%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU135+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n020.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 08:58:09 AM UTC 2026
% Result : Theorem 33.63s 33.96s
% Output : Proof 33.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 115 ( 60 unt; 0 def)
% Number of atoms : 384 ( 58 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 450 ( 181 ~; 173 |; 91 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-5 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 264 ( 22 sgn 180 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
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(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t39_xboole_1,conjecture,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(f_3_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_3_2,plain,
! [U_5,U_4] :
( ( U_5 = U_4
| ~ subset(U_4,U_5)
| ~ subset(U_5,U_4) )
& ( ( subset(U_4,U_5)
& subset(U_5,U_4) )
| U_5 != U_4 ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_9,U_7] :
( U_9 = U_7
| ~ subset(U_7,U_9)
| ~ subset(U_9,U_7) )
& ! [U_8,U_6] :
( ( subset(U_6,U_8)
& subset(U_8,U_6) )
| U_8 != U_6 ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_8,U_6] :
( subset(U_6,U_8)
| ~ sP0(U_8,U_6) )
& ! [U_8,U_6] :
( subset(U_8,U_6)
| ~ sP0(U_8,U_6) )
& ! [U_9,U_7] :
( U_9 = U_7
| ~ subset(U_7,U_9)
| ~ subset(U_9,U_7) )
& ! [U_8,U_6] :
( sP0(U_8,U_6)
| U_8 != U_6 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_3]) ).
cnf(f_3_6,plain,
( U_9 = U_7
| ~ subset(U_7,U_9)
| ~ subset(U_9,U_7) ),
inference(clausify,[status(thm)],[f_3_4]) ).
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_14,U_13,U_12] :
( ( U_12 = set_union2(U_14,U_13)
| ? [U_11] :
( ( ~ in(U_11,U_12)
& ( in(U_11,U_13)
| in(U_11,U_14) ) )
| ( ~ in(U_11,U_13)
& ~ in(U_11,U_14)
& in(U_11,U_12) ) ) )
& ( ! [U_10] :
( ( in(U_10,U_12)
| ( ~ in(U_10,U_13)
& ~ in(U_10,U_14) ) )
& ( in(U_10,U_13)
| in(U_10,U_14)
| ~ in(U_10,U_12) ) )
| U_12 != set_union2(U_14,U_13) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_24,U_22,U_20] :
( U_20 = set_union2(U_24,U_22)
| ? [U_18] :
( ~ in(U_18,U_20)
& ( in(U_18,U_22)
| in(U_18,U_24) ) )
| ? [U_17] :
( ~ in(U_17,U_22)
& ~ in(U_17,U_24)
& in(U_17,U_20) ) )
& ! [U_23,U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ( ~ in(U_16,U_21)
& ~ in(U_16,U_23) ) )
& ! [U_15] :
( in(U_15,U_21)
| in(U_15,U_23)
| ~ in(U_15,U_19) ) )
| U_19 != set_union2(U_23,U_21) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_24,U_22,U_20] :
( U_20 = set_union2(U_24,U_22)
| ? [U_18] :
( ~ in(U_18,U_20)
& ( in(U_18,U_22)
| in(U_18,U_24) ) )
| ( ~ in(sK1(U_24,U_22,U_20),U_22)
& ~ in(sK1(U_24,U_22,U_20),U_24)
& in(sK1(U_24,U_22,U_20),U_20) ) )
& ! [U_23,U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ( ~ in(U_16,U_21)
& ~ in(U_16,U_23) ) )
& ! [U_15] :
( in(U_15,U_21)
| in(U_15,U_23)
| ~ in(U_15,U_19) ) )
| U_19 != set_union2(U_23,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_17,sK1(U_24,U_22,U_20))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_24,U_22,U_20] :
( U_20 = set_union2(U_24,U_22)
| ( ~ in(sK2(U_24,U_22,U_20),U_20)
& ( in(sK2(U_24,U_22,U_20),U_22)
| in(sK2(U_24,U_22,U_20),U_24) ) )
| ( ~ in(sK1(U_24,U_22,U_20),U_22)
& ~ in(sK1(U_24,U_22,U_20),U_24)
& in(sK1(U_24,U_22,U_20),U_20) ) )
& ! [U_23,U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ( ~ in(U_16,U_21)
& ~ in(U_16,U_23) ) )
& ! [U_15] :
( in(U_15,U_21)
| in(U_15,U_23)
| ~ in(U_15,U_19) ) )
| U_19 != set_union2(U_23,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_18,sK2(U_24,U_22,U_20))],[f_4_4]) ).
fof(f_4_6,plain,
( ! [U_20,U_22,U_24] :
( ~ in(sK2(U_24,U_22,U_20),U_20)
| ~ sP4(U_20,U_22,U_24) )
& ! [U_20,U_22,U_24] :
( in(sK2(U_24,U_22,U_20),U_22)
| in(sK2(U_24,U_22,U_20),U_24)
| ~ sP4(U_20,U_22,U_24) )
& ! [U_20,U_22,U_24] :
( ~ in(sK1(U_24,U_22,U_20),U_22)
| ~ sP3(U_20,U_22,U_24) )
& ! [U_20,U_22,U_24] :
( ~ in(sK1(U_24,U_22,U_20),U_24)
| ~ sP3(U_20,U_22,U_24) )
& ! [U_20,U_22,U_24] :
( in(sK1(U_24,U_22,U_20),U_20)
| ~ sP3(U_20,U_22,U_24) )
& ! [U_16,U_21,U_23] :
( ~ in(U_16,U_21)
| ~ sP1(U_16,U_21,U_23) )
& ! [U_16,U_21,U_23] :
( ~ in(U_16,U_23)
| ~ sP1(U_16,U_21,U_23) )
& ! [U_19,U_15,U_16,U_21,U_23] :
( in(U_16,U_19)
| sP1(U_16,U_21,U_23)
| ~ sP2(U_19,U_15,U_16,U_21,U_23) )
& ! [U_19,U_15,U_16,U_21,U_23] :
( in(U_15,U_21)
| in(U_15,U_23)
| ~ in(U_15,U_19)
| ~ sP2(U_19,U_15,U_16,U_21,U_23) )
& ! [U_20,U_22,U_24] :
( U_20 = set_union2(U_24,U_22)
| sP4(U_20,U_22,U_24)
| sP3(U_20,U_22,U_24) )
& ! [U_19,U_15,U_16,U_21,U_23] :
( sP2(U_19,U_15,U_16,U_21,U_23)
| U_19 != set_union2(U_23,U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3,sP4])],[f_4_5]) ).
cnf(f_4_7,plain,
( sP2(U_19,U_15,U_16,U_21,U_23)
| U_19 != set_union2(U_23,U_21) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_8,plain,
( U_20 = set_union2(U_24,U_22)
| sP4(U_20,U_22,U_24)
| sP3(U_20,U_22,U_24) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_9,plain,
( in(U_15,U_21)
| in(U_15,U_23)
| ~ in(U_15,U_19)
| ~ sP2(U_19,U_15,U_16,U_21,U_23) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_10,plain,
( in(U_16,U_19)
| sP1(U_16,U_21,U_23)
| ~ sP2(U_19,U_15,U_16,U_21,U_23) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_11,plain,
( ~ in(U_16,U_23)
| ~ sP1(U_16,U_21,U_23) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_12,plain,
( ~ in(U_16,U_21)
| ~ sP1(U_16,U_21,U_23) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_13,plain,
( in(sK1(U_24,U_22,U_20),U_20)
| ~ sP3(U_20,U_22,U_24) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_14,plain,
( ~ in(sK1(U_24,U_22,U_20),U_24)
| ~ sP3(U_20,U_22,U_24) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_15,plain,
( ~ in(sK1(U_24,U_22,U_20),U_22)
| ~ sP3(U_20,U_22,U_24) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_16,plain,
( in(sK2(U_24,U_22,U_20),U_22)
| in(sK2(U_24,U_22,U_20),U_24)
| ~ sP4(U_20,U_22,U_24) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_17,plain,
( ~ in(sK2(U_24,U_22,U_20),U_20)
| ~ sP4(U_20,U_22,U_24) ),
inference(clausify,[status(thm)],[f_4_6]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( C = set_difference(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_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_6_2,plain,
! [U_37,U_36,U_35] :
( ( U_35 = set_difference(U_37,U_36)
| ? [U_34] :
( ( ~ in(U_34,U_35)
& ~ in(U_34,U_36)
& in(U_34,U_37) )
| ( ( in(U_34,U_36)
| ~ in(U_34,U_37) )
& in(U_34,U_35) ) ) )
& ( ! [U_33] :
( ( in(U_33,U_35)
| in(U_33,U_36)
| ~ in(U_33,U_37) )
& ( ( ~ in(U_33,U_36)
& in(U_33,U_37) )
| ~ in(U_33,U_35) ) )
| U_35 != set_difference(U_37,U_36) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_47,U_45,U_43] :
( U_43 = set_difference(U_47,U_45)
| ? [U_41] :
( ~ in(U_41,U_43)
& ~ in(U_41,U_45)
& in(U_41,U_47) )
| ? [U_40] :
( ( in(U_40,U_45)
| ~ in(U_40,U_47) )
& in(U_40,U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| in(U_39,U_44)
| ~ in(U_39,U_46) )
& ! [U_38] :
( ( ~ in(U_38,U_44)
& in(U_38,U_46) )
| ~ in(U_38,U_42) ) )
| U_42 != set_difference(U_46,U_44) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_47,U_45,U_43] :
( U_43 = set_difference(U_47,U_45)
| ? [U_41] :
( ~ in(U_41,U_43)
& ~ in(U_41,U_45)
& in(U_41,U_47) )
| ( ( in(sK4(U_47,U_45,U_43),U_45)
| ~ in(sK4(U_47,U_45,U_43),U_47) )
& in(sK4(U_47,U_45,U_43),U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| in(U_39,U_44)
| ~ in(U_39,U_46) )
& ! [U_38] :
( ( ~ in(U_38,U_44)
& in(U_38,U_46) )
| ~ in(U_38,U_42) ) )
| U_42 != set_difference(U_46,U_44) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_40,sK4(U_47,U_45,U_43))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_47,U_45,U_43] :
( U_43 = set_difference(U_47,U_45)
| ( ~ in(sK5(U_47,U_45,U_43),U_43)
& ~ in(sK5(U_47,U_45,U_43),U_45)
& in(sK5(U_47,U_45,U_43),U_47) )
| ( ( in(sK4(U_47,U_45,U_43),U_45)
| ~ in(sK4(U_47,U_45,U_43),U_47) )
& in(sK4(U_47,U_45,U_43),U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| in(U_39,U_44)
| ~ in(U_39,U_46) )
& ! [U_38] :
( ( ~ in(U_38,U_44)
& in(U_38,U_46) )
| ~ in(U_38,U_42) ) )
| U_42 != set_difference(U_46,U_44) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_41,sK5(U_47,U_45,U_43))],[f_6_4]) ).
fof(f_6_6,plain,
( ! [U_45,U_47,U_43] :
( ~ in(sK5(U_47,U_45,U_43),U_43)
| ~ sP9(U_45,U_47,U_43) )
& ! [U_45,U_47,U_43] :
( ~ in(sK5(U_47,U_45,U_43),U_45)
| ~ sP9(U_45,U_47,U_43) )
& ! [U_45,U_47,U_43] :
( in(sK5(U_47,U_45,U_43),U_47)
| ~ sP9(U_45,U_47,U_43) )
& ! [U_45,U_47,U_43] :
( in(sK4(U_47,U_45,U_43),U_45)
| ~ in(sK4(U_47,U_45,U_43),U_47)
| ~ sP8(U_45,U_47,U_43) )
& ! [U_45,U_47,U_43] :
( in(sK4(U_47,U_45,U_43),U_43)
| ~ sP8(U_45,U_47,U_43) )
& ! [U_38,U_46,U_44] :
( ~ in(U_38,U_44)
| ~ sP6(U_38,U_46,U_44) )
& ! [U_38,U_46,U_44] :
( in(U_38,U_46)
| ~ sP6(U_38,U_46,U_44) )
& ! [U_42,U_39,U_38,U_46,U_44] :
( in(U_39,U_42)
| in(U_39,U_44)
| ~ in(U_39,U_46)
| ~ sP7(U_42,U_39,U_38,U_46,U_44) )
& ! [U_42,U_39,U_38,U_46,U_44] :
( sP6(U_38,U_46,U_44)
| ~ in(U_38,U_42)
| ~ sP7(U_42,U_39,U_38,U_46,U_44) )
& ! [U_45,U_47,U_43] :
( U_43 = set_difference(U_47,U_45)
| sP9(U_45,U_47,U_43)
| sP8(U_45,U_47,U_43) )
& ! [U_42,U_39,U_38,U_46,U_44] :
( sP7(U_42,U_39,U_38,U_46,U_44)
| U_42 != set_difference(U_46,U_44) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7,sP8,sP9])],[f_6_5]) ).
cnf(f_6_7,plain,
( sP7(U_42,U_39,U_38,U_46,U_44)
| U_42 != set_difference(U_46,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_9,plain,
( sP6(U_38,U_46,U_44)
| ~ in(U_38,U_42)
| ~ sP7(U_42,U_39,U_38,U_46,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_10,plain,
( in(U_39,U_42)
| in(U_39,U_44)
| ~ in(U_39,U_46)
| ~ sP7(U_42,U_39,U_38,U_46,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_11,plain,
( in(U_38,U_46)
| ~ sP6(U_38,U_46,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
fof(f_16_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_16_2,plain,
! [U_57,U_56] : subset(U_57,U_57),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_57] : subset(U_57,U_57),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_57] : subset(U_57,U_57),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
subset(U_57,U_57),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_18_1,negated_conjecture,
~ ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(negate,[status(cth)],[t39_xboole_1]) ).
fof(f_18_2,negated_conjecture,
? [A,B] : set_union2(A,set_difference(B,A)) != set_union2(A,B),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_60,U_59] : set_union2(U_60,set_difference(U_59,U_60)) != set_union2(U_60,U_59),
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
? [U_59] : set_union2(sK8,set_difference(U_59,sK8)) != set_union2(sK8,U_59),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_60,sK8)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
set_union2(sK8,set_difference(sK9,sK8)) != set_union2(sK8,sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_59,sK9)],[f_18_4]) ).
fof(f_18_6,negated_conjecture,
set_union2(sK8,set_difference(sK9,sK8)) != set_union2(sK8,sK9),
inference(definitional_conversion,[status(esa)],[f_18_5]) ).
cnf(f_18_7,negated_conjecture,
set_union2(sK8,set_difference(sK9,sK8)) != set_union2(sK8,sK9),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
set_union2(sK8,set_difference(sK9,sK8)) != set_union2(sK8,sK9),
inference(start,[status(thm),parent(0:0)],[f_18_7]) ).
cnf(t2,plain,
( sP4(set_union2(sK8,set_difference(sK9,sK8)),sK9,sK8)
| sP3(set_union2(sK8,set_difference(sK9,sK8)),sK9,sK8)
| set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,sK9) ),
inference(extension,[status(thm),parent(t1:1)],[f_4_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( in(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_union2(sK8,set_difference(sK9,sK8)))
| ~ sP3(set_union2(sK8,set_difference(sK9,sK8)),sK9,sK8) ),
inference(extension,[status(thm),parent(t2:2)],[f_4_13]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( in(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8))
| in(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK8)
| ~ sP2(set_union2(sK8,set_difference(sK9,sK8)),sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),U_1251,set_difference(sK9,sK8),sK8)
| ~ in(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_union2(sK8,set_difference(sK9,sK8))) ),
inference(extension,[status(thm),parent(t4:2)],[f_4_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( set_union2(sK8,set_difference(sK9,sK8)) != set_union2(sK8,set_difference(sK9,sK8))
| sP2(set_union2(sK8,set_difference(sK9,sK8)),sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),U_1251,set_difference(sK9,sK8),sK8) ),
inference(extension,[status(thm),parent(t6:2)],[f_4_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8)))
| ~ subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8)))
| set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,set_difference(sK9,sK8)) ),
inference(extension,[status(thm),parent(t8:2)],[f_3_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8))),
inference(extension,[status(thm),parent(t10:2)],[f_16_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(l6,lemma,
subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8))),
inference(lemma,[status(cth),parent(t10:2),below(t8:2)],[t10:2]) ).
cnf(t14,plain,
subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8))),
inference(lemma_extension,[status(thm),parent(t10:3)],[l6:1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( ~ sP3(set_union2(sK8,set_difference(sK9,sK8)),sK9,sK8)
| ~ in(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK8) ),
inference(extension,[status(thm),parent(t6:3)],[f_4_14]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:3]) ).
cnf(t18,plain,
$false,
inference(reduction,[status(thm),parent(t16:2)],[t16:2,t2:2]) ).
cnf(t19,plain,
( sP6(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK9,sK8)
| ~ sP7(set_difference(sK9,sK8),U_1266,sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK9,sK8)
| ~ in(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8)) ),
inference(extension,[status(thm),parent(t6:4)],[f_6_9]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t6:4]) ).
cnf(t21,plain,
( set_difference(sK9,sK8) != set_difference(sK9,sK8)
| sP7(set_difference(sK9,sK8),U_1266,sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK9,sK8) ),
inference(extension,[status(thm),parent(t19:2)],[f_6_7]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
( ~ subset(set_difference(sK9,sK8),set_difference(sK9,sK8))
| ~ subset(set_difference(sK9,sK8),set_difference(sK9,sK8))
| set_difference(sK9,sK8) = set_difference(sK9,sK8) ),
inference(extension,[status(thm),parent(t21:2)],[f_3_6]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t21:2]) ).
cnf(t25,plain,
subset(set_difference(sK9,sK8),set_difference(sK9,sK8)),
inference(extension,[status(thm),parent(t23:2)],[f_16_5]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(l12,lemma,
subset(set_difference(sK9,sK8),set_difference(sK9,sK8)),
inference(lemma,[status(cth),parent(t23:2),below(t21:2)],[t23:2]) ).
cnf(t27,plain,
subset(set_difference(sK9,sK8),set_difference(sK9,sK8)),
inference(lemma_extension,[status(thm),parent(t23:3)],[l12:1]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t23:3]) ).
cnf(t29,plain,
( in(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK9)
| ~ sP6(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK9,sK8) ),
inference(extension,[status(thm),parent(t19:3)],[f_6_11]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t19:3]) ).
cnf(t31,plain,
( ~ sP3(set_union2(sK8,set_difference(sK9,sK8)),sK9,sK8)
| ~ in(sK1(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK9) ),
inference(extension,[status(thm),parent(t29:2)],[f_4_15]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
$false,
inference(reduction,[status(thm),parent(t31:2)],[t31:2,t2:2]) ).
cnf(t34,plain,
( ~ in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_union2(sK8,set_difference(sK9,sK8)))
| ~ sP4(set_union2(sK8,set_difference(sK9,sK8)),sK9,sK8) ),
inference(extension,[status(thm),parent(t2:3)],[f_4_17]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t2:3]) ).
cnf(t36,plain,
( sP1(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8),sK8)
| ~ sP2(set_union2(sK8,set_difference(sK9,sK8)),U_1288,sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8),sK8)
| in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_union2(sK8,set_difference(sK9,sK8))) ),
inference(extension,[status(thm),parent(t34:2)],[f_4_10]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( set_union2(sK8,set_difference(sK9,sK8)) != set_union2(sK8,set_difference(sK9,sK8))
| sP2(set_union2(sK8,set_difference(sK9,sK8)),U_1288,sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8),sK8) ),
inference(extension,[status(thm),parent(t36:2)],[f_4_7]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( ~ subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8)))
| ~ subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8)))
| set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,set_difference(sK9,sK8)) ),
inference(extension,[status(thm),parent(t38:2)],[f_3_6]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8))),
inference(extension,[status(thm),parent(t40:2)],[f_16_5]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(l20,lemma,
subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8))),
inference(lemma,[status(cth),parent(t40:2),below(t38:2)],[t40:2]) ).
cnf(t44,plain,
subset(set_union2(sK8,set_difference(sK9,sK8)),set_union2(sK8,set_difference(sK9,sK8))),
inference(lemma_extension,[status(thm),parent(t40:3)],[l20:1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
( ~ in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8))
| ~ sP1(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8),sK8) ),
inference(extension,[status(thm),parent(t36:3)],[f_4_12]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t36:3]) ).
cnf(t48,plain,
( ~ in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK9)
| in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK8)
| ~ sP7(set_difference(sK9,sK8),sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),U_1305,sK9,sK8)
| in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8)) ),
inference(extension,[status(thm),parent(t46:2)],[f_6_10]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
( set_difference(sK9,sK8) != set_difference(sK9,sK8)
| sP7(set_difference(sK9,sK8),sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),U_1305,sK9,sK8) ),
inference(extension,[status(thm),parent(t48:2)],[f_6_7]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
set_difference(sK9,sK8) = set_difference(sK9,sK8),
inference(extension,[status(thm),parent(t50:2)],[equality_1]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
( ~ sP1(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),set_difference(sK9,sK8),sK8)
| ~ in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK8) ),
inference(extension,[status(thm),parent(t48:3)],[f_4_11]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t48:3]) ).
cnf(t56,plain,
$false,
inference(reduction,[status(thm),parent(t54:2)],[t54:2,t36:3]) ).
cnf(l25,lemma,
~ in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK8),
inference(lemma,[status(cth),parent(t48:3),below(t46:2)],[t48:3]) ).
cnf(t57,plain,
( in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK8)
| ~ sP4(set_union2(sK8,set_difference(sK9,sK8)),sK9,sK8)
| in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK9) ),
inference(extension,[status(thm),parent(t48:4)],[f_4_16]) ).
cnf(t58,plain,
$false,
inference(connection,[status(thm),parent(t57:1)],[t57:1,t48:4]) ).
cnf(t59,plain,
$false,
inference(reduction,[status(thm),parent(t57:2)],[t57:2,t2:3]) ).
cnf(t60,plain,
~ in(sK2(sK8,sK9,set_union2(sK8,set_difference(sK9,sK8))),sK8),
inference(lemma_extension,[status(thm),parent(t57:3)],[l25:1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t57:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU135+1 : 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/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 : n020.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:22:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 33.63/33.96 % SZS status Theorem for theBenchmark
% 33.63/33.96 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------