,U_40) )
| ~ in(U_32,U_36) ) )
| U_36 != set_difference(U_40,U_38) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_35,sK10(U_41,U_39,U_37))],[f_22_4]) ).
cnf(f_22_7,plain,
( ~ in(U_32,U_38)
| ~ in(U_32,U_36)
| U_36 != set_difference(U_40,U_38) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(t1,plain,
( ~ in(sK7,subset_complement(sK6,sK8))
| ~ in(sK7,sK8)
| subset_complement(sK6,sK8) != set_difference(sK6,sK8) ),
inference(start,[status(thm),parent(0:0)],[f_22_7]) ).
cnf(t2,plain,
( ~ element(sK8,powerset(sK6))
| subset_complement(sK6,sK8) = set_difference(sK6,sK8) ),
inference(extension,[status(thm),parent(t1:1)],[f_20_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
element(sK8,powerset(sK6)),
inference(extension,[status(thm),parent(t2:2)],[f_21_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
in(sK7,sK8),
inference(extension,[status(thm),parent(t1:2)],[f_21_10]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:2]) ).
cnf(t8,plain,
in(sK7,subset_complement(sK6,sK8)),
inference(extension,[status(thm),parent(t1:3)],[f_21_9]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU172+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 23:28:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.21/0.50 % SZS status Theorem for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------