%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET906+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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:57:46 AM UTC 2026
% Result : Theorem 4.67s 5.01s
% Output : Proof 4.84s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t47_zfmisc_1,conjecture,
! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
file('theBenchmark.p',t47_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_2_2,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : set_union2(U_5,U_4) = set_union2(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
set_union2(U_5,U_4) = set_union2(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_4_2,plain,
! [U_10,U_9,U_8] :
( ( U_8 = unordered_pair(U_10,U_9)
| ? [U_7] :
( ( ~ in(U_7,U_8)
& ( U_7 = U_9
| U_7 = U_10 ) )
| ( U_7 != U_9
& U_7 != U_10
& in(U_7,U_8) ) ) )
& ( ! [U_6] :
( ( in(U_6,U_8)
| ( U_6 != U_9
& U_6 != U_10 ) )
& ( U_6 = U_9
| U_6 = U_10
| ~ in(U_6,U_8) ) )
| U_8 != unordered_pair(U_10,U_9) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ? [U_14] :
( ~ in(U_14,U_16)
& ( U_14 = U_18
| U_14 = U_20 ) )
| ? [U_13] :
( U_13 != U_18
& U_13 != U_20
& in(U_13,U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ? [U_14] :
( ~ in(U_14,U_16)
& ( U_14 = U_18
| U_14 = U_20 ) )
| ( sK1(U_20,U_18,U_16) != U_18
& sK1(U_20,U_18,U_16) != U_20
& in(sK1(U_20,U_18,U_16),U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_13,sK1(U_20,U_18,U_16))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ( ~ in(sK2(U_20,U_18,U_16),U_16)
& ( sK2(U_20,U_18,U_16) = U_18
| sK2(U_20,U_18,U_16) = U_20 ) )
| ( sK1(U_20,U_18,U_16) != U_18
& sK1(U_20,U_18,U_16) != U_20
& in(sK1(U_20,U_18,U_16),U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_20,U_18,U_16))],[f_4_4]) ).
cnf(f_4_6,plain,
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15)
| U_15 != unordered_pair(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( U_12 != U_19
| in(U_12,U_15)
| U_15 != unordered_pair(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( U_12 != U_17
| in(U_12,U_15)
| U_15 != unordered_pair(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( sK2(U_20,U_18,U_16) = U_18
| sK2(U_20,U_18,U_16) = U_20
| in(sK1(U_20,U_18,U_16),U_16)
| U_16 = unordered_pair(U_20,U_18) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_10,plain,
( ~ in(sK2(U_20,U_18,U_16),U_16)
| in(sK1(U_20,U_18,U_16),U_16)
| U_16 = unordered_pair(U_20,U_18) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_11,plain,
( sK1(U_20,U_18,U_16) != U_20
| sK2(U_20,U_18,U_16) = U_18
| sK2(U_20,U_18,U_16) = U_20
| U_16 = unordered_pair(U_20,U_18) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_12,plain,
( sK1(U_20,U_18,U_16) != U_18
| sK2(U_20,U_18,U_16) = U_18
| sK2(U_20,U_18,U_16) = U_20
| U_16 = unordered_pair(U_20,U_18) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_13,plain,
( sK1(U_20,U_18,U_16) != U_20
| ~ in(sK2(U_20,U_18,U_16),U_16)
| U_16 = unordered_pair(U_20,U_18) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_14,plain,
( sK1(U_20,U_18,U_16) != U_18
| ~ in(sK2(U_20,U_18,U_16),U_16)
| U_16 = unordered_pair(U_20,U_18) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_5_2,plain,
! [U_25,U_24,U_23] :
( ( U_23 = set_union2(U_25,U_24)
| ? [U_22] :
( ( ~ in(U_22,U_23)
& ( in(U_22,U_24)
| in(U_22,U_25) ) )
| ( ~ in(U_22,U_24)
& ~ in(U_22,U_25)
& in(U_22,U_23) ) ) )
& ( ! [U_21] :
( ( in(U_21,U_23)
| ( ~ in(U_21,U_24)
& ~ in(U_21,U_25) ) )
& ( in(U_21,U_24)
| in(U_21,U_25)
| ~ in(U_21,U_23) ) )
| U_23 != set_union2(U_25,U_24) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_union2(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_31)
& ( in(U_29,U_33)
| in(U_29,U_35) ) )
| ? [U_28] :
( ~ in(U_28,U_33)
& ~ in(U_28,U_35)
& in(U_28,U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ( ~ in(U_27,U_32)
& ~ in(U_27,U_34) ) )
& ! [U_26] :
( in(U_26,U_32)
| in(U_26,U_34)
| ~ in(U_26,U_30) ) )
| U_30 != set_union2(U_34,U_32) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_union2(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_31)
& ( in(U_29,U_33)
| in(U_29,U_35) ) )
| ( ~ in(sK3(U_35,U_33,U_31),U_33)
& ~ in(sK3(U_35,U_33,U_31),U_35)
& in(sK3(U_35,U_33,U_31),U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ( ~ in(U_27,U_32)
& ~ in(U_27,U_34) ) )
& ! [U_26] :
( in(U_26,U_32)
| in(U_26,U_34)
| ~ in(U_26,U_30) ) )
| U_30 != set_union2(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_28,sK3(U_35,U_33,U_31))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_union2(U_35,U_33)
| ( ~ in(sK4(U_35,U_33,U_31),U_31)
& ( in(sK4(U_35,U_33,U_31),U_33)
| in(sK4(U_35,U_33,U_31),U_35) ) )
| ( ~ in(sK3(U_35,U_33,U_31),U_33)
& ~ in(sK3(U_35,U_33,U_31),U_35)
& in(sK3(U_35,U_33,U_31),U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ( ~ in(U_27,U_32)
& ~ in(U_27,U_34) ) )
& ! [U_26] :
( in(U_26,U_32)
| in(U_26,U_34)
| ~ in(U_26,U_30) ) )
| U_30 != set_union2(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_29,sK4(U_35,U_33,U_31))],[f_5_4]) ).
cnf(f_5_6,plain,
( in(U_26,U_32)
| in(U_26,U_34)
| ~ in(U_26,U_30)
| U_30 != set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( ~ in(U_27,U_34)
| in(U_27,U_30)
| U_30 != set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( ~ in(U_27,U_32)
| in(U_27,U_30)
| U_30 != set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( in(sK4(U_35,U_33,U_31),U_33)
| in(sK4(U_35,U_33,U_31),U_35)
| in(sK3(U_35,U_33,U_31),U_31)
| U_31 = set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_10,plain,
( ~ in(sK4(U_35,U_33,U_31),U_31)
| in(sK3(U_35,U_33,U_31),U_31)
| U_31 = set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_11,plain,
( ~ in(sK3(U_35,U_33,U_31),U_35)
| in(sK4(U_35,U_33,U_31),U_33)
| in(sK4(U_35,U_33,U_31),U_35)
| U_31 = set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_12,plain,
( ~ in(sK3(U_35,U_33,U_31),U_33)
| in(sK4(U_35,U_33,U_31),U_33)
| in(sK4(U_35,U_33,U_31),U_35)
| U_31 = set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_13,plain,
( ~ in(sK3(U_35,U_33,U_31),U_35)
| ~ in(sK4(U_35,U_33,U_31),U_31)
| U_31 = set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_14,plain,
( ~ in(sK3(U_35,U_33,U_31),U_33)
| ~ in(sK4(U_35,U_33,U_31),U_31)
| U_31 = set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_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_6_2,plain,
! [U_39,U_38] :
( ( subset(U_39,U_38)
| ? [U_37] :
( ~ in(U_37,U_38)
& in(U_37,U_39) ) )
& ( ! [U_36] :
( in(U_36,U_38)
| ~ in(U_36,U_39) )
| ~ subset(U_39,U_38) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_43,U_41] :
( subset(U_43,U_41)
| ? [U_37] :
( ~ in(U_37,U_41)
& in(U_37,U_43) ) )
& ! [U_42,U_40] :
( ! [U_36] :
( in(U_36,U_40)
| ~ in(U_36,U_42) )
| ~ subset(U_42,U_40) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_43,U_41] :
( subset(U_43,U_41)
| ( ~ in(sK5(U_43,U_41),U_41)
& in(sK5(U_43,U_41),U_43) ) )
& ! [U_42,U_40] :
( ! [U_36] :
( in(U_36,U_40)
| ~ in(U_36,U_42) )
| ~ subset(U_42,U_40) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_37,sK5(U_43,U_41))],[f_6_3]) ).
cnf(f_6_5,plain,
( in(U_36,U_40)
| ~ in(U_36,U_42)
| ~ subset(U_42,U_40) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( in(sK5(U_43,U_41),U_43)
| subset(U_43,U_41) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ~ in(sK5(U_43,U_41),U_41)
| subset(U_43,U_41) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_7_2,plain,
! [U_45,U_44] :
( ~ empty(set_union2(U_45,U_44))
| empty(U_45) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_45] :
( ! [U_44] : ~ empty(set_union2(U_45,U_44))
| empty(U_45) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( ~ empty(set_union2(U_45,U_44))
| empty(U_45) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_8_2,plain,
! [U_47,U_46] :
( ~ empty(set_union2(U_46,U_47))
| empty(U_47) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_47] :
( ! [U_46] : ~ empty(set_union2(U_46,U_47))
| empty(U_47) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( ~ empty(set_union2(U_46,U_47))
| empty(U_47) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_9_2,plain,
! [U_49,U_48] : set_union2(U_49,U_49) = U_49,
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_49] : set_union2(U_49,U_49) = U_49,
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
set_union2(U_49,U_49) = U_49,
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_10_2,plain,
? [U_50] : empty(U_50),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_50,sK6)],[f_10_2]) ).
cnf(f_10_4,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_11_2,plain,
? [U_51] : ~ empty(U_51),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_51,sK7)],[f_11_2]) ).
cnf(f_11_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_12_2,plain,
! [U_53,U_52] : subset(U_53,U_53),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_53] : subset(U_53,U_53),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
subset(U_53,U_53),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,negated_conjecture,
~ ! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
inference(negate,[status(cth)],[t47_zfmisc_1]) ).
fof(f_13_2,negated_conjecture,
? [A,B,C] :
( ~ in(A,C)
& subset(set_union2(unordered_pair(A,B),C),C) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_56,U_55,U_54] :
( ~ in(U_56,U_54)
& subset(set_union2(unordered_pair(U_56,U_55),U_54),U_54) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_55,U_54] :
( ~ in(sK8,U_54)
& subset(set_union2(unordered_pair(sK8,U_55),U_54),U_54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_56,sK8)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
? [U_54] :
( ~ in(sK8,U_54)
& subset(set_union2(unordered_pair(sK8,sK9),U_54),U_54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_55,sK9)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ~ in(sK8,sK10)
& subset(set_union2(unordered_pair(sK8,sK9),sK10),sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_54,sK10)],[f_13_5]) ).
fof(f_13_7,negated_conjecture,
( ~ in(sK8,sK10)
& subset(set_union2(unordered_pair(sK8,sK9),sK10),sK10) ),
inference(definitional_conversion,[status(esa)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
subset(set_union2(unordered_pair(sK8,sK9),sK10),sK10),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,negated_conjecture,
~ in(sK8,sK10),
inference(clausify,[status(thm)],[f_13_7]) ).
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,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(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,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,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_9,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(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,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET906+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
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 23:02:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 4.67/5.01 % SZS status Theorem for theBenchmark
% 4.67/5.01 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------