%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU124+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 : n013.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 08:58:06 AM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : Proof 0.09s
% 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(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(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
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_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
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(t7_xboole_1,conjecture,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
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] : 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]) ).
cnf(f_2_3,plain,
set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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_3_2,plain,
! [U_8,U_7,U_6] :
( ( U_6 = set_union2(U_8,U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& ( in(U_5,U_7)
| in(U_5,U_8) ) )
| ( ~ in(U_5,U_7)
& ~ in(U_5,U_8)
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| ( ~ in(U_4,U_7)
& ~ in(U_4,U_8) ) )
& ( in(U_4,U_7)
| in(U_4,U_8)
| ~ in(U_4,U_6) ) )
| U_6 != set_union2(U_8,U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( in(U_12,U_16)
| in(U_12,U_18) ) )
| ? [U_11] :
( ~ in(U_11,U_16)
& ~ in(U_11,U_18)
& in(U_11,U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( in(U_12,U_16)
| in(U_12,U_18) ) )
| ( ~ in(sK1(U_18,U_16,U_14),U_16)
& ~ in(sK1(U_18,U_16,U_14),U_18)
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_18,U_16,U_14))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ( ~ in(sK2(U_18,U_16,U_14),U_14)
& ( in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18) ) )
| ( ~ in(sK1(U_18,U_16,U_14),U_16)
& ~ in(sK1(U_18,U_16,U_14),U_18)
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_12,sK2(U_18,U_16,U_14))],[f_3_4]) ).
cnf(f_3_6,plain,
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13)
| U_13 != set_union2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( ~ in(U_10,U_17)
| in(U_10,U_13)
| U_13 != set_union2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( ~ in(U_10,U_15)
| in(U_10,U_13)
| U_13 != set_union2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18)
| in(sK1(U_18,U_16,U_14),U_14)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( ~ in(sK2(U_18,U_16,U_14),U_14)
| in(sK1(U_18,U_16,U_14),U_14)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ in(sK1(U_18,U_16,U_14),U_18)
| in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_12,plain,
( ~ in(sK1(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_13,plain,
( ~ in(sK1(U_18,U_16,U_14),U_18)
| ~ in(sK2(U_18,U_16,U_14),U_14)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_14,plain,
( ~ in(sK1(U_18,U_16,U_14),U_16)
| ~ in(sK2(U_18,U_16,U_14),U_14)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
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_22,U_21] :
( ( subset(U_22,U_21)
| ? [U_20] :
( ~ in(U_20,U_21)
& in(U_20,U_22) ) )
& ( ! [U_19] :
( in(U_19,U_21)
| ~ in(U_19,U_22) )
| ~ subset(U_22,U_21) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_26,U_24] :
( subset(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_24)
& in(U_20,U_26) ) )
& ! [U_25,U_23] :
( ! [U_19] :
( in(U_19,U_23)
| ~ in(U_19,U_25) )
| ~ subset(U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_26,U_24] :
( subset(U_26,U_24)
| ( ~ in(sK3(U_26,U_24),U_24)
& in(sK3(U_26,U_24),U_26) ) )
& ! [U_25,U_23] :
( ! [U_19] :
( in(U_19,U_23)
| ~ in(U_19,U_25) )
| ~ subset(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3(U_26,U_24))],[f_4_3]) ).
cnf(f_4_5,plain,
( in(U_19,U_23)
| ~ in(U_19,U_25)
| ~ subset(U_25,U_23) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( in(sK3(U_26,U_24),U_26)
| subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( ~ in(sK3(U_26,U_24),U_24)
| subset(U_26,U_24) ),
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_k2_xboole_0]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_7_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_8_2,plain,
! [U_28,U_27] :
( ~ empty(set_union2(U_28,U_27))
| empty(U_28) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_28] :
( ! [U_27] : ~ empty(set_union2(U_28,U_27))
| empty(U_28) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( ~ empty(set_union2(U_28,U_27))
| empty(U_28) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_9_2,plain,
! [U_30,U_29] :
( ~ empty(set_union2(U_29,U_30))
| empty(U_30) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_30] :
( ! [U_29] : ~ empty(set_union2(U_29,U_30))
| empty(U_30) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( ~ empty(set_union2(U_29,U_30))
| empty(U_30) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_10_2,plain,
! [U_32,U_31] : set_union2(U_32,U_32) = U_32,
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_32] : set_union2(U_32,U_32) = U_32,
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
set_union2(U_32,U_32) = U_32,
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_11_2,plain,
? [U_33] : empty(U_33),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4)],[f_11_2]) ).
cnf(f_11_4,plain,
empty(sK4),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_12_2,plain,
? [U_34] : ~ empty(U_34),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
~ empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_34,sK5)],[f_12_2]) ).
cnf(f_12_4,plain,
~ empty(sK5),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_13_2,plain,
! [U_36,U_35] : subset(U_36,U_36),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_36] : subset(U_36,U_36),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
subset(U_36,U_36),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_14_2,plain,
! [U_37] : set_union2(U_37,empty_set) = U_37,
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
set_union2(U_37,empty_set) = U_37,
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_15_2,plain,
! [U_38] :
( U_38 = empty_set
| ~ empty(U_38) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( U_38 = empty_set
| ~ empty(U_38) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_16_2,plain,
! [U_40,U_39] :
( ~ empty(U_39)
| ~ in(U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( ~ empty(U_39)
| ~ in(U_40,U_39) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,negated_conjecture,
~ ! [A,B] : subset(A,set_union2(A,B)),
inference(negate,[status(cth)],[t7_xboole_1]) ).
fof(f_17_2,negated_conjecture,
? [A,B] : ~ subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[f_17_1]) ).
fof(f_17_3,negated_conjecture,
? [U_42,U_41] : ~ subset(U_42,set_union2(U_42,U_41)),
inference(variable_rename,[status(thm)],[f_17_2]) ).
fof(f_17_4,negated_conjecture,
? [U_41] : ~ subset(sK6,set_union2(sK6,U_41)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_17_3]) ).
fof(f_17_5,negated_conjecture,
~ subset(sK6,set_union2(sK6,sK7)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7)],[f_17_4]) ).
fof(f_17_6,negated_conjecture,
~ subset(sK6,set_union2(sK6,sK7)),
inference(definitional_conversion,[status(esa)],[f_17_5]) ).
cnf(f_17_7,negated_conjecture,
~ subset(sK6,set_union2(sK6,sK7)),
inference(clausify,[status(thm)],[f_17_6]) ).
fof(f_18_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_18_2,plain,
! [U_44,U_43] :
( ~ empty(U_43)
| U_44 = U_43
| ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_44] :
( ! [U_43] :
( ~ empty(U_43)
| U_44 = U_43 )
| ~ empty(U_44) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( ~ empty(U_43)
| U_44 = U_43
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_18_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(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,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(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_6,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(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_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,
( 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_9,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_10,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| 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 : SEU124+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 23:20:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.42 % SZS status Theorem for theBenchmark
% 0.09/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------