%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% 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 : n004.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 08:58:19 AM UTC 2026
% Result : Theorem 165.08s 165.49s
% Output : Proof 165.44s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t136_zfmisc_1,conjecture,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t136_zfmisc_1) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
& subset(C,A) )
| ( ~ subset(C,A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ subset(C,A) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( ( U_4 = powerset(U_5)
| ? [U_3] :
( ( ~ in(U_3,U_4)
& subset(U_3,U_5) )
| ( ~ subset(U_3,U_5)
& in(U_3,U_4) ) ) )
& ( ! [U_2] :
( ( in(U_2,U_4)
| ~ subset(U_2,U_5) )
& ( subset(U_2,U_5)
| ~ in(U_2,U_4) ) )
| U_4 != powerset(U_5) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( U_11 = powerset(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& subset(U_9,U_13) )
| ? [U_8] :
( ~ subset(U_8,U_13)
& in(U_8,U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| ~ subset(U_7,U_12) )
& ! [U_6] :
( subset(U_6,U_12)
| ~ in(U_6,U_10) ) )
| U_10 != powerset(U_12) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_13,U_11] :
( U_11 = powerset(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& subset(U_9,U_13) )
| ( ~ subset(sK1(U_13,U_11),U_13)
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| ~ subset(U_7,U_12) )
& ! [U_6] :
( subset(U_6,U_12)
| ~ in(U_6,U_10) ) )
| U_10 != powerset(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_13,U_11))],[f_2_3]) ).
fof(f_2_5,plain,
( ! [U_13,U_11] :
( U_11 = powerset(U_13)
| ( ~ in(sK2(U_13,U_11),U_11)
& subset(sK2(U_13,U_11),U_13) )
| ( ~ subset(sK1(U_13,U_11),U_13)
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| ~ subset(U_7,U_12) )
& ! [U_6] :
( subset(U_6,U_12)
| ~ in(U_6,U_10) ) )
| U_10 != powerset(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2(U_13,U_11))],[f_2_4]) ).
cnf(f_2_6,plain,
( subset(U_6,U_12)
| ~ in(U_6,U_10)
| U_10 != powerset(U_12) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_7,plain,
( in(U_7,U_10)
| ~ subset(U_7,U_12)
| U_10 != powerset(U_12) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_8,plain,
( subset(sK2(U_13,U_11),U_13)
| in(sK1(U_13,U_11),U_11)
| U_11 = powerset(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_9,plain,
( ~ in(sK2(U_13,U_11),U_11)
| in(sK1(U_13,U_11),U_11)
| U_11 = powerset(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_10,plain,
( subset(sK2(U_13,U_11),U_13)
| ~ subset(sK1(U_13,U_11),U_13)
| U_11 = powerset(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_11,plain,
( ~ in(sK2(U_13,U_11),U_11)
| ~ subset(sK1(U_13,U_11),U_13)
| U_11 = powerset(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
fof(f_3_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_3_2,plain,
! [U_17,U_16] :
( ( subset(U_17,U_16)
| ? [U_15] :
( ~ in(U_15,U_16)
& in(U_15,U_17) ) )
& ( ! [U_14] :
( in(U_14,U_16)
| ~ in(U_14,U_17) )
| ~ subset(U_17,U_16) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_21,U_19] :
( subset(U_21,U_19)
| ? [U_15] :
( ~ in(U_15,U_19)
& in(U_15,U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( in(U_14,U_18)
| ~ in(U_14,U_20) )
| ~ subset(U_20,U_18) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_21,U_19] :
( subset(U_21,U_19)
| ( ~ in(sK3(U_21,U_19),U_19)
& in(sK3(U_21,U_19),U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( in(U_14,U_18)
| ~ in(U_14,U_20) )
| ~ subset(U_20,U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3(U_21,U_19))],[f_3_3]) ).
cnf(f_3_5,plain,
( in(U_14,U_18)
| ~ in(U_14,U_20)
| ~ subset(U_20,U_18) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( in(sK3(U_21,U_19),U_21)
| subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( ~ in(sK3(U_21,U_19),U_19)
| subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_4_2,plain,
? [U_22] : empty(U_22),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_22,sK4)],[f_4_2]) ).
cnf(f_4_4,plain,
empty(sK4),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_5_2,plain,
? [U_23] : ~ empty(U_23),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
~ empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_23,sK5)],[f_5_2]) ).
cnf(f_5_4,plain,
~ empty(sK5),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_6_2,plain,
! [U_25,U_24] : subset(U_25,U_25),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_25] : subset(U_25,U_25),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
subset(U_25,U_25),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,negated_conjecture,
~ ! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
inference(negate,[status(cth)],[t136_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A] :
! [B] :
( ? [C] :
( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
| ? [C] :
( ~ in(powerset(C),B)
& in(C,B) )
| ? [C,D] :
( ~ in(D,B)
& subset(D,C)
& in(C,B) )
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_31] :
! [U_30] :
( ? [U_29] :
( ~ in(U_29,U_30)
& ~ are_equipotent(U_29,U_30)
& subset(U_29,U_30) )
| ? [U_28] :
( ~ in(powerset(U_28),U_30)
& in(U_28,U_30) )
| ? [U_27,U_26] :
( ~ in(U_26,U_30)
& subset(U_26,U_27)
& in(U_27,U_30) )
| ~ in(U_31,U_30) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
! [U_30] :
( ? [U_29] :
( ~ in(U_29,U_30)
& ~ are_equipotent(U_29,U_30)
& subset(U_29,U_30) )
| ? [U_28] :
( ~ in(powerset(U_28),U_30)
& in(U_28,U_30) )
| ? [U_27,U_26] :
( ~ in(U_26,U_30)
& subset(U_26,U_27)
& in(U_27,U_30) )
| ~ in(sK6,U_30) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_31,sK6)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
! [U_30] :
( ? [U_29] :
( ~ in(U_29,U_30)
& ~ are_equipotent(U_29,U_30)
& subset(U_29,U_30) )
| ? [U_28] :
( ~ in(powerset(U_28),U_30)
& in(U_28,U_30) )
| ? [U_26] :
( ~ in(U_26,U_30)
& subset(U_26,sK7(U_30))
& in(sK7(U_30),U_30) )
| ~ in(sK6,U_30) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_27,sK7(U_30))],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
! [U_30] :
( ? [U_29] :
( ~ in(U_29,U_30)
& ~ are_equipotent(U_29,U_30)
& subset(U_29,U_30) )
| ? [U_28] :
( ~ in(powerset(U_28),U_30)
& in(U_28,U_30) )
| ( ~ in(sK8(U_30),U_30)
& subset(sK8(U_30),sK7(U_30))
& in(sK7(U_30),U_30) )
| ~ in(sK6,U_30) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_26,sK8(U_30))],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
! [U_30] :
( ? [U_29] :
( ~ in(U_29,U_30)
& ~ are_equipotent(U_29,U_30)
& subset(U_29,U_30) )
| ( ~ in(powerset(sK9(U_30)),U_30)
& in(sK9(U_30),U_30) )
| ( ~ in(sK8(U_30),U_30)
& subset(sK8(U_30),sK7(U_30))
& in(sK7(U_30),U_30) )
| ~ in(sK6,U_30) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_28,sK9(U_30))],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
! [U_30] :
( ( ~ in(sK10(U_30),U_30)
& ~ are_equipotent(sK10(U_30),U_30)
& subset(sK10(U_30),U_30) )
| ( ~ in(powerset(sK9(U_30)),U_30)
& in(sK9(U_30),U_30) )
| ( ~ in(sK8(U_30),U_30)
& subset(sK8(U_30),sK7(U_30))
& in(sK7(U_30),U_30) )
| ~ in(sK6,U_30) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_29,sK10(U_30))],[f_7_7]) ).
cnf(f_7_9,negated_conjecture,
( in(sK7(U_30),U_30)
| in(sK9(U_30),U_30)
| subset(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,negated_conjecture,
( subset(sK8(U_30),sK7(U_30))
| in(sK9(U_30),U_30)
| subset(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,negated_conjecture,
( in(sK7(U_30),U_30)
| ~ in(powerset(sK9(U_30)),U_30)
| subset(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_12,negated_conjecture,
( subset(sK8(U_30),sK7(U_30))
| ~ in(powerset(sK9(U_30)),U_30)
| subset(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_13,negated_conjecture,
( in(sK9(U_30),U_30)
| ~ in(sK8(U_30),U_30)
| subset(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_14,negated_conjecture,
( ~ in(powerset(sK9(U_30)),U_30)
| ~ in(sK8(U_30),U_30)
| subset(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_15,negated_conjecture,
( in(sK7(U_30),U_30)
| in(sK9(U_30),U_30)
| ~ are_equipotent(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_16,negated_conjecture,
( subset(sK8(U_30),sK7(U_30))
| in(sK9(U_30),U_30)
| ~ are_equipotent(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_17,negated_conjecture,
( in(sK7(U_30),U_30)
| ~ in(powerset(sK9(U_30)),U_30)
| ~ are_equipotent(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_18,negated_conjecture,
( subset(sK8(U_30),sK7(U_30))
| ~ in(powerset(sK9(U_30)),U_30)
| ~ are_equipotent(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_19,negated_conjecture,
( in(sK9(U_30),U_30)
| ~ in(sK8(U_30),U_30)
| ~ are_equipotent(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_20,negated_conjecture,
( ~ in(powerset(sK9(U_30)),U_30)
| ~ in(sK8(U_30),U_30)
| ~ are_equipotent(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_21,negated_conjecture,
( in(sK7(U_30),U_30)
| in(sK9(U_30),U_30)
| ~ in(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_22,negated_conjecture,
( subset(sK8(U_30),sK7(U_30))
| in(sK9(U_30),U_30)
| ~ in(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_23,negated_conjecture,
( in(sK7(U_30),U_30)
| ~ in(powerset(sK9(U_30)),U_30)
| ~ in(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_24,negated_conjecture,
( subset(sK8(U_30),sK7(U_30))
| ~ in(powerset(sK9(U_30)),U_30)
| ~ in(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_25,negated_conjecture,
( in(sK9(U_30),U_30)
| ~ in(sK8(U_30),U_30)
| ~ in(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_26,negated_conjecture,
( ~ in(powerset(sK9(U_30)),U_30)
| ~ in(sK8(U_30),U_30)
| ~ in(sK10(U_30),U_30)
| ~ in(sK6,U_30) ),
inference(clausify,[status(thm)],[f_7_8]) ).
fof(f_8_1,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(E,D)
| ~ subset(E,C) )
& in(D,B) )
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t9_tarski]) ).
fof(f_8_2,plain,
! [U_39] :
? [U_38] :
( ! [U_37] :
( in(U_37,U_38)
| are_equipotent(U_37,U_38)
| ~ subset(U_37,U_38) )
& ! [U_36] :
( ? [U_35] :
( ! [U_34] :
( in(U_34,U_35)
| ~ subset(U_34,U_36) )
& in(U_35,U_38) )
| ~ in(U_36,U_38) )
& ! [U_33,U_32] :
( in(U_32,U_38)
| ~ subset(U_32,U_33)
| ~ in(U_33,U_38) )
& in(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_39] :
( ! [U_37] :
( in(U_37,sK11(U_39))
| are_equipotent(U_37,sK11(U_39))
| ~ subset(U_37,sK11(U_39)) )
& ! [U_36] :
( ? [U_35] :
( ! [U_34] :
( in(U_34,U_35)
| ~ subset(U_34,U_36) )
& in(U_35,sK11(U_39)) )
| ~ in(U_36,sK11(U_39)) )
& ! [U_33,U_32] :
( in(U_32,sK11(U_39))
| ~ subset(U_32,U_33)
| ~ in(U_33,sK11(U_39)) )
& in(U_39,sK11(U_39)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_38,sK11(U_39))],[f_8_2]) ).
fof(f_8_4,plain,
! [U_39] :
( ! [U_37] :
( in(U_37,sK11(U_39))
| are_equipotent(U_37,sK11(U_39))
| ~ subset(U_37,sK11(U_39)) )
& ! [U_36] :
( ( ! [U_34] :
( in(U_34,sK12(U_39,U_36))
| ~ subset(U_34,U_36) )
& in(sK12(U_39,U_36),sK11(U_39)) )
| ~ in(U_36,sK11(U_39)) )
& ! [U_33,U_32] :
( in(U_32,sK11(U_39))
| ~ subset(U_32,U_33)
| ~ in(U_33,sK11(U_39)) )
& in(U_39,sK11(U_39)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_35,sK12(U_39,U_36))],[f_8_3]) ).
cnf(f_8_5,plain,
in(U_39,sK11(U_39)),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( in(U_32,sK11(U_39))
| ~ subset(U_32,U_33)
| ~ in(U_33,sK11(U_39)) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( in(sK12(U_39,U_36),sK11(U_39))
| ~ in(U_36,sK11(U_39)) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_8,plain,
( in(U_34,sK12(U_39,U_36))
| ~ subset(U_34,U_36)
| ~ in(U_36,sK11(U_39)) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_9,plain,
( in(U_37,sK11(U_39))
| are_equipotent(U_37,sK11(U_39))
| ~ subset(U_37,sK11(U_39)) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% 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 : n004.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 23:25:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 165.08/165.49 % SZS status Theorem for theBenchmark
% 165.08/165.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------