%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET934+1 : 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 : n010.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 08:57:50 AM UTC 2026
% Result : Theorem 246.82s 247.34s
% Output : Proof 248.32s
% 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(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
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(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t81_zfmisc_1,conjecture,
! [A,B] : subset(set_union2(powerset(A),powerset(B)),powerset(set_union2(A,B))),
file('theBenchmark.p',t81_zfmisc_1) ).
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]) ).
fof(f_1_3,plain,
! [U_0,U_1] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2,U_3] : set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_7,U_6] :
( ( U_6 = powerset(U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& subset(U_5,U_7) )
| ( ~ subset(U_5,U_7)
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| ~ subset(U_4,U_7) )
& ( subset(U_4,U_7)
| ~ in(U_4,U_6) ) )
| U_6 != powerset(U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_15,U_13] :
( U_13 = powerset(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& subset(U_11,U_15) )
| ? [U_10] :
( ~ subset(U_10,U_15)
& in(U_10,U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| ~ subset(U_9,U_14) )
& ! [U_8] :
( subset(U_8,U_14)
| ~ in(U_8,U_12) ) )
| U_12 != powerset(U_14) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_15,U_13] :
( U_13 = powerset(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& subset(U_11,U_15) )
| ( ~ subset(sK1(U_15,U_13),U_15)
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| ~ subset(U_9,U_14) )
& ! [U_8] :
( subset(U_8,U_14)
| ~ in(U_8,U_12) ) )
| U_12 != powerset(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_15,U_13))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_15,U_13] :
( U_13 = powerset(U_15)
| ( ~ in(sK2(U_15,U_13),U_13)
& subset(sK2(U_15,U_13),U_15) )
| ( ~ subset(sK1(U_15,U_13),U_15)
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| ~ subset(U_9,U_14) )
& ! [U_8] :
( subset(U_8,U_14)
| ~ in(U_8,U_12) ) )
| U_12 != powerset(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2(U_15,U_13))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_13,U_15] :
( ~ in(sK2(U_15,U_13),U_13)
| ~ sP2(U_13,U_15) )
& ! [U_13,U_15] :
( subset(sK2(U_15,U_13),U_15)
| ~ sP2(U_13,U_15) )
& ! [U_13,U_15] :
( ~ subset(sK1(U_15,U_13),U_15)
| ~ sP1(U_13,U_15) )
& ! [U_13,U_15] :
( in(sK1(U_15,U_13),U_13)
| ~ sP1(U_13,U_15) )
& ! [U_14,U_9,U_8,U_12] :
( in(U_9,U_12)
| ~ subset(U_9,U_14)
| ~ sP0(U_14,U_9,U_8,U_12) )
& ! [U_14,U_9,U_8,U_12] :
( subset(U_8,U_14)
| ~ in(U_8,U_12)
| ~ sP0(U_14,U_9,U_8,U_12) )
& ! [U_13,U_15] :
( U_13 = powerset(U_15)
| sP2(U_13,U_15)
| sP1(U_13,U_15) )
& ! [U_14,U_9,U_8,U_12] :
( sP0(U_14,U_9,U_8,U_12)
| U_12 != powerset(U_14) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2])],[f_3_5]) ).
cnf(f_3_7,plain,
( sP0(U_14,U_9,U_8,U_12)
| U_12 != powerset(U_14) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_8,plain,
( U_13 = powerset(U_15)
| sP2(U_13,U_15)
| sP1(U_13,U_15) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_9,plain,
( subset(U_8,U_14)
| ~ in(U_8,U_12)
| ~ sP0(U_14,U_9,U_8,U_12) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_10,plain,
( in(U_9,U_12)
| ~ subset(U_9,U_14)
| ~ sP0(U_14,U_9,U_8,U_12) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_11,plain,
( in(sK1(U_15,U_13),U_13)
| ~ sP1(U_13,U_15) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_12,plain,
( ~ subset(sK1(U_15,U_13),U_15)
| ~ sP1(U_13,U_15) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_13,plain,
( subset(sK2(U_15,U_13),U_15)
| ~ sP2(U_13,U_15) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_14,plain,
( ~ in(sK2(U_15,U_13),U_13)
| ~ sP2(U_13,U_15) ),
inference(clausify,[status(thm)],[f_3_6]) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_4_2,plain,
! [U_20,U_19,U_18] :
( ( U_18 = set_union2(U_20,U_19)
| ? [U_17] :
( ( ~ in(U_17,U_18)
& ( in(U_17,U_19)
| in(U_17,U_20) ) )
| ( ~ in(U_17,U_19)
& ~ in(U_17,U_20)
& in(U_17,U_18) ) ) )
& ( ! [U_16] :
( ( in(U_16,U_18)
| ( ~ in(U_16,U_19)
& ~ in(U_16,U_20) ) )
& ( in(U_16,U_19)
| in(U_16,U_20)
| ~ in(U_16,U_18) ) )
| U_18 != set_union2(U_20,U_19) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_30,U_28,U_26] :
( U_26 = set_union2(U_30,U_28)
| ? [U_24] :
( ~ in(U_24,U_26)
& ( in(U_24,U_28)
| in(U_24,U_30) ) )
| ? [U_23] :
( ~ in(U_23,U_28)
& ~ in(U_23,U_30)
& in(U_23,U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( ~ in(U_22,U_27)
& ~ in(U_22,U_29) ) )
& ! [U_21] :
( in(U_21,U_27)
| in(U_21,U_29)
| ~ in(U_21,U_25) ) )
| U_25 != set_union2(U_29,U_27) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_30,U_28,U_26] :
( U_26 = set_union2(U_30,U_28)
| ? [U_24] :
( ~ in(U_24,U_26)
& ( in(U_24,U_28)
| in(U_24,U_30) ) )
| ( ~ in(sK3(U_30,U_28,U_26),U_28)
& ~ in(sK3(U_30,U_28,U_26),U_30)
& in(sK3(U_30,U_28,U_26),U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( ~ in(U_22,U_27)
& ~ in(U_22,U_29) ) )
& ! [U_21] :
( in(U_21,U_27)
| in(U_21,U_29)
| ~ in(U_21,U_25) ) )
| U_25 != set_union2(U_29,U_27) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_23,sK3(U_30,U_28,U_26))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_30,U_28,U_26] :
( U_26 = set_union2(U_30,U_28)
| ( ~ in(sK4(U_30,U_28,U_26),U_26)
& ( in(sK4(U_30,U_28,U_26),U_28)
| in(sK4(U_30,U_28,U_26),U_30) ) )
| ( ~ in(sK3(U_30,U_28,U_26),U_28)
& ~ in(sK3(U_30,U_28,U_26),U_30)
& in(sK3(U_30,U_28,U_26),U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( ~ in(U_22,U_27)
& ~ in(U_22,U_29) ) )
& ! [U_21] :
( in(U_21,U_27)
| in(U_21,U_29)
| ~ in(U_21,U_25) ) )
| U_25 != set_union2(U_29,U_27) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_24,sK4(U_30,U_28,U_26))],[f_4_4]) ).
fof(f_4_6,plain,
( ! [U_28,U_30,U_26] :
( ~ in(sK4(U_30,U_28,U_26),U_26)
| ~ sP6(U_28,U_30,U_26) )
& ! [U_28,U_30,U_26] :
( in(sK4(U_30,U_28,U_26),U_28)
| in(sK4(U_30,U_28,U_26),U_30)
| ~ sP6(U_28,U_30,U_26) )
& ! [U_28,U_30,U_26] :
( ~ in(sK3(U_30,U_28,U_26),U_28)
| ~ sP5(U_28,U_30,U_26) )
& ! [U_28,U_30,U_26] :
( ~ in(sK3(U_30,U_28,U_26),U_30)
| ~ sP5(U_28,U_30,U_26) )
& ! [U_28,U_30,U_26] :
( in(sK3(U_30,U_28,U_26),U_26)
| ~ sP5(U_28,U_30,U_26) )
& ! [U_22,U_27,U_29] :
( ~ in(U_22,U_27)
| ~ sP3(U_22,U_27,U_29) )
& ! [U_22,U_27,U_29] :
( ~ in(U_22,U_29)
| ~ sP3(U_22,U_27,U_29) )
& ! [U_22,U_25,U_27,U_29,U_21] :
( in(U_22,U_25)
| sP3(U_22,U_27,U_29)
| ~ sP4(U_22,U_25,U_27,U_29,U_21) )
& ! [U_22,U_25,U_27,U_29,U_21] :
( in(U_21,U_27)
| in(U_21,U_29)
| ~ in(U_21,U_25)
| ~ sP4(U_22,U_25,U_27,U_29,U_21) )
& ! [U_28,U_30,U_26] :
( U_26 = set_union2(U_30,U_28)
| sP6(U_28,U_30,U_26)
| sP5(U_28,U_30,U_26) )
& ! [U_22,U_25,U_27,U_29,U_21] :
( sP4(U_22,U_25,U_27,U_29,U_21)
| U_25 != set_union2(U_29,U_27) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4,sP5,sP6])],[f_4_5]) ).
cnf(f_4_7,plain,
( sP4(U_22,U_25,U_27,U_29,U_21)
| U_25 != set_union2(U_29,U_27) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_8,plain,
( U_26 = set_union2(U_30,U_28)
| sP6(U_28,U_30,U_26)
| sP5(U_28,U_30,U_26) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_9,plain,
( in(U_21,U_27)
| in(U_21,U_29)
| ~ in(U_21,U_25)
| ~ sP4(U_22,U_25,U_27,U_29,U_21) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_10,plain,
( in(U_22,U_25)
| sP3(U_22,U_27,U_29)
| ~ sP4(U_22,U_25,U_27,U_29,U_21) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_11,plain,
( ~ in(U_22,U_29)
| ~ sP3(U_22,U_27,U_29) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_12,plain,
( ~ in(U_22,U_27)
| ~ sP3(U_22,U_27,U_29) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_13,plain,
( in(sK3(U_30,U_28,U_26),U_26)
| ~ sP5(U_28,U_30,U_26) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_14,plain,
( ~ in(sK3(U_30,U_28,U_26),U_30)
| ~ sP5(U_28,U_30,U_26) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_15,plain,
( ~ in(sK3(U_30,U_28,U_26),U_28)
| ~ sP5(U_28,U_30,U_26) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_16,plain,
( in(sK4(U_30,U_28,U_26),U_28)
| in(sK4(U_30,U_28,U_26),U_30)
| ~ sP6(U_28,U_30,U_26) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_17,plain,
( ~ in(sK4(U_30,U_28,U_26),U_26)
| ~ sP6(U_28,U_30,U_26) ),
inference(clausify,[status(thm)],[f_4_6]) ).
fof(f_5_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_5_2,plain,
! [U_34,U_33] :
( ( subset(U_34,U_33)
| ? [U_32] :
( ~ in(U_32,U_33)
& in(U_32,U_34) ) )
& ( ! [U_31] :
( in(U_31,U_33)
| ~ in(U_31,U_34) )
| ~ subset(U_34,U_33) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_38,U_36] :
( subset(U_38,U_36)
| ? [U_32] :
( ~ in(U_32,U_36)
& in(U_32,U_38) ) )
& ! [U_37,U_35] :
( ! [U_31] :
( in(U_31,U_35)
| ~ in(U_31,U_37) )
| ~ subset(U_37,U_35) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_38,U_36] :
( subset(U_38,U_36)
| ( ~ in(sK5(U_38,U_36),U_36)
& in(sK5(U_38,U_36),U_38) ) )
& ! [U_37,U_35] :
( ! [U_31] :
( in(U_31,U_35)
| ~ in(U_31,U_37) )
| ~ subset(U_37,U_35) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_32,sK5(U_38,U_36))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_36,U_38] :
( ~ in(sK5(U_38,U_36),U_36)
| ~ sP7(U_36,U_38) )
& ! [U_36,U_38] :
( in(sK5(U_38,U_36),U_38)
| ~ sP7(U_36,U_38) )
& ! [U_36,U_38] :
( subset(U_38,U_36)
| sP7(U_36,U_38) )
& ! [U_37,U_35,U_31] :
( in(U_31,U_35)
| ~ in(U_31,U_37)
| ~ subset(U_37,U_35) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_5_4]) ).
cnf(f_5_6,plain,
( in(U_31,U_35)
| ~ in(U_31,U_37)
| ~ subset(U_37,U_35) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( subset(U_38,U_36)
| sP7(U_36,U_38) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( in(sK5(U_38,U_36),U_38)
| ~ sP7(U_36,U_38) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( ~ in(sK5(U_38,U_36),U_36)
| ~ sP7(U_36,U_38) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_6_2,plain,
! [U_40,U_39] :
( ~ empty(set_union2(U_40,U_39))
| empty(U_40) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_40] :
( ! [U_39] : ~ empty(set_union2(U_40,U_39))
| empty(U_40) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_39,U_40] :
( ~ empty(set_union2(U_40,U_39))
| empty(U_40) ),
inference(definitional_conversion,[status(esa)],[f_6_3]) ).
cnf(f_6_5,plain,
( ~ empty(set_union2(U_40,U_39))
| empty(U_40) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_7_2,plain,
! [U_42,U_41] :
( ~ empty(set_union2(U_41,U_42))
| empty(U_42) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_42] :
( ! [U_41] : ~ empty(set_union2(U_41,U_42))
| empty(U_42) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_42,U_41] :
( ~ empty(set_union2(U_41,U_42))
| empty(U_42) ),
inference(definitional_conversion,[status(esa)],[f_7_3]) ).
cnf(f_7_5,plain,
( ~ empty(set_union2(U_41,U_42))
| empty(U_42) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_8_2,plain,
! [U_44,U_43] : set_union2(U_44,U_44) = U_44,
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_44] : set_union2(U_44,U_44) = U_44,
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
! [U_44] : set_union2(U_44,U_44) = U_44,
inference(definitional_conversion,[status(esa)],[f_8_3]) ).
cnf(f_8_5,plain,
set_union2(U_44,U_44) = U_44,
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_9_2,plain,
? [U_45] : empty(U_45),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_45,sK6)],[f_9_2]) ).
fof(f_9_4,plain,
empty(sK6),
inference(definitional_conversion,[status(esa)],[f_9_3]) ).
cnf(f_9_5,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_10_2,plain,
? [U_46] : ~ empty(U_46),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_46,sK7)],[f_10_2]) ).
fof(f_10_4,plain,
~ empty(sK7),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_11_2,plain,
! [U_48,U_47] : subset(U_48,U_48),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_48] : subset(U_48,U_48),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
! [U_48] : subset(U_48,U_48),
inference(definitional_conversion,[status(esa)],[f_11_3]) ).
cnf(f_11_5,plain,
subset(U_48,U_48),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_12_2,plain,
! [U_51,U_50,U_49] :
( subset(U_51,U_49)
| ~ subset(U_50,U_49)
| ~ subset(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_50,U_49,U_51] :
( subset(U_51,U_49)
| ~ subset(U_50,U_49)
| ~ subset(U_51,U_50) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( subset(U_51,U_49)
| ~ subset(U_50,U_49)
| ~ subset(U_51,U_50) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_13_2,plain,
! [U_53,U_52] : subset(U_53,set_union2(U_53,U_52)),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_53,U_52] : subset(U_53,set_union2(U_53,U_52)),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
subset(U_53,set_union2(U_53,U_52)),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,negated_conjecture,
~ ! [A,B] : subset(set_union2(powerset(A),powerset(B)),powerset(set_union2(A,B))),
inference(negate,[status(cth)],[t81_zfmisc_1]) ).
fof(f_14_2,negated_conjecture,
? [A,B] : ~ subset(set_union2(powerset(A),powerset(B)),powerset(set_union2(A,B))),
inference(fof_nnf,[status(thm)],[f_14_1]) ).
fof(f_14_3,negated_conjecture,
? [U_55,U_54] : ~ subset(set_union2(powerset(U_55),powerset(U_54)),powerset(set_union2(U_55,U_54))),
inference(variable_rename,[status(thm)],[f_14_2]) ).
fof(f_14_4,negated_conjecture,
? [U_54] : ~ subset(set_union2(powerset(sK8),powerset(U_54)),powerset(set_union2(sK8,U_54))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_55,sK8)],[f_14_3]) ).
fof(f_14_5,negated_conjecture,
~ subset(set_union2(powerset(sK8),powerset(sK9)),powerset(set_union2(sK8,sK9))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_54,sK9)],[f_14_4]) ).
fof(f_14_6,negated_conjecture,
~ subset(set_union2(powerset(sK8),powerset(sK9)),powerset(set_union2(sK8,sK9))),
inference(definitional_conversion,[status(esa)],[f_14_5]) ).
cnf(f_14_7,negated_conjecture,
~ subset(set_union2(powerset(sK8),powerset(sK9)),powerset(set_union2(sK8,sK9))),
inference(clausify,[status(thm)],[f_14_6]) ).
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,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,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_8,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,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_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(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,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( sP7(Eq_y_0,Eq_y_1)
| ~ sP7(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 : SET934+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.10/0.58 % Computer : n010.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Sat Sep 19 23:08:11 UTC 2026
% 0.10/0.58 % CPUTime :
% 246.82/247.34 % SZS status Theorem for theBenchmark
% 246.82/247.34 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------