%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n008.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 08:58:17 AM UTC 2026
% Result : Theorem 71.55s 86.89s
% Output : Proof 71.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 84 ( 28 unt; 0 def)
% Number of atoms : 236 ( 44 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 258 ( 106 ~; 94 |; 52 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 142 ( 4 sgn 109 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(l3_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t65_zfmisc_1,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(f_6_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_6_2,plain,
! [U_11,U_10] :
( ( U_11 = U_10
| ~ subset(U_10,U_11)
| ~ subset(U_11,U_10) )
& ( ( subset(U_10,U_11)
& subset(U_11,U_10) )
| U_11 != U_10 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_15,U_13] :
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) )
& ! [U_14,U_12] :
( ( subset(U_12,U_14)
& subset(U_14,U_12) )
| U_14 != U_12 ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_14,U_12] :
( subset(U_12,U_14)
| ~ sP0(U_14,U_12) )
& ! [U_14,U_12] :
( subset(U_14,U_12)
| ~ sP0(U_14,U_12) )
& ! [U_15,U_13] :
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) )
& ! [U_14,U_12] :
( sP0(U_14,U_12)
| U_14 != U_12 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_6_3]) ).
cnf(f_6_6,plain,
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_43_1,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[l3_zfmisc_1]) ).
fof(f_43_2,plain,
! [U_199,U_198,U_197] :
( subset(U_199,set_difference(U_198,singleton(U_197)))
| in(U_197,U_199)
| ~ subset(U_199,U_198) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_199,U_198] :
( ! [U_197] :
( subset(U_199,set_difference(U_198,singleton(U_197)))
| in(U_197,U_199) )
| ~ subset(U_199,U_198) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
! [U_198,U_197,U_199] :
( subset(U_199,set_difference(U_198,singleton(U_197)))
| in(U_197,U_199)
| ~ subset(U_199,U_198) ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
( subset(U_199,set_difference(U_198,singleton(U_197)))
| in(U_197,U_199)
| ~ subset(U_199,U_198) ),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_49_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_49_2,plain,
! [U_223,U_222] : subset(U_223,U_223),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_223] : subset(U_223,U_223),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
! [U_223] : subset(U_223,U_223),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
subset(U_223,U_223),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_65_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_65_2,plain,
! [U_261,U_260] : subset(set_difference(U_261,U_260),U_261),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_261,U_260] : subset(set_difference(U_261,U_260),U_261),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
subset(set_difference(U_261,U_260),U_261),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_67_1,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[t37_zfmisc_1]) ).
fof(f_67_2,plain,
! [U_269,U_268] :
( ( subset(singleton(U_269),U_268)
| ~ in(U_269,U_268) )
& ( in(U_269,U_268)
| ~ subset(singleton(U_269),U_268) ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_273,U_271] :
( subset(singleton(U_273),U_271)
| ~ in(U_273,U_271) )
& ! [U_272,U_270] :
( in(U_272,U_270)
| ~ subset(singleton(U_272),U_270) ) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
( ! [U_271,U_273] :
( subset(singleton(U_273),U_271)
| ~ in(U_273,U_271) )
& ! [U_270,U_272] :
( in(U_272,U_270)
| ~ subset(singleton(U_272),U_270) ) ),
inference(definitional_conversion,[status(esa)],[f_67_3]) ).
cnf(f_67_5,plain,
( in(U_272,U_270)
| ~ subset(singleton(U_272),U_270) ),
inference(clausify,[status(thm)],[f_67_4]) ).
fof(f_72_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0]) ).
fof(f_72_2,plain,
! [U_295,U_294] :
( ( ~ disjoint(U_295,U_294)
| ! [U_293] :
( ~ in(U_293,U_294)
| ~ in(U_293,U_295) ) )
& ( ? [U_292] :
( in(U_292,U_294)
& in(U_292,U_295) )
| disjoint(U_295,U_294) ) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ! [U_299,U_297] :
( ~ disjoint(U_299,U_297)
| ! [U_293] :
( ~ in(U_293,U_297)
| ~ in(U_293,U_299) ) )
& ! [U_298,U_296] :
( ? [U_292] :
( in(U_292,U_296)
& in(U_292,U_298) )
| disjoint(U_298,U_296) ) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
( ! [U_299,U_297] :
( ~ disjoint(U_299,U_297)
| ! [U_293] :
( ~ in(U_293,U_297)
| ~ in(U_293,U_299) ) )
& ! [U_298,U_296] :
( ( in(sK29(U_298,U_296),U_296)
& in(sK29(U_298,U_296),U_298) )
| disjoint(U_298,U_296) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_292,sK29(U_298,U_296))],[f_72_3]) ).
fof(f_72_5,plain,
( ! [U_296,U_298] :
( in(sK29(U_298,U_296),U_296)
| ~ sP40(U_296,U_298) )
& ! [U_296,U_298] :
( in(sK29(U_298,U_296),U_298)
| ~ sP40(U_296,U_298) )
& ! [U_297,U_299,U_293] :
( ~ disjoint(U_299,U_297)
| ~ in(U_293,U_297)
| ~ in(U_293,U_299) )
& ! [U_296,U_298] :
( sP40(U_296,U_298)
| disjoint(U_298,U_296) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_72_4]) ).
cnf(f_72_7,plain,
( ~ disjoint(U_299,U_297)
| ~ in(U_293,U_297)
| ~ in(U_293,U_299) ),
inference(clausify,[status(thm)],[f_72_5]) ).
fof(f_82_1,negated_conjecture,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
inference(negate,[status(cth)],[t65_zfmisc_1]) ).
fof(f_82_2,negated_conjecture,
? [A,B] :
( ( set_difference(A,singleton(B)) != A
& ~ in(B,A) )
| ( in(B,A)
& set_difference(A,singleton(B)) = A ) ),
inference(fof_nnf,[status(thm)],[f_82_1]) ).
fof(f_82_3,negated_conjecture,
? [U_324,U_323] :
( ( set_difference(U_324,singleton(U_323)) != U_324
& ~ in(U_323,U_324) )
| ( in(U_323,U_324)
& set_difference(U_324,singleton(U_323)) = U_324 ) ),
inference(variable_rename,[status(thm)],[f_82_2]) ).
fof(f_82_4,negated_conjecture,
( ? [U_328,U_326] :
( set_difference(U_328,singleton(U_326)) != U_328
& ~ in(U_326,U_328) )
| ? [U_327,U_325] :
( in(U_325,U_327)
& set_difference(U_327,singleton(U_325)) = U_327 ) ),
inference(miniscope,[status(thm)],[f_82_3]) ).
fof(f_82_5,negated_conjecture,
( ? [U_328,U_326] :
( set_difference(U_328,singleton(U_326)) != U_328
& ~ in(U_326,U_328) )
| ? [U_325] :
( in(U_325,sK31)
& set_difference(sK31,singleton(U_325)) = sK31 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_327,sK31)],[f_82_4]) ).
fof(f_82_6,negated_conjecture,
( ? [U_328,U_326] :
( set_difference(U_328,singleton(U_326)) != U_328
& ~ in(U_326,U_328) )
| ( in(sK32,sK31)
& set_difference(sK31,singleton(sK32)) = sK31 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_325,sK32)],[f_82_5]) ).
fof(f_82_7,negated_conjecture,
( ? [U_326] :
( set_difference(sK33,singleton(U_326)) != sK33
& ~ in(U_326,sK33) )
| ( in(sK32,sK31)
& set_difference(sK31,singleton(sK32)) = sK31 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_328,sK33)],[f_82_6]) ).
fof(f_82_8,negated_conjecture,
( ( set_difference(sK33,singleton(sK34)) != sK33
& ~ in(sK34,sK33) )
| ( in(sK32,sK31)
& set_difference(sK31,singleton(sK32)) = sK31 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_326,sK34)],[f_82_7]) ).
fof(f_82_9,negated_conjecture,
( ( set_difference(sK33,singleton(sK34)) != sK33
| ~ sP42 )
& ( ~ in(sK34,sK33)
| ~ sP42 )
& ( in(sK32,sK31)
| ~ sP41 )
& ( set_difference(sK31,singleton(sK32)) = sK31
| ~ sP41 )
& ( sP42
| sP41 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41,sP42])],[f_82_8]) ).
cnf(f_82_10,negated_conjecture,
( sP42
| sP41 ),
inference(clausify,[status(thm)],[f_82_9]) ).
cnf(f_82_11,negated_conjecture,
( set_difference(sK31,singleton(sK32)) = sK31
| ~ sP41 ),
inference(clausify,[status(thm)],[f_82_9]) ).
cnf(f_82_12,negated_conjecture,
( in(sK32,sK31)
| ~ sP41 ),
inference(clausify,[status(thm)],[f_82_9]) ).
cnf(f_82_13,negated_conjecture,
( ~ in(sK34,sK33)
| ~ sP42 ),
inference(clausify,[status(thm)],[f_82_9]) ).
cnf(f_82_14,negated_conjecture,
( set_difference(sK33,singleton(sK34)) != sK33
| ~ sP42 ),
inference(clausify,[status(thm)],[f_82_9]) ).
fof(f_88_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_difference(A,B) != A )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1]) ).
fof(f_88_2,plain,
! [U_338,U_337] :
( ( disjoint(U_338,U_337)
| set_difference(U_338,U_337) != U_338 )
& ( set_difference(U_338,U_337) = U_338
| ~ disjoint(U_338,U_337) ) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
( ! [U_342,U_340] :
( disjoint(U_342,U_340)
| set_difference(U_342,U_340) != U_342 )
& ! [U_341,U_339] :
( set_difference(U_341,U_339) = U_341
| ~ disjoint(U_341,U_339) ) ),
inference(miniscope,[status(thm)],[f_88_2]) ).
fof(f_88_4,plain,
( ! [U_340,U_342] :
( disjoint(U_342,U_340)
| set_difference(U_342,U_340) != U_342 )
& ! [U_341,U_339] :
( set_difference(U_341,U_339) = U_341
| ~ disjoint(U_341,U_339) ) ),
inference(definitional_conversion,[status(esa)],[f_88_3]) ).
cnf(f_88_6,plain,
( disjoint(U_342,U_340)
| set_difference(U_342,U_340) != U_342 ),
inference(clausify,[status(thm)],[f_88_4]) ).
cnf(t1,plain,
( sP42
| sP41 ),
inference(start,[status(thm),parent(0:0)],[f_82_10]) ).
cnf(t2,plain,
( in(sK32,sK31)
| ~ sP41 ),
inference(extension,[status(thm),parent(t1:1)],[f_82_12]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ in(sK32,singleton(sK32))
| ~ disjoint(sK31,singleton(sK32))
| ~ in(sK32,sK31) ),
inference(extension,[status(thm),parent(t2:2)],[f_72_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( set_difference(sK31,singleton(sK32)) != sK31
| disjoint(sK31,singleton(sK32)) ),
inference(extension,[status(thm),parent(t4:2)],[f_88_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ sP41
| set_difference(sK31,singleton(sK32)) = sK31 ),
inference(extension,[status(thm),parent(t6:2)],[f_82_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t1:1]) ).
cnf(t11,plain,
( ~ subset(singleton(sK32),singleton(sK32))
| in(sK32,singleton(sK32)) ),
inference(extension,[status(thm),parent(t4:3)],[f_67_5]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t4:3]) ).
cnf(t13,plain,
subset(singleton(sK32),singleton(sK32)),
inference(extension,[status(thm),parent(t11:2)],[f_49_5]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,plain,
( set_difference(sK33,singleton(sK34)) != sK33
| ~ sP42 ),
inference(extension,[status(thm),parent(t1:2)],[f_82_14]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t1:2]) ).
cnf(t17,plain,
( ~ subset(sK33,set_difference(sK33,singleton(sK34)))
| ~ subset(set_difference(sK33,singleton(sK34)),sK33)
| set_difference(sK33,singleton(sK34)) = sK33 ),
inference(extension,[status(thm),parent(t15:2)],[f_6_6]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
subset(set_difference(sK33,singleton(sK34)),sK33),
inference(extension,[status(thm),parent(t17:2)],[f_65_4]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
( in(sK34,sK33)
| ~ subset(sK33,sK33)
| subset(sK33,set_difference(sK33,singleton(sK34))) ),
inference(extension,[status(thm),parent(t17:3)],[f_43_5]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t17:3]) ).
cnf(t23,plain,
subset(sK33,sK33),
inference(extension,[status(thm),parent(t21:2)],[f_49_5]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t21:2]) ).
cnf(t25,plain,
( ~ sP42
| ~ in(sK34,sK33) ),
inference(extension,[status(thm),parent(t21:3)],[f_82_13]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t21:3]) ).
cnf(t27,plain,
$false,
inference(reduction,[status(thm),parent(t25:2)],[t25:2,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.38 % Computer : n008.cluster.edu
% 0.11/15.38 % Model : x86_64 x86_64
% 0.11/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.38 % Memory : 8046.5625MB
% 0.11/15.38 % OS : Linux 6.8.0-71-generic
% 0.11/15.38 % CPULimit : 300
% 0.11/15.38 % WCLimit : 300
% 0.11/15.38 % DateTime : Sat Sep 19 23:25:41 UTC 2026
% 0.11/15.39 % CPUTime :
% 71.55/86.89 % SZS status Theorem for theBenchmark
% 71.55/86.89 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------