%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 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 : n011.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 08:57:24 AM UTC 2026
% Result : Theorem 78.14s 78.44s
% Output : Proof 78.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 54 ~; 42 |; 30 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 90 ( 1 sgn 63 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('SET006+0.ax',subset) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('SET006+0.ax',equal_set) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('SET006+0.ax',empty_set) ).
fof(inverse_image2,axiom,
! [F,B,X] :
( member(X,inverse_image2(F,B))
<=> ? [Y] :
( apply(F,X,Y)
& member(Y,B) ) ),
file('SET006+1.ax',inverse_image2) ).
fof(thIIa14,conjecture,
! [F,A,B] :
( maps(F,A,B)
=> equal_set(inverse_image2(F,empty_set),empty_set) ),
file('theBenchmark.p',thIIa14) ).
fof(f_1_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [X] :
( ~ member(X,B)
& member(X,A) ) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(f_1_2,plain,
! [U_3,U_2] :
( ( subset(U_3,U_2)
| ? [U_1] :
( ~ member(U_1,U_2)
& member(U_1,U_3) ) )
& ( ! [U_0] :
( member(U_0,U_2)
| ~ member(U_0,U_3) )
| ~ subset(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( subset(U_7,U_5)
| ? [U_1] :
( ~ member(U_1,U_5)
& member(U_1,U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subset(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( subset(U_7,U_5)
| ( ~ member(sK1(U_7,U_5),U_5)
& member(sK1(U_7,U_5),U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subset(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_7,U_5))],[f_1_3]) ).
cnf(f_1_6,plain,
( member(sK1(U_7,U_5),U_7)
| subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [A,B] :
( ( equal_set(A,B)
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(fof_nnf,[status(thm)],[equal_set]) ).
fof(f_2_2,plain,
! [U_9,U_8] :
( ( equal_set(U_9,U_8)
| ~ subset(U_8,U_9)
| ~ subset(U_9,U_8) )
& ( ( subset(U_8,U_9)
& subset(U_9,U_8) )
| ~ equal_set(U_9,U_8) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) )
& ! [U_12,U_10] :
( ( subset(U_10,U_12)
& subset(U_12,U_10) )
| ~ equal_set(U_12,U_10) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_6,plain,
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_6_1,plain,
! [X] : ~ member(X,empty_set),
inference(fof_nnf,[status(thm)],[empty_set]) ).
fof(f_6_2,plain,
! [U_38] : ~ member(U_38,empty_set),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
~ member(U_38,empty_set),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_24_1,plain,
! [F,B,X] :
( ( member(X,inverse_image2(F,B))
| ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) ) )
& ( ? [Y] :
( apply(F,X,Y)
& member(Y,B) )
| ~ member(X,inverse_image2(F,B)) ) ),
inference(fof_nnf,[status(thm)],[inverse_image2]) ).
fof(f_24_2,plain,
! [U_246,U_245,U_244] :
( ( member(U_244,inverse_image2(U_246,U_245))
| ! [U_243] :
( ~ apply(U_246,U_244,U_243)
| ~ member(U_243,U_245) ) )
& ( ? [U_242] :
( apply(U_246,U_244,U_242)
& member(U_242,U_245) )
| ~ member(U_244,inverse_image2(U_246,U_245)) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_252,U_250,U_248] :
( member(U_248,inverse_image2(U_252,U_250))
| ! [U_243] :
( ~ apply(U_252,U_248,U_243)
| ~ member(U_243,U_250) ) )
& ! [U_251,U_249,U_247] :
( ? [U_242] :
( apply(U_251,U_247,U_242)
& member(U_242,U_249) )
| ~ member(U_247,inverse_image2(U_251,U_249)) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_252,U_250,U_248] :
( member(U_248,inverse_image2(U_252,U_250))
| ! [U_243] :
( ~ apply(U_252,U_248,U_243)
| ~ member(U_243,U_250) ) )
& ! [U_251,U_249,U_247] :
( ( apply(U_251,U_247,sK27(U_251,U_249,U_247))
& member(sK27(U_251,U_249,U_247),U_249) )
| ~ member(U_247,inverse_image2(U_251,U_249)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_242,sK27(U_251,U_249,U_247))],[f_24_3]) ).
cnf(f_24_5,plain,
( member(sK27(U_251,U_249,U_247),U_249)
| ~ member(U_247,inverse_image2(U_251,U_249)) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_29_1,negated_conjecture,
~ ! [F,A,B] :
( maps(F,A,B)
=> equal_set(inverse_image2(F,empty_set),empty_set) ),
inference(negate,[status(cth)],[thIIa14]) ).
fof(f_29_2,negated_conjecture,
? [F,A,B] :
( ~ equal_set(inverse_image2(F,empty_set),empty_set)
& maps(F,A,B) ),
inference(fof_nnf,[status(thm)],[f_29_1]) ).
fof(f_29_3,negated_conjecture,
? [U_338,U_337,U_336] :
( ~ equal_set(inverse_image2(U_338,empty_set),empty_set)
& maps(U_338,U_337,U_336) ),
inference(variable_rename,[status(thm)],[f_29_2]) ).
fof(f_29_4,negated_conjecture,
? [U_338] :
( ? [U_337,U_336] : maps(U_338,U_337,U_336)
& ~ equal_set(inverse_image2(U_338,empty_set),empty_set) ),
inference(miniscope,[status(thm)],[f_29_3]) ).
fof(f_29_5,negated_conjecture,
( ? [U_337,U_336] : maps(sK41,U_337,U_336)
& ~ equal_set(inverse_image2(sK41,empty_set),empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_338,sK41)],[f_29_4]) ).
fof(f_29_6,negated_conjecture,
( ? [U_336] : maps(sK41,sK42,U_336)
& ~ equal_set(inverse_image2(sK41,empty_set),empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_337,sK42)],[f_29_5]) ).
fof(f_29_7,negated_conjecture,
( maps(sK41,sK42,sK43)
& ~ equal_set(inverse_image2(sK41,empty_set),empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_336,sK43)],[f_29_6]) ).
cnf(f_29_8,negated_conjecture,
~ equal_set(inverse_image2(sK41,empty_set),empty_set),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(t1,plain,
~ equal_set(inverse_image2(sK41,empty_set),empty_set),
inference(start,[status(thm),parent(0:0)],[f_29_8]) ).
cnf(t2,plain,
( ~ subset(empty_set,inverse_image2(sK41,empty_set))
| ~ subset(inverse_image2(sK41,empty_set),empty_set)
| equal_set(inverse_image2(sK41,empty_set),empty_set) ),
inference(extension,[status(thm),parent(t1:1)],[f_2_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( member(sK1(inverse_image2(sK41,empty_set),empty_set),inverse_image2(sK41,empty_set))
| subset(inverse_image2(sK41,empty_set),empty_set) ),
inference(extension,[status(thm),parent(t2:2)],[f_1_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( member(sK27(sK41,empty_set,sK1(inverse_image2(sK41,empty_set),empty_set)),empty_set)
| ~ member(sK1(inverse_image2(sK41,empty_set),empty_set),inverse_image2(sK41,empty_set)) ),
inference(extension,[status(thm),parent(t4:2)],[f_24_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
~ member(sK27(sK41,empty_set,sK1(inverse_image2(sK41,empty_set),empty_set)),empty_set),
inference(extension,[status(thm),parent(t6:2)],[f_6_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( member(sK1(empty_set,inverse_image2(sK41,empty_set)),empty_set)
| subset(empty_set,inverse_image2(sK41,empty_set)) ),
inference(extension,[status(thm),parent(t2:3)],[f_1_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
~ member(sK1(empty_set,inverse_image2(sK41,empty_set)),empty_set),
inference(extension,[status(thm),parent(t10:2)],[f_6_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 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
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 22:55:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 78.14/78.44 % SZS status Theorem for theBenchmark
% 78.14/78.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------