%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU114+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n016.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 08:58:04 AM UTC 2026
% Result : Theorem 8.36s 8.62s
% Output : Proof 8.48s
% 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(cc3_finsub_1,axiom,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
file('theBenchmark.p',cc3_finsub_1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d5_finsub_1,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [A] : preboolean(finite_subsets(A)),
file('theBenchmark.p',dt_k5_finsub_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_finsub_1,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('theBenchmark.p',fc1_finsub_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(fc2_finsub_1,axiom,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
file('theBenchmark.p',fc2_finsub_1) ).
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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t13_finset_1,axiom,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t26_finsub_1,axiom,
! [A] : subset(finite_subsets(A),powerset(A)),
file('theBenchmark.p',t26_finsub_1) ).
fof(t27_finsub_1,conjecture,
! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
file('theBenchmark.p',t27_finsub_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
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]) ).
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] :
( 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]) ).
cnf(f_2_3,plain,
( finite(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
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]) ).
cnf(f_3_3,plain,
( cup_closed(U_3)
| ~ preboolean(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( diff_closed(U_3)
| ~ preboolean(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
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]) ).
cnf(f_4_3,plain,
( finite(U_4)
| ~ element(U_4,powerset(U_5))
| ~ finite(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
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]) ).
cnf(f_5_3,plain,
( preboolean(U_6)
| ~ diff_closed(U_6)
| ~ cup_closed(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] :
( finite(B)
| ~ element(B,finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[cc3_finsub_1]) ).
fof(f_6_2,plain,
! [U_8,U_7] :
( finite(U_7)
| ~ element(U_7,finite_subsets(U_8)) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( finite(U_7)
| ~ element(U_7,finite_subsets(U_8)) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_10,U_9] :
( ( U_10 = U_9
| ~ subset(U_9,U_10)
| ~ subset(U_10,U_9) )
& ( ( subset(U_9,U_10)
& subset(U_10,U_9) )
| U_10 != U_9 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_14,U_12] :
( U_14 = U_12
| ~ subset(U_12,U_14)
| ~ subset(U_14,U_12) )
& ! [U_13,U_11] :
( ( subset(U_11,U_13)
& subset(U_13,U_11) )
| U_13 != U_11 ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( subset(U_13,U_11)
| U_13 != U_11 ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( subset(U_11,U_13)
| U_13 != U_11 ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( U_14 = U_12
| ~ subset(U_12,U_14)
| ~ subset(U_14,U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_2,plain,
! [U_18,U_17] :
( ( subset(U_18,U_17)
| ? [U_16] :
( ~ in(U_16,U_17)
& in(U_16,U_18) ) )
& ( ! [U_15] :
( in(U_15,U_17)
| ~ in(U_15,U_18) )
| ~ subset(U_18,U_17) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_22,U_20] :
( subset(U_22,U_20)
| ? [U_16] :
( ~ in(U_16,U_20)
& in(U_16,U_22) ) )
& ! [U_21,U_19] :
( ! [U_15] :
( in(U_15,U_19)
| ~ in(U_15,U_21) )
| ~ subset(U_21,U_19) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_22,U_20] :
( subset(U_22,U_20)
| ( ~ in(sK1(U_22,U_20),U_20)
& in(sK1(U_22,U_20),U_22) ) )
& ! [U_21,U_19] :
( ! [U_15] :
( in(U_15,U_19)
| ~ in(U_15,U_21) )
| ~ subset(U_21,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_16,sK1(U_22,U_20))],[f_8_3]) ).
cnf(f_8_5,plain,
( in(U_15,U_19)
| ~ in(U_15,U_21)
| ~ subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( in(sK1(U_22,U_20),U_22)
| subset(U_22,U_20) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( ~ in(sK1(U_22,U_20),U_20)
| subset(U_22,U_20) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [A,B] :
( ( ( B = finite_subsets(A)
| ? [C] :
( ( ~ in(C,B)
& finite(C)
& subset(C,A) )
| ( ( ~ finite(C)
| ~ subset(C,A) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ finite(C)
| ~ subset(C,A) )
& ( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(fof_nnf,[status(thm)],[d5_finsub_1]) ).
fof(f_9_2,plain,
! [U_26,U_25] :
( ( ( U_25 = finite_subsets(U_26)
| ? [U_24] :
( ( ~ in(U_24,U_25)
& finite(U_24)
& subset(U_24,U_26) )
| ( ( ~ finite(U_24)
| ~ subset(U_24,U_26) )
& in(U_24,U_25) ) ) )
& ( ! [U_23] :
( ( in(U_23,U_25)
| ~ finite(U_23)
| ~ subset(U_23,U_26) )
& ( ( finite(U_23)
& subset(U_23,U_26) )
| ~ in(U_23,U_25) ) )
| U_25 != finite_subsets(U_26) ) )
| ~ preboolean(U_25) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_26,U_25] :
( ( ( U_25 = finite_subsets(U_26)
| ? [U_30] :
( ~ in(U_30,U_25)
& finite(U_30)
& subset(U_30,U_26) )
| ? [U_29] :
( ( ~ finite(U_29)
| ~ subset(U_29,U_26) )
& in(U_29,U_25) ) )
& ( ( ! [U_28] :
( in(U_28,U_25)
| ~ finite(U_28)
| ~ subset(U_28,U_26) )
& ! [U_27] :
( ( finite(U_27)
& subset(U_27,U_26) )
| ~ in(U_27,U_25) ) )
| U_25 != finite_subsets(U_26) ) )
| ~ preboolean(U_25) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_26,U_25] :
( ( ( U_25 = finite_subsets(U_26)
| ? [U_30] :
( ~ in(U_30,U_25)
& finite(U_30)
& subset(U_30,U_26) )
| ( ( ~ finite(sK2(U_26,U_25))
| ~ subset(sK2(U_26,U_25),U_26) )
& in(sK2(U_26,U_25),U_25) ) )
& ( ( ! [U_28] :
( in(U_28,U_25)
| ~ finite(U_28)
| ~ subset(U_28,U_26) )
& ! [U_27] :
( ( finite(U_27)
& subset(U_27,U_26) )
| ~ in(U_27,U_25) ) )
| U_25 != finite_subsets(U_26) ) )
| ~ preboolean(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_29,sK2(U_26,U_25))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_26,U_25] :
( ( ( U_25 = finite_subsets(U_26)
| ( ~ in(sK3(U_26,U_25),U_25)
& finite(sK3(U_26,U_25))
& subset(sK3(U_26,U_25),U_26) )
| ( ( ~ finite(sK2(U_26,U_25))
| ~ subset(sK2(U_26,U_25),U_26) )
& in(sK2(U_26,U_25),U_25) ) )
& ( ( ! [U_28] :
( in(U_28,U_25)
| ~ finite(U_28)
| ~ subset(U_28,U_26) )
& ! [U_27] :
( ( finite(U_27)
& subset(U_27,U_26) )
| ~ in(U_27,U_25) ) )
| U_25 != finite_subsets(U_26) ) )
| ~ preboolean(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_30,sK3(U_26,U_25))],[f_9_4]) ).
cnf(f_9_6,plain,
( subset(U_27,U_26)
| ~ in(U_27,U_25)
| U_25 != finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( finite(U_27)
| ~ in(U_27,U_25)
| U_25 != finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( in(U_28,U_25)
| ~ finite(U_28)
| ~ subset(U_28,U_26)
| U_25 != finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( subset(sK3(U_26,U_25),U_26)
| in(sK2(U_26,U_25),U_25)
| U_25 = finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( finite(sK3(U_26,U_25))
| in(sK2(U_26,U_25),U_25)
| U_25 = finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ~ in(sK3(U_26,U_25),U_25)
| in(sK2(U_26,U_25),U_25)
| U_25 = finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_12,plain,
( subset(sK3(U_26,U_25),U_26)
| ~ finite(sK2(U_26,U_25))
| ~ subset(sK2(U_26,U_25),U_26)
| U_25 = finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_13,plain,
( finite(sK3(U_26,U_25))
| ~ finite(sK2(U_26,U_25))
| ~ subset(sK2(U_26,U_25),U_26)
| U_25 = finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_14,plain,
( ~ in(sK3(U_26,U_25),U_25)
| ~ finite(sK2(U_26,U_25))
| ~ subset(sK2(U_26,U_25),U_26)
| U_25 = finite_subsets(U_26)
| ~ preboolean(U_25) ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_1,plain,
! [A] : preboolean(finite_subsets(A)),
inference(fof_nnf,[status(thm)],[dt_k5_finsub_1]) ).
fof(f_10_2,plain,
! [U_31] : preboolean(finite_subsets(U_31)),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
preboolean(finite_subsets(U_31)),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_11_2,plain,
! [U_33] :
? [U_32] : element(U_32,U_33),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_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_11_2]) ).
cnf(f_11_4,plain,
element(sK4(U_33),U_33),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(fof_nnf,[status(thm)],[fc1_finsub_1]) ).
fof(f_12_2,plain,
! [U_34] :
( preboolean(powerset(U_34))
& diff_closed(powerset(U_34))
& cup_closed(powerset(U_34))
& ~ empty(powerset(U_34)) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_38] : preboolean(powerset(U_38))
& ! [U_37] : diff_closed(powerset(U_37))
& ! [U_36] : cup_closed(powerset(U_36))
& ! [U_35] : ~ empty(powerset(U_35)) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
~ empty(powerset(U_35)),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
cup_closed(powerset(U_36)),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
diff_closed(powerset(U_37)),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_7,plain,
preboolean(powerset(U_38)),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_13_2,plain,
! [U_39] : ~ empty(powerset(U_39)),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
~ empty(powerset(U_39)),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_14_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[fc2_finsub_1]) ).
fof(f_15_2,plain,
! [U_40] :
( preboolean(finite_subsets(U_40))
& diff_closed(finite_subsets(U_40))
& cup_closed(finite_subsets(U_40))
& ~ empty(finite_subsets(U_40)) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_44] : preboolean(finite_subsets(U_44))
& ! [U_43] : diff_closed(finite_subsets(U_43))
& ! [U_42] : cup_closed(finite_subsets(U_42))
& ! [U_41] : ~ empty(finite_subsets(U_41)) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
~ empty(finite_subsets(U_41)),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
cup_closed(finite_subsets(U_42)),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
diff_closed(finite_subsets(U_43)),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_7,plain,
preboolean(finite_subsets(U_44)),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_16_2,plain,
? [U_45] :
( finite(U_45)
& ~ empty(U_45) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( finite(sK5)
& ~ empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_45,sK5)],[f_16_2]) ).
cnf(f_16_4,plain,
~ empty(sK5),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
finite(sK5),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_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_17_2,plain,
? [U_46] :
( preboolean(U_46)
& diff_closed(U_46)
& cap_closed(U_46)
& cup_closed(U_46)
& ~ empty(U_46) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( preboolean(sK6)
& diff_closed(sK6)
& cap_closed(sK6)
& cup_closed(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_46,sK6)],[f_17_2]) ).
cnf(f_17_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
cup_closed(sK6),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
cap_closed(sK6),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_7,plain,
diff_closed(sK6),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_8,plain,
preboolean(sK6),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_18_2,plain,
! [U_48] :
( ? [U_47] :
( ~ empty(U_47)
& element(U_47,powerset(U_48)) )
| empty(U_48) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_48] :
( ( ~ empty(sK7(U_48))
& element(sK7(U_48),powerset(U_48)) )
| empty(U_48) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_47,sK7(U_48))],[f_18_2]) ).
cnf(f_18_4,plain,
( element(sK7(U_48),powerset(U_48))
| empty(U_48) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( ~ empty(sK7(U_48))
| empty(U_48) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_19_2,plain,
? [U_49] : empty(U_49),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_49,sK8)],[f_19_2]) ).
cnf(f_19_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_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_20_2,plain,
! [U_51] :
? [U_50] :
( finite(U_50)
& natural(U_50)
& ordinal(U_50)
& epsilon_connected(U_50)
& epsilon_transitive(U_50)
& one_to_one(U_50)
& function(U_50)
& relation(U_50)
& empty(U_50)
& element(U_50,powerset(U_51)) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_51] :
( finite(sK9(U_51))
& natural(sK9(U_51))
& ordinal(sK9(U_51))
& epsilon_connected(sK9(U_51))
& epsilon_transitive(sK9(U_51))
& one_to_one(sK9(U_51))
& function(sK9(U_51))
& relation(sK9(U_51))
& empty(sK9(U_51))
& element(sK9(U_51),powerset(U_51)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_50,sK9(U_51))],[f_20_2]) ).
cnf(f_20_4,plain,
element(sK9(U_51),powerset(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
empty(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
relation(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
function(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_8,plain,
one_to_one(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_9,plain,
epsilon_transitive(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_10,plain,
epsilon_connected(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_11,plain,
ordinal(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_12,plain,
natural(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_13,plain,
finite(sK9(U_51)),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_21_2,plain,
! [U_53] :
? [U_52] :
( empty(U_52)
& element(U_52,powerset(U_53)) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_53] :
( empty(sK10(U_53))
& element(sK10(U_53),powerset(U_53)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_52,sK10(U_53))],[f_21_2]) ).
cnf(f_21_4,plain,
element(sK10(U_53),powerset(U_53)),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
empty(sK10(U_53)),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_22_2,plain,
? [U_54] : ~ empty(U_54),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
~ empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_54,sK11)],[f_22_2]) ).
cnf(f_22_4,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_23_2,plain,
! [U_56] :
( ? [U_55] :
( finite(U_55)
& ~ empty(U_55)
& element(U_55,powerset(U_56)) )
| empty(U_56) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_56] :
( ( finite(sK12(U_56))
& ~ empty(sK12(U_56))
& element(sK12(U_56),powerset(U_56)) )
| empty(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_55,sK12(U_56))],[f_23_2]) ).
cnf(f_23_4,plain,
( element(sK12(U_56),powerset(U_56))
| empty(U_56) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( ~ empty(sK12(U_56))
| empty(U_56) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
( finite(sK12(U_56))
| empty(U_56) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc4_finset_1]) ).
fof(f_24_2,plain,
! [U_58] :
( ? [U_57] :
( finite(U_57)
& ~ empty(U_57)
& element(U_57,powerset(U_58)) )
| empty(U_58) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_58] :
( ( finite(sK13(U_58))
& ~ empty(sK13(U_58))
& element(sK13(U_58),powerset(U_58)) )
| empty(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_57,sK13(U_58))],[f_24_2]) ).
cnf(f_24_4,plain,
( element(sK13(U_58),powerset(U_58))
| empty(U_58) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( ~ empty(sK13(U_58))
| empty(U_58) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
( finite(sK13(U_58))
| empty(U_58) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_25_2,plain,
! [U_60,U_59] : subset(U_60,U_60),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_60] : subset(U_60,U_60),
inference(miniscope,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
subset(U_60,U_60),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] :
( finite(A)
| ~ finite(B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t13_finset_1]) ).
fof(f_26_2,plain,
! [U_62,U_61] :
( finite(U_62)
| ~ finite(U_61)
| ~ subset(U_62,U_61) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_62] :
( ! [U_61] :
( ~ finite(U_61)
| ~ subset(U_62,U_61) )
| finite(U_62) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ finite(U_61)
| ~ subset(U_62,U_61)
| finite(U_62) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_27_2,plain,
! [U_64,U_63] :
( element(U_64,U_63)
| ~ in(U_64,U_63) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( element(U_64,U_63)
| ~ in(U_64,U_63) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A] : subset(finite_subsets(A),powerset(A)),
inference(fof_nnf,[status(thm)],[t26_finsub_1]) ).
fof(f_28_2,plain,
! [U_65] : subset(finite_subsets(U_65),powerset(U_65)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
subset(finite_subsets(U_65),powerset(U_65)),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,negated_conjecture,
~ ! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
inference(negate,[status(cth)],[t27_finsub_1]) ).
fof(f_29_2,negated_conjecture,
? [A] :
( finite_subsets(A) != powerset(A)
& finite(A) ),
inference(fof_nnf,[status(thm)],[f_29_1]) ).
fof(f_29_3,negated_conjecture,
? [U_66] :
( finite_subsets(U_66) != powerset(U_66)
& finite(U_66) ),
inference(variable_rename,[status(thm)],[f_29_2]) ).
fof(f_29_4,negated_conjecture,
( finite_subsets(sK14) != powerset(sK14)
& finite(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_66,sK14)],[f_29_3]) ).
fof(f_29_5,negated_conjecture,
( finite_subsets(sK14) != powerset(sK14)
& finite(sK14) ),
inference(definitional_conversion,[status(esa)],[f_29_4]) ).
cnf(f_29_6,negated_conjecture,
finite(sK14),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_7,negated_conjecture,
finite_subsets(sK14) != powerset(sK14),
inference(clausify,[status(thm)],[f_29_5]) ).
fof(f_30_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_30_2,plain,
! [U_68,U_67] :
( in(U_68,U_67)
| empty(U_67)
| ~ element(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( in(U_68,U_67)
| empty(U_67)
| ~ element(U_68,U_67) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_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_31_2,plain,
! [U_70,U_69] :
( ( element(U_70,powerset(U_69))
| ~ subset(U_70,U_69) )
& ( subset(U_70,U_69)
| ~ element(U_70,powerset(U_69)) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_74,U_72] :
( element(U_74,powerset(U_72))
| ~ subset(U_74,U_72) )
& ! [U_73,U_71] :
( subset(U_73,U_71)
| ~ element(U_73,powerset(U_71)) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( subset(U_73,U_71)
| ~ element(U_73,powerset(U_71)) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( element(U_74,powerset(U_72))
| ~ subset(U_74,U_72) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_32_2,plain,
! [U_77,U_76,U_75] :
( element(U_77,U_75)
| ~ element(U_76,powerset(U_75))
| ~ in(U_77,U_76) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( element(U_77,U_75)
| ~ element(U_76,powerset(U_75))
| ~ in(U_77,U_76) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_33_2,plain,
! [U_80,U_79,U_78] :
( ~ empty(U_78)
| ~ element(U_79,powerset(U_78))
| ~ in(U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_80,U_79] :
( ! [U_78] :
( ~ empty(U_78)
| ~ element(U_79,powerset(U_78)) )
| ~ in(U_80,U_79) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( ~ empty(U_78)
| ~ element(U_79,powerset(U_78))
| ~ in(U_80,U_79) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_34_2,plain,
! [U_81] :
( U_81 = empty_set
| ~ empty(U_81) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( U_81 = empty_set
| ~ empty(U_81) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_35_2,plain,
! [U_83,U_82] :
( ~ empty(U_82)
| ~ in(U_83,U_82) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ empty(U_82)
| ~ in(U_83,U_82) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_85,U_84] :
( ~ empty(U_84)
| U_85 = U_84
| ~ empty(U_85) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_85] :
( ! [U_84] :
( ~ empty(U_84)
| U_85 = U_84 )
| ~ empty(U_85) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_84)
| U_85 = U_84
| ~ empty(U_85) ),
inference(clausify,[status(thm)],[f_36_3]) ).
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,
( finite_subsets(Eq_x_0) = finite_subsets(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK3(Eq_x_0,Eq_x_1) = 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_9,axiom,
( sK4(Eq_x_0) = sK4(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,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( preboolean(Eq_y_0)
| ~ preboolean(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( cup_closed(Eq_y_0)
| ~ cup_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( diff_closed(Eq_y_0)
| ~ diff_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,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_22,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_23,axiom,
( cap_closed(Eq_y_0)
| ~ cap_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,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_27,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( natural(Eq_y_0)
| ~ natural(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 : SEU114+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/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 : n016.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 23:24:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 8.36/8.62 % SZS status Theorem for theBenchmark
% 8.36/8.62 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------