%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET950+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 : n015.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 08:57:51 AM UTC 2026
% Result : Theorem 30.24s 35.56s
% Output : Proof 30.24s
% 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(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
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(t103_zfmisc_1,conjecture,
! [A,B,C,D] :
~ ( ! [E,F] :
~ ( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
& in(D,A)
& subset(A,cartesian_product2(B,C)) ),
file('theBenchmark.p',t103_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]) ).
fof(f_1_3,plain,
! [U_0,U_1] :
( ~ 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] : 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]) ).
fof(f_2_3,plain,
! [U_2,U_3] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B,C] :
( ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) )
| ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) ) )
& ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_zfmisc_1]) ).
fof(f_3_2,plain,
! [U_16,U_15,U_14] :
( ( U_14 = cartesian_product2(U_16,U_15)
| ? [U_13] :
( ( ~ in(U_13,U_14)
& ? [U_12,U_11] :
( U_13 = ordered_pair(U_12,U_11)
& in(U_11,U_15)
& in(U_12,U_16) ) )
| ( ! [U_10,U_9] :
( U_13 != ordered_pair(U_10,U_9)
| ~ in(U_9,U_15)
| ~ in(U_10,U_16) )
& in(U_13,U_14) ) ) )
& ( ! [U_8] :
( ( in(U_8,U_14)
| ! [U_7,U_6] :
( U_8 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_15)
| ~ in(U_7,U_16) ) )
& ( ? [U_5,U_4] :
( U_8 = ordered_pair(U_5,U_4)
& in(U_4,U_15)
& in(U_5,U_16) )
| ~ in(U_8,U_14) ) )
| U_14 != cartesian_product2(U_16,U_15) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ? [U_12] :
( ? [U_11] :
( U_20 = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ? [U_19] :
( ! [U_10] :
( ! [U_9] :
( U_19 != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(U_19,U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ? [U_5] :
( ? [U_4] :
( U_17 = ordered_pair(U_5,U_4)
& in(U_4,U_23) )
& in(U_5,U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ? [U_12] :
( ? [U_11] :
( U_20 = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ? [U_19] :
( ! [U_10] :
( ! [U_9] :
( U_19 != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(U_19,U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( ? [U_4] :
( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),U_4)
& in(U_4,U_23) )
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_25,U_23,U_21,U_17))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ? [U_12] :
( ? [U_11] :
( U_20 = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ? [U_19] :
( ! [U_10] :
( ! [U_9] :
( U_19 != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(U_19,U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2(U_25,U_23,U_21,U_17))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ? [U_12] :
( ? [U_11] :
( U_20 = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ( ! [U_10] :
( ! [U_9] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(sK3(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3(U_26,U_24,U_22))],[f_3_5]) ).
fof(f_3_7,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ( ~ in(sK4(U_26,U_24,U_22),U_22)
& ? [U_12] :
( ? [U_11] :
( sK4(U_26,U_24,U_22) = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ( ! [U_10] :
( ! [U_9] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(sK3(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4(U_26,U_24,U_22))],[f_3_6]) ).
fof(f_3_8,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ( ~ in(sK4(U_26,U_24,U_22),U_22)
& ? [U_11] :
( sK4(U_26,U_24,U_22) = ordered_pair(sK5(U_26,U_24,U_22),U_11)
& in(U_11,U_24) )
& in(sK5(U_26,U_24,U_22),U_26) )
| ( ! [U_10] :
( ! [U_9] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(sK3(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_12,sK5(U_26,U_24,U_22))],[f_3_7]) ).
fof(f_3_9,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ( ~ in(sK4(U_26,U_24,U_22),U_22)
& sK4(U_26,U_24,U_22) = ordered_pair(sK5(U_26,U_24,U_22),sK6(U_26,U_24,U_22))
& in(sK6(U_26,U_24,U_22),U_24)
& in(sK5(U_26,U_24,U_22),U_26) )
| ( ! [U_10] :
( ! [U_9] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(sK3(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_11,sK6(U_26,U_24,U_22))],[f_3_8]) ).
fof(f_3_10,plain,
( ! [U_22,U_24,U_26] :
( ~ in(sK4(U_26,U_24,U_22),U_22)
| ~ sP3(U_22,U_24,U_26) )
& ! [U_22,U_24,U_26] :
( sK4(U_26,U_24,U_22) = ordered_pair(sK5(U_26,U_24,U_22),sK6(U_26,U_24,U_22))
| ~ sP3(U_22,U_24,U_26) )
& ! [U_22,U_24,U_26] :
( in(sK6(U_26,U_24,U_22),U_24)
| ~ sP3(U_22,U_24,U_26) )
& ! [U_22,U_24,U_26] :
( in(sK5(U_26,U_24,U_22),U_26)
| ~ sP3(U_22,U_24,U_26) )
& ! [U_9,U_10,U_22,U_24,U_26] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24)
| ~ in(U_10,U_26)
| ~ sP2(U_9,U_10,U_22,U_24,U_26) )
& ! [U_9,U_10,U_22,U_24,U_26] :
( in(sK3(U_26,U_24,U_22),U_22)
| ~ sP2(U_9,U_10,U_22,U_24,U_26) )
& ! [U_23,U_17,U_21,U_25] :
( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
| ~ sP0(U_23,U_17,U_21,U_25) )
& ! [U_23,U_17,U_21,U_25] :
( in(sK2(U_25,U_23,U_21,U_17),U_23)
| ~ sP0(U_23,U_17,U_21,U_25) )
& ! [U_23,U_17,U_21,U_25] :
( in(sK1(U_25,U_23,U_21,U_17),U_25)
| ~ sP0(U_23,U_17,U_21,U_25) )
& ! [U_23,U_6,U_7,U_17,U_18,U_21,U_25] :
( in(U_18,U_21)
| U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23)
| ~ in(U_7,U_25)
| ~ sP1(U_23,U_6,U_7,U_17,U_18,U_21,U_25) )
& ! [U_23,U_6,U_7,U_17,U_18,U_21,U_25] :
( sP0(U_23,U_17,U_21,U_25)
| ~ in(U_17,U_21)
| ~ sP1(U_23,U_6,U_7,U_17,U_18,U_21,U_25) )
& ! [U_9,U_10,U_22,U_24,U_26] :
( U_22 = cartesian_product2(U_26,U_24)
| sP3(U_22,U_24,U_26)
| sP2(U_9,U_10,U_22,U_24,U_26) )
& ! [U_23,U_6,U_7,U_17,U_18,U_21,U_25] :
( sP1(U_23,U_6,U_7,U_17,U_18,U_21,U_25)
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_3_9]) ).
cnf(f_3_11,plain,
( sP1(U_23,U_6,U_7,U_17,U_18,U_21,U_25)
| U_21 != cartesian_product2(U_25,U_23) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_12,plain,
( U_22 = cartesian_product2(U_26,U_24)
| sP3(U_22,U_24,U_26)
| sP2(U_9,U_10,U_22,U_24,U_26) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_13,plain,
( sP0(U_23,U_17,U_21,U_25)
| ~ in(U_17,U_21)
| ~ sP1(U_23,U_6,U_7,U_17,U_18,U_21,U_25) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_14,plain,
( in(U_18,U_21)
| U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23)
| ~ in(U_7,U_25)
| ~ sP1(U_23,U_6,U_7,U_17,U_18,U_21,U_25) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_15,plain,
( in(sK1(U_25,U_23,U_21,U_17),U_25)
| ~ sP0(U_23,U_17,U_21,U_25) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_16,plain,
( in(sK2(U_25,U_23,U_21,U_17),U_23)
| ~ sP0(U_23,U_17,U_21,U_25) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_17,plain,
( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
| ~ sP0(U_23,U_17,U_21,U_25) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_18,plain,
( in(sK3(U_26,U_24,U_22),U_22)
| ~ sP2(U_9,U_10,U_22,U_24,U_26) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_19,plain,
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24)
| ~ in(U_10,U_26)
| ~ sP2(U_9,U_10,U_22,U_24,U_26) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_20,plain,
( in(sK5(U_26,U_24,U_22),U_26)
| ~ sP3(U_22,U_24,U_26) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_21,plain,
( in(sK6(U_26,U_24,U_22),U_24)
| ~ sP3(U_22,U_24,U_26) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_22,plain,
( sK4(U_26,U_24,U_22) = ordered_pair(sK5(U_26,U_24,U_22),sK6(U_26,U_24,U_22))
| ~ sP3(U_22,U_24,U_26) ),
inference(clausify,[status(thm)],[f_3_10]) ).
cnf(f_3_23,plain,
( ~ in(sK4(U_26,U_24,U_22),U_22)
| ~ sP3(U_22,U_24,U_26) ),
inference(clausify,[status(thm)],[f_3_10]) ).
fof(f_4_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_4_2,plain,
! [U_30,U_29] :
( ( subset(U_30,U_29)
| ? [U_28] :
( ~ in(U_28,U_29)
& in(U_28,U_30) ) )
& ( ! [U_27] :
( in(U_27,U_29)
| ~ in(U_27,U_30) )
| ~ subset(U_30,U_29) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_34,U_32] :
( subset(U_34,U_32)
| ? [U_28] :
( ~ in(U_28,U_32)
& in(U_28,U_34) ) )
& ! [U_33,U_31] :
( ! [U_27] :
( in(U_27,U_31)
| ~ in(U_27,U_33) )
| ~ subset(U_33,U_31) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_34,U_32] :
( subset(U_34,U_32)
| ( ~ in(sK7(U_34,U_32),U_32)
& in(sK7(U_34,U_32),U_34) ) )
& ! [U_33,U_31] :
( ! [U_27] :
( in(U_27,U_31)
| ~ in(U_27,U_33) )
| ~ subset(U_33,U_31) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_28,sK7(U_34,U_32))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_34,U_32] :
( ~ in(sK7(U_34,U_32),U_32)
| ~ sP4(U_34,U_32) )
& ! [U_34,U_32] :
( in(sK7(U_34,U_32),U_34)
| ~ sP4(U_34,U_32) )
& ! [U_34,U_32] :
( subset(U_34,U_32)
| sP4(U_34,U_32) )
& ! [U_27,U_31,U_33] :
( in(U_27,U_31)
| ~ in(U_27,U_33)
| ~ subset(U_33,U_31) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_4_4]) ).
cnf(f_4_6,plain,
( in(U_27,U_31)
| ~ in(U_27,U_33)
| ~ subset(U_33,U_31) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( subset(U_34,U_32)
| sP4(U_34,U_32) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( in(sK7(U_34,U_32),U_34)
| ~ sP4(U_34,U_32) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( ~ in(sK7(U_34,U_32),U_32)
| ~ sP4(U_34,U_32) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_5_2,plain,
! [U_36,U_35] : ordered_pair(U_36,U_35) = unordered_pair(unordered_pair(U_36,U_35),singleton(U_36)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_35,U_36] : ordered_pair(U_36,U_35) = unordered_pair(unordered_pair(U_36,U_35),singleton(U_36)),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
ordered_pair(U_36,U_35) = unordered_pair(unordered_pair(U_36,U_35),singleton(U_36)),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_38,U_37] : ~ empty(ordered_pair(U_38,U_37)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_37,U_38] : ~ empty(ordered_pair(U_38,U_37)),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
~ empty(ordered_pair(U_38,U_37)),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_7_2,plain,
? [U_39] : empty(U_39),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_39,sK8)],[f_7_2]) ).
fof(f_7_4,plain,
empty(sK8),
inference(definitional_conversion,[status(esa)],[f_7_3]) ).
cnf(f_7_5,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_8_2,plain,
? [U_40] : ~ empty(U_40),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_40,sK9)],[f_8_2]) ).
fof(f_8_4,plain,
~ empty(sK9),
inference(definitional_conversion,[status(esa)],[f_8_3]) ).
cnf(f_8_5,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_9_2,plain,
! [U_42,U_41] : subset(U_42,U_42),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_42] : subset(U_42,U_42),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_42] : subset(U_42,U_42),
inference(definitional_conversion,[status(esa)],[f_9_3]) ).
cnf(f_9_5,plain,
subset(U_42,U_42),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,negated_conjecture,
~ ! [A,B,C,D] :
~ ( ! [E,F] :
~ ( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
& in(D,A)
& subset(A,cartesian_product2(B,C)) ),
inference(negate,[status(cth)],[t103_zfmisc_1]) ).
fof(f_10_2,negated_conjecture,
? [A,B,C,D] :
( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,C)
| ~ in(E,B) )
& in(D,A)
& subset(A,cartesian_product2(B,C)) ),
inference(fof_nnf,[status(thm)],[f_10_1]) ).
fof(f_10_3,negated_conjecture,
? [U_48,U_47,U_46,U_45] :
( ! [U_44,U_43] :
( U_45 != ordered_pair(U_44,U_43)
| ~ in(U_43,U_46)
| ~ in(U_44,U_47) )
& in(U_45,U_48)
& subset(U_48,cartesian_product2(U_47,U_46)) ),
inference(variable_rename,[status(thm)],[f_10_2]) ).
fof(f_10_4,negated_conjecture,
? [U_48,U_47,U_46] :
( ? [U_45] :
( ! [U_44] :
( ! [U_43] :
( U_45 != ordered_pair(U_44,U_43)
| ~ in(U_43,U_46) )
| ~ in(U_44,U_47) )
& in(U_45,U_48) )
& subset(U_48,cartesian_product2(U_47,U_46)) ),
inference(miniscope,[status(thm)],[f_10_3]) ).
fof(f_10_5,negated_conjecture,
? [U_47,U_46] :
( ? [U_45] :
( ! [U_44] :
( ! [U_43] :
( U_45 != ordered_pair(U_44,U_43)
| ~ in(U_43,U_46) )
| ~ in(U_44,U_47) )
& in(U_45,sK10) )
& subset(sK10,cartesian_product2(U_47,U_46)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_48,sK10)],[f_10_4]) ).
fof(f_10_6,negated_conjecture,
? [U_46] :
( ? [U_45] :
( ! [U_44] :
( ! [U_43] :
( U_45 != ordered_pair(U_44,U_43)
| ~ in(U_43,U_46) )
| ~ in(U_44,sK11) )
& in(U_45,sK10) )
& subset(sK10,cartesian_product2(sK11,U_46)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_47,sK11)],[f_10_5]) ).
fof(f_10_7,negated_conjecture,
( ? [U_45] :
( ! [U_44] :
( ! [U_43] :
( U_45 != ordered_pair(U_44,U_43)
| ~ in(U_43,sK12) )
| ~ in(U_44,sK11) )
& in(U_45,sK10) )
& subset(sK10,cartesian_product2(sK11,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_46,sK12)],[f_10_6]) ).
fof(f_10_8,negated_conjecture,
( ! [U_44] :
( ! [U_43] :
( sK13 != ordered_pair(U_44,U_43)
| ~ in(U_43,sK12) )
| ~ in(U_44,sK11) )
& in(sK13,sK10)
& subset(sK10,cartesian_product2(sK11,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_45,sK13)],[f_10_7]) ).
fof(f_10_9,negated_conjecture,
( ! [U_43,U_44] :
( sK13 != ordered_pair(U_44,U_43)
| ~ in(U_43,sK12)
| ~ in(U_44,sK11) )
& in(sK13,sK10)
& subset(sK10,cartesian_product2(sK11,sK12)) ),
inference(definitional_conversion,[status(esa)],[f_10_8]) ).
cnf(f_10_10,negated_conjecture,
subset(sK10,cartesian_product2(sK11,sK12)),
inference(clausify,[status(thm)],[f_10_9]) ).
cnf(f_10_11,negated_conjecture,
in(sK13,sK10),
inference(clausify,[status(thm)],[f_10_9]) ).
cnf(f_10_12,negated_conjecture,
( sK13 != ordered_pair(U_44,U_43)
| ~ in(U_43,sK12)
| ~ in(U_44,sK11) ),
inference(clausify,[status(thm)],[f_10_9]) ).
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,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(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,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_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_7,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| 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_functions]) ).
cnf(equality_9,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| 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_functions]) ).
cnf(equality_10,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_11,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_12,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(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_13,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(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_14,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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,
( 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_17,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| 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_19,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_20,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_21,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_22,axiom,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(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 : SET950+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
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 23:11:40 UTC 2026
% 0.09/5.37 % CPUTime :
% 30.24/35.56 % SZS status Theorem for theBenchmark
% 30.24/35.56 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------