%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET589+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 : n019.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 08:57:02 AM UTC 2026
% Result : Theorem 0.13s 5.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_of_subset,axiom,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('theBenchmark.p',transitivity_of_subset) ).
fof(difference_subset1,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(difference(B,D),difference(C,D)) ),
file('theBenchmark.p',difference_subset1) ).
fof(difference_subset2,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('theBenchmark.p',difference_subset2) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B),
file('theBenchmark.p',reflexivity_of_subset) ).
fof(prove_th48,conjecture,
! [B,C,D,E] :
( ( subset(D,E)
& subset(B,C) )
=> subset(difference(B,E),difference(C,D)) ),
file('theBenchmark.p',prove_th48) ).
fof(f_1_1,plain,
! [B,C,D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[transitivity_of_subset]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B,C,D] :
( subset(difference(B,D),difference(C,D))
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[difference_subset1]) ).
fof(f_2_2,plain,
! [U_5,U_4,U_3] :
( subset(difference(U_5,U_3),difference(U_4,U_3))
| ~ subset(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_5,U_4] :
( ! [U_3] : subset(difference(U_5,U_3),difference(U_4,U_3))
| ~ subset(U_5,U_4) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(difference(U_5,U_3),difference(U_4,U_3))
| ~ subset(U_5,U_4) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B,C,D] :
( subset(difference(D,C),difference(D,B))
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[difference_subset2]) ).
fof(f_3_2,plain,
! [U_8,U_7,U_6] :
( subset(difference(U_6,U_7),difference(U_6,U_8))
| ~ subset(U_8,U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_8,U_7] :
( ! [U_6] : subset(difference(U_6,U_7),difference(U_6,U_8))
| ~ subset(U_8,U_7) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( subset(difference(U_6,U_7),difference(U_6,U_8))
| ~ subset(U_8,U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [B,C,D] :
( ( member(D,difference(B,C))
| member(D,C)
| ~ member(D,B) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(fof_nnf,[status(thm)],[difference_defn]) ).
fof(f_4_2,plain,
! [U_11,U_10,U_9] :
( ( member(U_9,difference(U_11,U_10))
| member(U_9,U_10)
| ~ member(U_9,U_11) )
& ( ( ~ member(U_9,U_10)
& member(U_9,U_11) )
| ~ member(U_9,difference(U_11,U_10)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_17,U_15,U_13] :
( member(U_13,difference(U_17,U_15))
| member(U_13,U_15)
| ~ member(U_13,U_17) )
& ! [U_16,U_14,U_12] :
( ( ~ member(U_12,U_14)
& member(U_12,U_16) )
| ~ member(U_12,difference(U_16,U_14)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( member(U_12,U_16)
| ~ member(U_12,difference(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ member(U_12,U_14)
| ~ member(U_12,difference(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( member(U_13,difference(U_17,U_15))
| member(U_13,U_15)
| ~ member(U_13,U_17) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_21,U_20] :
( ( subset(U_21,U_20)
| ? [U_19] :
( ~ member(U_19,U_20)
& member(U_19,U_21) ) )
& ( ! [U_18] :
( member(U_18,U_20)
| ~ member(U_18,U_21) )
| ~ subset(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_25,U_23] :
( subset(U_25,U_23)
| ? [U_19] :
( ~ member(U_19,U_23)
& member(U_19,U_25) ) )
& ! [U_24,U_22] :
( ! [U_18] :
( member(U_18,U_22)
| ~ member(U_18,U_24) )
| ~ subset(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_25,U_23] :
( subset(U_25,U_23)
| ( ~ member(sK1(U_25,U_23),U_23)
& member(sK1(U_25,U_23),U_25) ) )
& ! [U_24,U_22] :
( ! [U_18] :
( member(U_18,U_22)
| ~ member(U_18,U_24) )
| ~ subset(U_24,U_22) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_19,sK1(U_25,U_23))],[f_5_3]) ).
cnf(f_5_5,plain,
( member(U_18,U_22)
| ~ member(U_18,U_24)
| ~ subset(U_24,U_22) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( member(sK1(U_25,U_23),U_25)
| subset(U_25,U_23) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( ~ member(sK1(U_25,U_23),U_23)
| subset(U_25,U_23) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_6_2,plain,
! [U_26] : subset(U_26,U_26),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
subset(U_26,U_26),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,negated_conjecture,
~ ! [B,C,D,E] :
( ( subset(D,E)
& subset(B,C) )
=> subset(difference(B,E),difference(C,D)) ),
inference(negate,[status(cth)],[prove_th48]) ).
fof(f_7_2,negated_conjecture,
? [B,C,D,E] :
( ~ subset(difference(B,E),difference(C,D))
& subset(D,E)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_30,U_29,U_28,U_27] :
( ~ subset(difference(U_30,U_27),difference(U_29,U_28))
& subset(U_28,U_27)
& subset(U_30,U_29) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_29,U_28,U_27] :
( ~ subset(difference(sK2,U_27),difference(U_29,U_28))
& subset(U_28,U_27)
& subset(sK2,U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_30,sK2)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
? [U_28,U_27] :
( ~ subset(difference(sK2,U_27),difference(sK3,U_28))
& subset(U_28,U_27)
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_29,sK3)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
? [U_27] :
( ~ subset(difference(sK2,U_27),difference(sK3,sK4))
& subset(sK4,U_27)
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( ~ subset(difference(sK2,sK5),difference(sK3,sK4))
& subset(sK4,sK5)
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_27,sK5)],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( ~ subset(difference(sK2,sK5),difference(sK3,sK4))
& subset(sK4,sK5)
& subset(sK2,sK3) ),
inference(definitional_conversion,[status(esa)],[f_7_7]) ).
cnf(f_7_9,negated_conjecture,
subset(sK2,sK3),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,negated_conjecture,
subset(sK4,sK5),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,negated_conjecture,
~ subset(difference(sK2,sK5),difference(sK3,sK4)),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 This is a FOF_THM_RFO_NEQ 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
% 0.10/5.35 % Computer : n019.cluster.edu
% 0.10/5.35 % Model : x86_64 x86_64
% 0.10/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.35 % Memory : 8046.5625MB
% 0.10/5.35 % OS : Linux 6.8.0-71-generic
% 0.10/5.35 % CPULimit : 300
% 0.10/5.35 % WCLimit : 300
% 0.10/5.35 % DateTime : Sat Sep 19 22:41:40 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.13/5.40 % SZS status Theorem for theBenchmark
% 0.13/5.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------