%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU173+1 : 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 : n017.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 08:58:21 AM UTC 2026
% Result : Theorem 0.22s 0.46s
% Output : Proof 0.22s
% 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(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(l71_subset_1,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
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(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
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] :
( ( ( ( element(B,A)
| ~ empty(B) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( element(B,A)
| ~ in(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(fof_nnf,[status(thm)],[d2_subset_1]) ).
fof(f_3_2,plain,
! [U_15,U_14] :
( ( ( ( element(U_14,U_15)
| ~ empty(U_14) )
& ( empty(U_14)
| ~ element(U_14,U_15) ) )
| ~ empty(U_15) )
& ( ( ( element(U_14,U_15)
| ~ in(U_14,U_15) )
& ( in(U_14,U_15)
| ~ element(U_14,U_15) ) )
| empty(U_15) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_23] :
( ( ! [U_21] :
( element(U_21,U_23)
| ~ empty(U_21) )
& ! [U_20] :
( empty(U_20)
| ~ element(U_20,U_23) ) )
| ~ empty(U_23) )
& ! [U_22] :
( ( ! [U_19] :
( element(U_19,U_22)
| ~ in(U_19,U_22) )
& ! [U_18] :
( in(U_18,U_22)
| ~ element(U_18,U_22) ) )
| empty(U_22) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( in(U_18,U_22)
| ~ element(U_18,U_22)
| empty(U_22) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( element(U_19,U_22)
| ~ in(U_19,U_22)
| empty(U_22) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( empty(U_20)
| ~ element(U_20,U_23)
| ~ empty(U_23) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_7,plain,
( element(U_21,U_23)
| ~ empty(U_21)
| ~ empty(U_23) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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_4_2,plain,
! [U_27,U_26] :
( ( subset(U_27,U_26)
| ? [U_25] :
( ~ in(U_25,U_26)
& in(U_25,U_27) ) )
& ( ! [U_24] :
( in(U_24,U_26)
| ~ in(U_24,U_27) )
| ~ subset(U_27,U_26) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_31,U_29] :
( subset(U_31,U_29)
| ? [U_25] :
( ~ in(U_25,U_29)
& in(U_25,U_31) ) )
& ! [U_30,U_28] :
( ! [U_24] :
( in(U_24,U_28)
| ~ in(U_24,U_30) )
| ~ subset(U_30,U_28) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_31,U_29] :
( subset(U_31,U_29)
| ( ~ in(sK3(U_31,U_29),U_29)
& in(sK3(U_31,U_29),U_31) ) )
& ! [U_30,U_28] :
( ! [U_24] :
( in(U_24,U_28)
| ~ in(U_24,U_30) )
| ~ subset(U_30,U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3(U_31,U_29))],[f_4_3]) ).
cnf(f_4_5,plain,
( in(U_24,U_28)
| ~ in(U_24,U_30)
| ~ subset(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( in(sK3(U_31,U_29),U_31)
| subset(U_31,U_29) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( ~ in(sK3(U_31,U_29),U_29)
| subset(U_31,U_29) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_8_2,plain,
! [U_33] :
? [U_32] : element(U_32,U_33),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_33] : element(sK4(U_33),U_33),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_32,sK4(U_33))],[f_8_2]) ).
cnf(f_8_4,plain,
element(sK4(U_33),U_33),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_9_2,plain,
! [U_34] : ~ empty(powerset(U_34)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
~ empty(powerset(U_34)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_10_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(negate,[status(cth)],[l71_subset_1]) ).
fof(f_11_2,negated_conjecture,
? [A,B] :
( ~ element(A,powerset(B))
& ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_37,U_36] :
( ~ element(U_37,powerset(U_36))
& ! [U_35] :
( in(U_35,U_36)
| ~ in(U_35,U_37) ) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_36] :
( ~ element(sK5,powerset(U_36))
& ! [U_35] :
( in(U_35,U_36)
| ~ in(U_35,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_37,sK5)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
( ~ element(sK5,powerset(sK6))
& ! [U_35] :
( in(U_35,sK6)
| ~ in(U_35,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_36,sK6)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
( ~ element(sK5,powerset(sK6))
& ! [U_35] :
( in(U_35,sK6)
| ~ in(U_35,sK5) ) ),
inference(definitional_conversion,[status(esa)],[f_11_5]) ).
cnf(f_11_7,negated_conjecture,
( in(U_35,sK6)
| ~ in(U_35,sK5) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_8,negated_conjecture,
~ element(sK5,powerset(sK6)),
inference(clausify,[status(thm)],[f_11_6]) ).
fof(f_12_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_12_2,plain,
! [U_39] :
( ? [U_38] :
( ~ empty(U_38)
& element(U_38,powerset(U_39)) )
| empty(U_39) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_39] :
( ( ~ empty(sK7(U_39))
& element(sK7(U_39),powerset(U_39)) )
| empty(U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_38,sK7(U_39))],[f_12_2]) ).
cnf(f_12_4,plain,
( element(sK7(U_39),powerset(U_39))
| empty(U_39) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( ~ empty(sK7(U_39))
| empty(U_39) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_13_2,plain,
? [U_40] : empty(U_40),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_40,sK8)],[f_13_2]) ).
cnf(f_13_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_14_2,plain,
! [U_42] :
? [U_41] :
( empty(U_41)
& element(U_41,powerset(U_42)) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_42] :
( empty(sK9(U_42))
& element(sK9(U_42),powerset(U_42)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_41,sK9(U_42))],[f_14_2]) ).
cnf(f_14_4,plain,
element(sK9(U_42),powerset(U_42)),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
empty(sK9(U_42)),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_15_2,plain,
? [U_43] : ~ empty(U_43),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
~ empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_43,sK10)],[f_15_2]) ).
cnf(f_15_4,plain,
~ empty(sK10),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_16_2,plain,
! [U_45,U_44] : subset(U_45,U_45),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_45] : subset(U_45,U_45),
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
subset(U_45,U_45),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_17_2,plain,
! [U_46] :
( U_46 = empty_set
| ~ empty(U_46) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( U_46 = empty_set
| ~ empty(U_46) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_18_2,plain,
! [U_48,U_47] :
( ~ empty(U_47)
| ~ in(U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ~ empty(U_47)
| ~ in(U_48,U_47) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_19_2,plain,
! [U_50,U_49] :
( ~ empty(U_49)
| U_50 = U_49
| ~ empty(U_50) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_50] :
( ! [U_49] :
( ~ empty(U_49)
| U_50 = U_49 )
| ~ empty(U_50) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( ~ empty(U_49)
| U_50 = U_49
| ~ empty(U_50) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_2]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
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,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK7(Eq_x_0) = sK7(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,
( 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,
( element(Eq_y_0,Eq_y_1)
| ~ element(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 : SEU173+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n017.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 23:20:25 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.22/0.46 % SZS status Theorem for theBenchmark
% 0.22/0.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------