%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU170+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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:20 AM UTC 2026
% Result : Theorem 226.66s 226.92s
% Output : Proof 230.28s
% 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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
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_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
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(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(l3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_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(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_xboole_0,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t43_subset_1,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_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(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,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_2_2,plain,
! [U_5,U_4] :
( ( subset(U_5,U_4)
| ? [U_3] :
( ~ in(U_3,U_4)
& in(U_3,U_5) ) )
& ( ! [U_2] :
( in(U_2,U_4)
| ~ in(U_2,U_5) )
| ~ subset(U_5,U_4) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_9,U_7] :
( subset(U_9,U_7)
| ? [U_3] :
( ~ in(U_3,U_7)
& in(U_3,U_9) ) )
& ! [U_8,U_6] :
( ! [U_2] :
( in(U_2,U_6)
| ~ in(U_2,U_8) )
| ~ subset(U_8,U_6) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_9,U_7] :
( subset(U_9,U_7)
| ( ~ in(sK1(U_9,U_7),U_7)
& in(sK1(U_9,U_7),U_9) ) )
& ! [U_8,U_6] :
( ! [U_2] :
( in(U_2,U_6)
| ~ in(U_2,U_8) )
| ~ subset(U_8,U_6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_9,U_7))],[f_2_3]) ).
fof(f_2_5,plain,
( ! [U_9,U_7] :
( ~ in(sK1(U_9,U_7),U_7)
| ~ sP0(U_9,U_7) )
& ! [U_9,U_7] :
( in(sK1(U_9,U_7),U_9)
| ~ sP0(U_9,U_7) )
& ! [U_9,U_7] :
( subset(U_9,U_7)
| sP0(U_9,U_7) )
& ! [U_8,U_2,U_6] :
( in(U_2,U_6)
| ~ in(U_2,U_8)
| ~ subset(U_8,U_6) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_2_4]) ).
cnf(f_2_6,plain,
( in(U_2,U_6)
| ~ in(U_2,U_8)
| ~ subset(U_8,U_6) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_7,plain,
( subset(U_9,U_7)
| sP0(U_9,U_7) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_8,plain,
( in(sK1(U_9,U_7),U_9)
| ~ sP0(U_9,U_7) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_9,plain,
( ~ in(sK1(U_9,U_7),U_7)
| ~ sP0(U_9,U_7) ),
inference(clausify,[status(thm)],[f_2_5]) ).
fof(f_3_1,plain,
! [A,B,C] :
( ( C = set_difference(A,B)
| ? [D] :
( ( ~ in(D,C)
& ~ in(D,B)
& in(D,A) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| in(D,B)
| ~ in(D,A) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_3_2,plain,
! [U_14,U_13,U_12] :
( ( U_12 = set_difference(U_14,U_13)
| ? [U_11] :
( ( ~ in(U_11,U_12)
& ~ in(U_11,U_13)
& in(U_11,U_14) )
| ( ( in(U_11,U_13)
| ~ in(U_11,U_14) )
& in(U_11,U_12) ) ) )
& ( ! [U_10] :
( ( in(U_10,U_12)
| in(U_10,U_13)
| ~ in(U_10,U_14) )
& ( ( ~ in(U_10,U_13)
& in(U_10,U_14) )
| ~ in(U_10,U_12) ) )
| U_12 != set_difference(U_14,U_13) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_24,U_22,U_20] :
( U_20 = set_difference(U_24,U_22)
| ? [U_18] :
( ~ in(U_18,U_20)
& ~ in(U_18,U_22)
& in(U_18,U_24) )
| ? [U_17] :
( ( in(U_17,U_22)
| ~ in(U_17,U_24) )
& in(U_17,U_20) ) )
& ! [U_23,U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| in(U_16,U_21)
| ~ in(U_16,U_23) )
& ! [U_15] :
( ( ~ in(U_15,U_21)
& in(U_15,U_23) )
| ~ in(U_15,U_19) ) )
| U_19 != set_difference(U_23,U_21) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_24,U_22,U_20] :
( U_20 = set_difference(U_24,U_22)
| ? [U_18] :
( ~ in(U_18,U_20)
& ~ in(U_18,U_22)
& in(U_18,U_24) )
| ( ( in(sK2(U_24,U_22,U_20),U_22)
| ~ in(sK2(U_24,U_22,U_20),U_24) )
& in(sK2(U_24,U_22,U_20),U_20) ) )
& ! [U_23,U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| in(U_16,U_21)
| ~ in(U_16,U_23) )
& ! [U_15] :
( ( ~ in(U_15,U_21)
& in(U_15,U_23) )
| ~ in(U_15,U_19) ) )
| U_19 != set_difference(U_23,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_17,sK2(U_24,U_22,U_20))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_24,U_22,U_20] :
( U_20 = set_difference(U_24,U_22)
| ( ~ in(sK3(U_24,U_22,U_20),U_20)
& ~ in(sK3(U_24,U_22,U_20),U_22)
& in(sK3(U_24,U_22,U_20),U_24) )
| ( ( in(sK2(U_24,U_22,U_20),U_22)
| ~ in(sK2(U_24,U_22,U_20),U_24) )
& in(sK2(U_24,U_22,U_20),U_20) ) )
& ! [U_23,U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| in(U_16,U_21)
| ~ in(U_16,U_23) )
& ! [U_15] :
( ( ~ in(U_15,U_21)
& in(U_15,U_23) )
| ~ in(U_15,U_19) ) )
| U_19 != set_difference(U_23,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_18,sK3(U_24,U_22,U_20))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_20,U_24,U_22] :
( ~ in(sK3(U_24,U_22,U_20),U_20)
| ~ sP4(U_20,U_24,U_22) )
& ! [U_20,U_24,U_22] :
( ~ in(sK3(U_24,U_22,U_20),U_22)
| ~ sP4(U_20,U_24,U_22) )
& ! [U_20,U_24,U_22] :
( in(sK3(U_24,U_22,U_20),U_24)
| ~ sP4(U_20,U_24,U_22) )
& ! [U_20,U_24,U_22] :
( in(sK2(U_24,U_22,U_20),U_22)
| ~ in(sK2(U_24,U_22,U_20),U_24)
| ~ sP3(U_20,U_24,U_22) )
& ! [U_20,U_24,U_22] :
( in(sK2(U_24,U_22,U_20),U_20)
| ~ sP3(U_20,U_24,U_22) )
& ! [U_21,U_15,U_23] :
( ~ in(U_15,U_21)
| ~ sP1(U_21,U_15,U_23) )
& ! [U_21,U_15,U_23] :
( in(U_15,U_23)
| ~ sP1(U_21,U_15,U_23) )
& ! [U_21,U_19,U_16,U_15,U_23] :
( in(U_16,U_19)
| in(U_16,U_21)
| ~ in(U_16,U_23)
| ~ sP2(U_21,U_19,U_16,U_15,U_23) )
& ! [U_21,U_19,U_16,U_15,U_23] :
( sP1(U_21,U_15,U_23)
| ~ in(U_15,U_19)
| ~ sP2(U_21,U_19,U_16,U_15,U_23) )
& ! [U_20,U_24,U_22] :
( U_20 = set_difference(U_24,U_22)
| sP4(U_20,U_24,U_22)
| sP3(U_20,U_24,U_22) )
& ! [U_21,U_19,U_16,U_15,U_23] :
( sP2(U_21,U_19,U_16,U_15,U_23)
| U_19 != set_difference(U_23,U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3,sP4])],[f_3_5]) ).
cnf(f_3_7,plain,
( sP2(U_21,U_19,U_16,U_15,U_23)
| U_19 != set_difference(U_23,U_21) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_8,plain,
( U_20 = set_difference(U_24,U_22)
| sP4(U_20,U_24,U_22)
| sP3(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_9,plain,
( sP1(U_21,U_15,U_23)
| ~ in(U_15,U_19)
| ~ sP2(U_21,U_19,U_16,U_15,U_23) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_10,plain,
( in(U_16,U_19)
| in(U_16,U_21)
| ~ in(U_16,U_23)
| ~ sP2(U_21,U_19,U_16,U_15,U_23) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_11,plain,
( in(U_15,U_23)
| ~ sP1(U_21,U_15,U_23) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_12,plain,
( ~ in(U_15,U_21)
| ~ sP1(U_21,U_15,U_23) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_13,plain,
( in(sK2(U_24,U_22,U_20),U_20)
| ~ sP3(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_14,plain,
( in(sK2(U_24,U_22,U_20),U_22)
| ~ in(sK2(U_24,U_22,U_20),U_24)
| ~ sP3(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_15,plain,
( in(sK3(U_24,U_22,U_20),U_24)
| ~ sP4(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_16,plain,
( ~ in(sK3(U_24,U_22,U_20),U_22)
| ~ sP4(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_17,plain,
( ~ in(sK3(U_24,U_22,U_20),U_20)
| ~ sP4(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_6]) ).
fof(f_4_1,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[d5_subset_1]) ).
fof(f_4_2,plain,
! [U_26,U_25] :
( subset_complement(U_26,U_25) = set_difference(U_26,U_25)
| ~ element(U_25,powerset(U_26)) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_26,U_25] :
( subset_complement(U_26,U_25) = set_difference(U_26,U_25)
| ~ element(U_25,powerset(U_26)) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( subset_complement(U_26,U_25) = set_difference(U_26,U_25)
| ~ element(U_25,powerset(U_26)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_5_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
$true,
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_6_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
$true,
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_7_2,plain,
! [U_28,U_27] :
( element(subset_complement(U_28,U_27),powerset(U_28))
| ~ element(U_27,powerset(U_28)) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_28,U_27] :
( element(subset_complement(U_28,U_27),powerset(U_28))
| ~ element(U_27,powerset(U_28)) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( element(subset_complement(U_28,U_27),powerset(U_28))
| ~ element(U_27,powerset(U_28)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_8_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
$true,
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_9_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
$true,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_10_2,plain,
! [U_30] :
? [U_29] : element(U_29,U_30),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_30] : element(sK4(U_30),U_30),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_29,sK4(U_30))],[f_10_2]) ).
fof(f_10_4,plain,
! [U_30] : element(sK4(U_30),U_30),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
element(sK4(U_30),U_30),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_11_2,plain,
! [U_31] : ~ empty(powerset(U_31)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_31] : ~ empty(powerset(U_31)),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
~ empty(powerset(U_31)),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_12_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1]) ).
fof(f_13_2,plain,
! [U_33,U_32] :
( subset_complement(U_33,subset_complement(U_33,U_32)) = U_32
| ~ element(U_32,powerset(U_33)) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_33,U_32] :
( subset_complement(U_33,subset_complement(U_33,U_32)) = U_32
| ~ element(U_32,powerset(U_33)) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( subset_complement(U_33,subset_complement(U_33,U_32)) = U_32
| ~ element(U_32,powerset(U_33)) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B] :
( ! [C] :
( in(C,A)
| ~ in(C,B) )
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[l3_subset_1]) ).
fof(f_14_2,plain,
! [U_36,U_35] :
( ! [U_34] :
( in(U_34,U_36)
| ~ in(U_34,U_35) )
| ~ element(U_35,powerset(U_36)) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_34,U_35,U_36] :
( in(U_34,U_36)
| ~ in(U_34,U_35)
| ~ element(U_35,powerset(U_36)) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( in(U_34,U_36)
| ~ in(U_34,U_35)
| ~ element(U_35,powerset(U_36)) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_15_2,plain,
! [U_38] :
( ? [U_37] :
( ~ empty(U_37)
& element(U_37,powerset(U_38)) )
| empty(U_38) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_38] :
( ( ~ empty(sK5(U_38))
& element(sK5(U_38),powerset(U_38)) )
| empty(U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_37,sK5(U_38))],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_38] :
( ~ empty(sK5(U_38))
| ~ sP5(U_38) )
& ! [U_38] :
( element(sK5(U_38),powerset(U_38))
| ~ sP5(U_38) )
& ! [U_38] :
( sP5(U_38)
| empty(U_38) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_15_3]) ).
cnf(f_15_5,plain,
( sP5(U_38)
| empty(U_38) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( element(sK5(U_38),powerset(U_38))
| ~ sP5(U_38) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( ~ empty(sK5(U_38))
| ~ sP5(U_38) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_16_2,plain,
? [U_39] : empty(U_39),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_39,sK6)],[f_16_2]) ).
fof(f_16_4,plain,
empty(sK6),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_17_2,plain,
! [U_41] :
? [U_40] :
( empty(U_40)
& element(U_40,powerset(U_41)) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_41] :
( empty(sK7(U_41))
& element(sK7(U_41),powerset(U_41)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_40,sK7(U_41))],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_41] : empty(sK7(U_41))
& ! [U_41] : element(sK7(U_41),powerset(U_41)) ),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
element(sK7(U_41),powerset(U_41)),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
empty(sK7(U_41)),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_18_2,plain,
? [U_42] : ~ empty(U_42),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_42,sK8)],[f_18_2]) ).
fof(f_18_4,plain,
~ empty(sK8),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_19_2,plain,
! [U_44,U_43] : subset(U_44,U_44),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_44] : subset(U_44,U_44),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_44] : subset(U_44,U_44),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
subset(U_44,U_44),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_20_2,plain,
! [U_46,U_45] :
( disjoint(U_45,U_46)
| ~ disjoint(U_46,U_45) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_45,U_46] :
( disjoint(U_45,U_46)
| ~ disjoint(U_46,U_45) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( disjoint(U_45,U_46)
| ~ disjoint(U_46,U_45) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_21_2,plain,
! [U_47] : set_difference(U_47,empty_set) = U_47,
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_47] : set_difference(U_47,empty_set) = U_47,
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
set_difference(U_47,empty_set) = U_47,
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0]) ).
fof(f_22_2,plain,
! [U_51,U_50] :
( ( ~ disjoint(U_51,U_50)
| ! [U_49] :
( ~ in(U_49,U_50)
| ~ in(U_49,U_51) ) )
& ( ? [U_48] :
( in(U_48,U_50)
& in(U_48,U_51) )
| disjoint(U_51,U_50) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_55,U_53] :
( ~ disjoint(U_55,U_53)
| ! [U_49] :
( ~ in(U_49,U_53)
| ~ in(U_49,U_55) ) )
& ! [U_54,U_52] :
( ? [U_48] :
( in(U_48,U_52)
& in(U_48,U_54) )
| disjoint(U_54,U_52) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_55,U_53] :
( ~ disjoint(U_55,U_53)
| ! [U_49] :
( ~ in(U_49,U_53)
| ~ in(U_49,U_55) ) )
& ! [U_54,U_52] :
( ( in(sK9(U_54,U_52),U_52)
& in(sK9(U_54,U_52),U_54) )
| disjoint(U_54,U_52) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_48,sK9(U_54,U_52))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_52,U_54] :
( in(sK9(U_54,U_52),U_52)
| ~ sP6(U_52,U_54) )
& ! [U_52,U_54] :
( in(sK9(U_54,U_52),U_54)
| ~ sP6(U_52,U_54) )
& ! [U_49,U_53,U_55] :
( ~ disjoint(U_55,U_53)
| ~ in(U_49,U_53)
| ~ in(U_49,U_55) )
& ! [U_52,U_54] :
( sP6(U_52,U_54)
| disjoint(U_54,U_52) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_22_4]) ).
cnf(f_22_6,plain,
( sP6(U_52,U_54)
| disjoint(U_54,U_52) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,plain,
( ~ disjoint(U_55,U_53)
| ~ in(U_49,U_53)
| ~ in(U_49,U_55) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,plain,
( in(sK9(U_54,U_52),U_54)
| ~ sP6(U_52,U_54) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_9,plain,
( in(sK9(U_54,U_52),U_52)
| ~ sP6(U_52,U_54) ),
inference(clausify,[status(thm)],[f_22_5]) ).
fof(f_23_1,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
inference(negate,[status(cth)],[t43_subset_1]) ).
fof(f_23_2,negated_conjecture,
? [A,B] :
( ? [C] :
( ( ( ~ disjoint(B,C)
& subset(B,subset_complement(A,C)) )
| ( ~ subset(B,subset_complement(A,C))
& disjoint(B,C) ) )
& element(C,powerset(A)) )
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[f_23_1]) ).
fof(f_23_3,negated_conjecture,
? [U_58,U_57] :
( ? [U_56] :
( ( ( ~ disjoint(U_57,U_56)
& subset(U_57,subset_complement(U_58,U_56)) )
| ( ~ subset(U_57,subset_complement(U_58,U_56))
& disjoint(U_57,U_56) ) )
& element(U_56,powerset(U_58)) )
& element(U_57,powerset(U_58)) ),
inference(variable_rename,[status(thm)],[f_23_2]) ).
fof(f_23_4,negated_conjecture,
? [U_57] :
( ? [U_56] :
( ( ( ~ disjoint(U_57,U_56)
& subset(U_57,subset_complement(sK10,U_56)) )
| ( ~ subset(U_57,subset_complement(sK10,U_56))
& disjoint(U_57,U_56) ) )
& element(U_56,powerset(sK10)) )
& element(U_57,powerset(sK10)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_58,sK10)],[f_23_3]) ).
fof(f_23_5,negated_conjecture,
( ? [U_56] :
( ( ( ~ disjoint(sK11,U_56)
& subset(sK11,subset_complement(sK10,U_56)) )
| ( ~ subset(sK11,subset_complement(sK10,U_56))
& disjoint(sK11,U_56) ) )
& element(U_56,powerset(sK10)) )
& element(sK11,powerset(sK10)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_57,sK11)],[f_23_4]) ).
fof(f_23_6,negated_conjecture,
( ( ( ~ disjoint(sK11,sK12)
& subset(sK11,subset_complement(sK10,sK12)) )
| ( ~ subset(sK11,subset_complement(sK10,sK12))
& disjoint(sK11,sK12) ) )
& element(sK12,powerset(sK10))
& element(sK11,powerset(sK10)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_56,sK12)],[f_23_5]) ).
fof(f_23_7,negated_conjecture,
( ( ~ disjoint(sK11,sK12)
| ~ sP8 )
& ( subset(sK11,subset_complement(sK10,sK12))
| ~ sP8 )
& ( ~ subset(sK11,subset_complement(sK10,sK12))
| ~ sP7 )
& ( disjoint(sK11,sK12)
| ~ sP7 )
& ( sP8
| sP7 )
& element(sK12,powerset(sK10))
& element(sK11,powerset(sK10)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7,sP8])],[f_23_6]) ).
cnf(f_23_8,negated_conjecture,
element(sK11,powerset(sK10)),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_9,negated_conjecture,
element(sK12,powerset(sK10)),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_10,negated_conjecture,
( sP8
| sP7 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_11,negated_conjecture,
( disjoint(sK11,sK12)
| ~ sP7 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_12,negated_conjecture,
( ~ subset(sK11,subset_complement(sK10,sK12))
| ~ sP7 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_13,negated_conjecture,
( subset(sK11,subset_complement(sK10,sK12))
| ~ sP8 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_14,negated_conjecture,
( ~ disjoint(sK11,sK12)
| ~ sP8 ),
inference(clausify,[status(thm)],[f_23_7]) ).
fof(f_24_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_24_2,plain,
! [U_59] : set_difference(empty_set,U_59) = empty_set,
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_59] : set_difference(empty_set,U_59) = empty_set,
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
set_difference(empty_set,U_59) = empty_set,
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_25_2,plain,
! [U_60] :
( U_60 = empty_set
| ~ empty(U_60) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_60] :
( U_60 = empty_set
| ~ empty(U_60) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( U_60 = empty_set
| ~ empty(U_60) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_26_2,plain,
! [U_62,U_61] :
( ~ empty(U_61)
| ~ in(U_62,U_61) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_61,U_62] :
( ~ empty(U_61)
| ~ in(U_62,U_61) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ empty(U_61)
| ~ in(U_62,U_61) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_27_2,plain,
! [U_64,U_63] :
( ~ empty(U_63)
| U_64 = U_63
| ~ empty(U_64) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_64] :
( ! [U_63] :
( ~ empty(U_63)
| U_64 = U_63 )
| ~ empty(U_64) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_63,U_64] :
( ~ empty(U_63)
| U_64 = U_63
| ~ empty(U_64) ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
( ~ empty(U_63)
| U_64 = U_63
| ~ empty(U_64) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_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,
( 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_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( subset_complement(Eq_x_0,Eq_x_1) = subset_complement(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,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_8,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_9,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(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_10,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,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_16,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_17,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(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,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(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
% 0.00/0.03 % Problem : SEU170+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 : n020.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 23:26:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 226.66/226.92 % SZS status Theorem for theBenchmark
% 226.66/226.92 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------