%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET014+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n007.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 08:55:54 AM UTC 2026
% Result : Theorem 0.35s 0.61s
% Output : Proof 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 40 ~; 36 |; 28 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 40 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_union_subset,conjecture,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('theBenchmark.p',prove_union_subset) ).
fof(f_1_1,plain,
! [B,C,D] :
( ( member(D,union(B,C))
| ( ~ member(D,C)
& ~ member(D,B) ) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(fof_nnf,[status(thm)],[union_defn]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( ( member(U_0,union(U_2,U_1))
| ( ~ member(U_0,U_1)
& ~ member(U_0,U_2) ) )
& ( member(U_0,U_1)
| member(U_0,U_2)
| ~ member(U_0,union(U_2,U_1)) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_8,U_6,U_4] :
( member(U_4,union(U_8,U_6))
| ( ~ member(U_4,U_6)
& ~ member(U_4,U_8) ) )
& ! [U_7,U_5,U_3] :
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [B,C] :
( ( subset(B,C)
| ? [D] :
( ~ member(D,C)
& member(D,B) ) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(f_2_2,plain,
! [U_12,U_11] :
( ( subset(U_12,U_11)
| ? [U_10] :
( ~ member(U_10,U_11)
& member(U_10,U_12) ) )
& ( ! [U_9] :
( member(U_9,U_11)
| ~ member(U_9,U_12) )
| ~ subset(U_12,U_11) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_16,U_14] :
( subset(U_16,U_14)
| ? [U_10] :
( ~ member(U_10,U_14)
& member(U_10,U_16) ) )
& ! [U_15,U_13] :
( ! [U_9] :
( member(U_9,U_13)
| ~ member(U_9,U_15) )
| ~ subset(U_15,U_13) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_16,U_14] :
( subset(U_16,U_14)
| ( ~ member(sK1(U_16,U_14),U_14)
& member(sK1(U_16,U_14),U_16) ) )
& ! [U_15,U_13] :
( ! [U_9] :
( member(U_9,U_13)
| ~ member(U_9,U_15) )
| ~ subset(U_15,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_16,U_14))],[f_2_3]) ).
cnf(f_2_5,plain,
( member(U_9,U_13)
| ~ member(U_9,U_15)
| ~ subset(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( member(sK1(U_16,U_14),U_16)
| subset(U_16,U_14) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( ~ member(sK1(U_16,U_14),U_14)
| subset(U_16,U_14) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_6_1,negated_conjecture,
~ ! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
inference(negate,[status(cth)],[prove_union_subset]) ).
fof(f_6_2,negated_conjecture,
? [B,C,D] :
( ~ subset(union(B,D),C)
& subset(D,C)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_34,U_33,U_32] :
( ~ subset(union(U_34,U_32),U_33)
& subset(U_32,U_33)
& subset(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
? [U_33,U_32] :
( ~ subset(union(sK4,U_32),U_33)
& subset(U_32,U_33)
& subset(sK4,U_33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_34,sK4)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
? [U_32] :
( ~ subset(union(sK4,U_32),sK5)
& subset(U_32,sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_33,sK5)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( ~ subset(union(sK4,sK6),sK5)
& subset(sK6,sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_32,sK6)],[f_6_5]) ).
fof(f_6_7,negated_conjecture,
( ~ subset(union(sK4,sK6),sK5)
& subset(sK6,sK5)
& subset(sK4,sK5) ),
inference(definitional_conversion,[status(esa)],[f_6_6]) ).
cnf(f_6_8,negated_conjecture,
subset(sK4,sK5),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_9,negated_conjecture,
subset(sK6,sK5),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_10,negated_conjecture,
~ subset(union(sK4,sK6),sK5),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(t1,plain,
~ subset(union(sK4,sK6),sK5),
inference(start,[status(thm),parent(0:0)],[f_6_10]) ).
cnf(t2,plain,
( ~ member(sK1(union(sK4,sK6),sK5),sK5)
| subset(union(sK4,sK6),sK5) ),
inference(extension,[status(thm),parent(t1:1)],[f_2_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(sK1(union(sK4,sK6),sK5),sK6)
| ~ subset(sK6,sK5)
| member(sK1(union(sK4,sK6),sK5),sK5) ),
inference(extension,[status(thm),parent(t2:2)],[f_2_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subset(sK6,sK5),
inference(extension,[status(thm),parent(t4:2)],[f_6_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( member(sK1(union(sK4,sK6),sK5),sK4)
| ~ member(sK1(union(sK4,sK6),sK5),union(sK4,sK6))
| member(sK1(union(sK4,sK6),sK5),sK6) ),
inference(extension,[status(thm),parent(t4:3)],[f_1_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( subset(union(sK4,sK6),sK5)
| member(sK1(union(sK4,sK6),sK5),union(sK4,sK6)) ),
inference(extension,[status(thm),parent(t8:2)],[f_2_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t10:2)],[t10:2,t1:1]) ).
cnf(t13,plain,
( member(sK1(union(sK4,sK6),sK5),sK5)
| ~ subset(sK4,sK5)
| ~ member(sK1(union(sK4,sK6),sK5),sK4) ),
inference(extension,[status(thm),parent(t8:3)],[f_2_5]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t8:3]) ).
cnf(t15,plain,
subset(sK4,sK5),
inference(extension,[status(thm),parent(t13:2)],[f_6_8]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
$false,
inference(reduction,[status(thm),parent(t13:3)],[t13:3,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 21:24:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.35/0.61 % SZS status Theorem for theBenchmark
% 0.35/0.61 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------