%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU107+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 : n014.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 08:58:03 AM UTC 2026
% Result : Theorem 216.32s 216.62s
% Output : Proof 218.85s
% 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(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(cc1_finsub_1,axiom,
! [A] :
( preboolean(A)
=> ( diff_closed(A)
& cup_closed(A) ) ),
file('theBenchmark.p',cc1_finsub_1) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(cc2_finsub_1,axiom,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
=> preboolean(A) ),
file('theBenchmark.p',cc2_finsub_1) ).
fof(dt_k2_finsub_1,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> element(prebool_difference(A,B,C),A) ),
file('theBenchmark.p',dt_k2_finsub_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('theBenchmark.p',fc12_finset_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(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_finsub_1,axiom,
? [A] :
( preboolean(A)
& diff_closed(A)
& cap_closed(A)
& cup_closed(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finsub_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_finset_1,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_finset_1) ).
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(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc3_finset_1) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc4_finset_1) ).
fof(redefinition_k2_finsub_1,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> prebool_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k2_finsub_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t18_finsub_1,conjecture,
! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
file('theBenchmark.p',t18_finsub_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
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]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ 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] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_2_2,plain,
! [U_2] :
( finite(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2] :
( finite(U_2)
| ~ empty(U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( finite(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ),
inference(fof_nnf,[status(thm)],[cc1_finsub_1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( diff_closed(U_3)
& cup_closed(U_3) )
| ~ preboolean(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_3] :
( diff_closed(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( cup_closed(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( sP0(U_3)
| ~ preboolean(U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_3)
| ~ preboolean(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( cup_closed(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( diff_closed(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_4_2,plain,
! [U_5] :
( ! [U_4] :
( finite(U_4)
| ~ element(U_4,powerset(U_5)) )
| ~ finite(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_4] :
( finite(U_4)
| ~ element(U_4,powerset(U_5))
| ~ finite(U_5) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( finite(U_4)
| ~ element(U_4,powerset(U_5))
| ~ finite(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(fof_nnf,[status(thm)],[cc2_finsub_1]) ).
fof(f_5_2,plain,
! [U_6] :
( preboolean(U_6)
| ~ diff_closed(U_6)
| ~ cup_closed(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_6] :
( preboolean(U_6)
| ~ diff_closed(U_6)
| ~ cup_closed(U_6) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( preboolean(U_6)
| ~ diff_closed(U_6)
| ~ cup_closed(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B,C] :
( element(prebool_difference(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_finsub_1]) ).
fof(f_6_2,plain,
! [U_9,U_8,U_7] :
( element(prebool_difference(U_9,U_8,U_7),U_9)
| ~ element(U_7,U_9)
| ~ element(U_8,U_9)
| ~ preboolean(U_9)
| empty(U_9) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_8,U_7,U_9] :
( element(prebool_difference(U_9,U_8,U_7),U_9)
| ~ element(U_7,U_9)
| ~ element(U_8,U_9)
| ~ preboolean(U_9)
| empty(U_9) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( element(prebool_difference(U_9,U_8,U_7),U_9)
| ~ element(U_7,U_9)
| ~ element(U_8,U_9)
| ~ preboolean(U_9)
| empty(U_9) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_7_2,plain,
! [U_11] :
? [U_10] : element(U_10,U_11),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_11] : element(sK1(U_11),U_11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_11))],[f_7_2]) ).
fof(f_7_4,plain,
! [U_11] : element(sK1(U_11),U_11),
inference(definitional_conversion,[status(esa)],[f_7_3]) ).
cnf(f_7_5,plain,
element(sK1(U_11),U_11),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc12_finset_1]) ).
fof(f_8_2,plain,
! [U_13,U_12] :
( finite(set_difference(U_13,U_12))
| ~ finite(U_13) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_13] :
( ! [U_12] : finite(set_difference(U_13,U_12))
| ~ finite(U_13) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
! [U_13,U_12] :
( finite(set_difference(U_13,U_12))
| ~ finite(U_13) ),
inference(definitional_conversion,[status(esa)],[f_8_3]) ).
cnf(f_8_5,plain,
( finite(set_difference(U_13,U_12))
| ~ finite(U_13) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_9_2,plain,
! [U_14] : ~ empty(powerset(U_14)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_14] : ~ empty(powerset(U_14)),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
~ empty(powerset(U_14)),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_10_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_11_2,plain,
? [U_15] :
( finite(U_15)
& ~ empty(U_15) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( finite(sK2)
& ~ empty(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2)],[f_11_2]) ).
fof(f_11_4,plain,
( finite(sK2)
& ~ empty(sK2) ),
inference(definitional_conversion,[status(esa)],[f_11_3]) ).
cnf(f_11_5,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
finite(sK2),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
? [A] :
( preboolean(A)
& diff_closed(A)
& cap_closed(A)
& cup_closed(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finsub_1]) ).
fof(f_12_2,plain,
? [U_16] :
( preboolean(U_16)
& diff_closed(U_16)
& cap_closed(U_16)
& cup_closed(U_16)
& ~ empty(U_16) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( preboolean(sK3)
& diff_closed(sK3)
& cap_closed(sK3)
& cup_closed(sK3)
& ~ empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_16,sK3)],[f_12_2]) ).
fof(f_12_4,plain,
( preboolean(sK3)
& diff_closed(sK3)
& cap_closed(sK3)
& cup_closed(sK3)
& ~ empty(sK3) ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
~ empty(sK3),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
cup_closed(sK3),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_7,plain,
cap_closed(sK3),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_8,plain,
diff_closed(sK3),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_9,plain,
preboolean(sK3),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_13_2,plain,
! [U_18] :
( ? [U_17] :
( ~ empty(U_17)
& element(U_17,powerset(U_18)) )
| empty(U_18) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_18] :
( ( ~ empty(sK4(U_18))
& element(sK4(U_18),powerset(U_18)) )
| empty(U_18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_17,sK4(U_18))],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_18] :
( ~ empty(sK4(U_18))
| ~ sP1(U_18) )
& ! [U_18] :
( element(sK4(U_18),powerset(U_18))
| ~ sP1(U_18) )
& ! [U_18] :
( sP1(U_18)
| empty(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_13_3]) ).
cnf(f_13_5,plain,
( sP1(U_18)
| empty(U_18) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( element(sK4(U_18),powerset(U_18))
| ~ sP1(U_18) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_7,plain,
( ~ empty(sK4(U_18))
| ~ sP1(U_18) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_14_2,plain,
? [U_19] : empty(U_19),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_19,sK5)],[f_14_2]) ).
fof(f_14_4,plain,
empty(sK5),
inference(definitional_conversion,[status(esa)],[f_14_3]) ).
cnf(f_14_5,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_finset_1]) ).
fof(f_15_2,plain,
! [U_21] :
? [U_20] :
( finite(U_20)
& natural(U_20)
& ordinal(U_20)
& epsilon_connected(U_20)
& epsilon_transitive(U_20)
& one_to_one(U_20)
& function(U_20)
& relation(U_20)
& empty(U_20)
& element(U_20,powerset(U_21)) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_21] :
( finite(sK6(U_21))
& natural(sK6(U_21))
& ordinal(sK6(U_21))
& epsilon_connected(sK6(U_21))
& epsilon_transitive(sK6(U_21))
& one_to_one(sK6(U_21))
& function(sK6(U_21))
& relation(sK6(U_21))
& empty(sK6(U_21))
& element(sK6(U_21),powerset(U_21)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_20,sK6(U_21))],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_21] : finite(sK6(U_21))
& ! [U_21] : natural(sK6(U_21))
& ! [U_21] : ordinal(sK6(U_21))
& ! [U_21] : epsilon_connected(sK6(U_21))
& ! [U_21] : epsilon_transitive(sK6(U_21))
& ! [U_21] : one_to_one(sK6(U_21))
& ! [U_21] : function(sK6(U_21))
& ! [U_21] : relation(sK6(U_21))
& ! [U_21] : empty(sK6(U_21))
& ! [U_21] : element(sK6(U_21),powerset(U_21)) ),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
element(sK6(U_21),powerset(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
empty(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
relation(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_8,plain,
function(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_9,plain,
one_to_one(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_10,plain,
epsilon_transitive(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_11,plain,
epsilon_connected(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_12,plain,
ordinal(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_13,plain,
natural(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_14,plain,
finite(sK6(U_21)),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_16_2,plain,
! [U_23] :
? [U_22] :
( empty(U_22)
& element(U_22,powerset(U_23)) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_23] :
( empty(sK7(U_23))
& element(sK7(U_23),powerset(U_23)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_22,sK7(U_23))],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_23] : empty(sK7(U_23))
& ! [U_23] : element(sK7(U_23),powerset(U_23)) ),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
element(sK7(U_23),powerset(U_23)),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_6,plain,
empty(sK7(U_23)),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_17_2,plain,
? [U_24] : ~ empty(U_24),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_24,sK8)],[f_17_2]) ).
fof(f_17_4,plain,
~ empty(sK8),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_18_2,plain,
! [U_26] :
( ? [U_25] :
( finite(U_25)
& ~ empty(U_25)
& element(U_25,powerset(U_26)) )
| empty(U_26) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_26] :
( ( finite(sK9(U_26))
& ~ empty(sK9(U_26))
& element(sK9(U_26),powerset(U_26)) )
| empty(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_25,sK9(U_26))],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_26] :
( finite(sK9(U_26))
| ~ sP2(U_26) )
& ! [U_26] :
( ~ empty(sK9(U_26))
| ~ sP2(U_26) )
& ! [U_26] :
( element(sK9(U_26),powerset(U_26))
| ~ sP2(U_26) )
& ! [U_26] :
( sP2(U_26)
| empty(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_18_3]) ).
cnf(f_18_5,plain,
( sP2(U_26)
| empty(U_26) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( element(sK9(U_26),powerset(U_26))
| ~ sP2(U_26) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_7,plain,
( ~ empty(sK9(U_26))
| ~ sP2(U_26) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_8,plain,
( finite(sK9(U_26))
| ~ sP2(U_26) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc4_finset_1]) ).
fof(f_19_2,plain,
! [U_28] :
( ? [U_27] :
( finite(U_27)
& ~ empty(U_27)
& element(U_27,powerset(U_28)) )
| empty(U_28) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_28] :
( ( finite(sK10(U_28))
& ~ empty(sK10(U_28))
& element(sK10(U_28),powerset(U_28)) )
| empty(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_27,sK10(U_28))],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_28] :
( finite(sK10(U_28))
| ~ sP3(U_28) )
& ! [U_28] :
( ~ empty(sK10(U_28))
| ~ sP3(U_28) )
& ! [U_28] :
( element(sK10(U_28),powerset(U_28))
| ~ sP3(U_28) )
& ! [U_28] :
( sP3(U_28)
| empty(U_28) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_19_3]) ).
cnf(f_19_5,plain,
( sP3(U_28)
| empty(U_28) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_6,plain,
( element(sK10(U_28),powerset(U_28))
| ~ sP3(U_28) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_7,plain,
( ~ empty(sK10(U_28))
| ~ sP3(U_28) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_8,plain,
( finite(sK10(U_28))
| ~ sP3(U_28) ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A,B,C] :
( prebool_difference(A,B,C) = set_difference(B,C)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k2_finsub_1]) ).
fof(f_20_2,plain,
! [U_31,U_30,U_29] :
( prebool_difference(U_31,U_30,U_29) = set_difference(U_30,U_29)
| ~ element(U_29,U_31)
| ~ element(U_30,U_31)
| ~ preboolean(U_31)
| empty(U_31) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_31,U_30,U_29] :
( prebool_difference(U_31,U_30,U_29) = set_difference(U_30,U_29)
| ~ element(U_29,U_31)
| ~ element(U_30,U_31)
| ~ preboolean(U_31)
| empty(U_31) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( prebool_difference(U_31,U_30,U_29) = set_difference(U_30,U_29)
| ~ element(U_29,U_31)
| ~ element(U_30,U_31)
| ~ preboolean(U_31)
| empty(U_31) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_21_2,plain,
! [U_33,U_32] : subset(U_33,U_33),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_33] : subset(U_33,U_33),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
! [U_33] : subset(U_33,U_33),
inference(definitional_conversion,[status(esa)],[f_21_3]) ).
cnf(f_21_5,plain,
subset(U_33,U_33),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,negated_conjecture,
~ ! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
inference(negate,[status(cth)],[t18_finsub_1]) ).
fof(f_22_2,negated_conjecture,
? [A] :
( ~ in(empty_set,A)
& preboolean(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[f_22_1]) ).
fof(f_22_3,negated_conjecture,
? [U_34] :
( ~ in(empty_set,U_34)
& preboolean(U_34)
& ~ empty(U_34) ),
inference(variable_rename,[status(thm)],[f_22_2]) ).
fof(f_22_4,negated_conjecture,
( ~ in(empty_set,sK11)
& preboolean(sK11)
& ~ empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_34,sK11)],[f_22_3]) ).
fof(f_22_5,negated_conjecture,
( ~ in(empty_set,sK11)
& preboolean(sK11)
& ~ empty(sK11) ),
inference(definitional_conversion,[status(esa)],[f_22_4]) ).
cnf(f_22_6,negated_conjecture,
~ empty(sK11),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,negated_conjecture,
preboolean(sK11),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,negated_conjecture,
~ in(empty_set,sK11),
inference(clausify,[status(thm)],[f_22_5]) ).
fof(f_23_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_23_2,plain,
! [U_36,U_35] :
( element(U_36,U_35)
| ~ in(U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_36,U_35] :
( element(U_36,U_35)
| ~ in(U_36,U_35) ),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
( element(U_36,U_35)
| ~ in(U_36,U_35) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_24_2,plain,
! [U_38,U_37] :
( in(U_38,U_37)
| empty(U_37)
| ~ element(U_38,U_37) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_38,U_37] :
( in(U_38,U_37)
| empty(U_37)
| ~ element(U_38,U_37) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( in(U_38,U_37)
| empty(U_37)
| ~ element(U_38,U_37) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1]) ).
fof(f_25_2,plain,
! [U_40,U_39] :
( ( set_difference(U_40,U_39) = empty_set
| ~ subset(U_40,U_39) )
& ( subset(U_40,U_39)
| set_difference(U_40,U_39) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_44,U_42] :
( set_difference(U_44,U_42) = empty_set
| ~ subset(U_44,U_42) )
& ! [U_43,U_41] :
( subset(U_43,U_41)
| set_difference(U_43,U_41) != empty_set ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_42,U_44] :
( set_difference(U_44,U_42) = empty_set
| ~ subset(U_44,U_42) )
& ! [U_43,U_41] :
( subset(U_43,U_41)
| set_difference(U_43,U_41) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
( subset(U_43,U_41)
| set_difference(U_43,U_41) != empty_set ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
( set_difference(U_44,U_42) = empty_set
| ~ subset(U_44,U_42) ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_26_2,plain,
! [U_45] : set_difference(U_45,empty_set) = U_45,
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_45] : set_difference(U_45,empty_set) = U_45,
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
set_difference(U_45,empty_set) = U_45,
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_27_2,plain,
! [U_47,U_46] :
( ( element(U_47,powerset(U_46))
| ~ subset(U_47,U_46) )
& ( subset(U_47,U_46)
| ~ element(U_47,powerset(U_46)) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_51,U_49] :
( element(U_51,powerset(U_49))
| ~ subset(U_51,U_49) )
& ! [U_50,U_48] :
( subset(U_50,U_48)
| ~ element(U_50,powerset(U_48)) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_51,U_49] :
( element(U_51,powerset(U_49))
| ~ subset(U_51,U_49) )
& ! [U_50,U_48] :
( subset(U_50,U_48)
| ~ element(U_50,powerset(U_48)) ) ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
( subset(U_50,U_48)
| ~ element(U_50,powerset(U_48)) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
( element(U_51,powerset(U_49))
| ~ subset(U_51,U_49) ),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_28_2,plain,
! [U_52] : set_difference(empty_set,U_52) = empty_set,
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_52] : set_difference(empty_set,U_52) = empty_set,
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
set_difference(empty_set,U_52) = empty_set,
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_29_2,plain,
! [U_55,U_54,U_53] :
( element(U_55,U_53)
| ~ element(U_54,powerset(U_53))
| ~ in(U_55,U_54) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_53,U_54,U_55] :
( element(U_55,U_53)
| ~ element(U_54,powerset(U_53))
| ~ in(U_55,U_54) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( element(U_55,U_53)
| ~ element(U_54,powerset(U_53))
| ~ in(U_55,U_54) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_30_2,plain,
! [U_58,U_57,U_56] :
( ~ empty(U_56)
| ~ element(U_57,powerset(U_56))
| ~ in(U_58,U_57) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_58,U_57] :
( ! [U_56] :
( ~ empty(U_56)
| ~ element(U_57,powerset(U_56)) )
| ~ in(U_58,U_57) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_57,U_58,U_56] :
( ~ empty(U_56)
| ~ element(U_57,powerset(U_56))
| ~ in(U_58,U_57) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ empty(U_56)
| ~ element(U_57,powerset(U_56))
| ~ in(U_58,U_57) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_31_2,plain,
! [U_59] :
( U_59 = empty_set
| ~ empty(U_59) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_59] :
( U_59 = empty_set
| ~ empty(U_59) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( U_59 = empty_set
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_32_2,plain,
! [U_61,U_60] :
( ~ empty(U_60)
| ~ in(U_61,U_60) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_60,U_61] :
( ~ empty(U_60)
| ~ in(U_61,U_60) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( ~ empty(U_60)
| ~ in(U_61,U_60) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_33_2,plain,
! [U_63,U_62] :
( ~ empty(U_62)
| U_63 = U_62
| ~ empty(U_63) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_63] :
( ! [U_62] :
( ~ empty(U_62)
| U_63 = U_62 )
| ~ empty(U_63) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_62,U_63] :
( ~ empty(U_62)
| U_63 = U_62
| ~ empty(U_63) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( ~ empty(U_62)
| U_63 = U_62
| ~ empty(U_63) ),
inference(clausify,[status(thm)],[f_33_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,
( prebool_difference(Eq_x_0,Eq_x_1,Eq_x_2) = prebool_difference(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,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(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,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| 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,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( preboolean(Eq_y_0)
| ~ preboolean(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( cup_closed(Eq_y_0)
| ~ cup_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( diff_closed(Eq_y_0)
| ~ diff_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,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(equality_20,axiom,
( cap_closed(Eq_y_0)
| ~ cap_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,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_29,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP3(Eq_y_0)
| ~ sP3(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
% 0.00/0.03 % Problem : SEU107+1 : 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
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:19:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 216.32/216.62 % SZS status Theorem for theBenchmark
% 216.32/216.62 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------