%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET988+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 : n001.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 08:57:54 AM UTC 2026
% Result : Theorem 3.79s 4.10s
% Output : Proof 3.92s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_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(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
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(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(t2_funct_1,conjecture,
! [A] :
( ( ! [B,C,D] :
( ( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
=> C = D )
& ! [B] :
~ ( ! [C,D] : ordered_pair(C,D) != B
& in(B,A) ) )
=> ( function(A)
& relation(A) ) ),
file('theBenchmark.p',t2_funct_1) ).
fof(d1_funct_1,axiom,
! [A] :
( function(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
=> C = D ) ),
file('theBenchmark.p',d1_funct_1) ).
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(f_1_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_1_2,plain,
! [U_1,U_0] : subset(U_1,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1] : subset(U_1,U_1),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
subset(U_1,U_1),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_2_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_3_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_3_1]) ).
cnf(f_3_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_4_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_5_2,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_6_2,plain,
! [U_5] :
? [U_4] : element(U_4,U_5),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_5] : element(sK1(U_5),U_5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1(U_5))],[f_6_2]) ).
cnf(f_6_4,plain,
element(sK1(U_5),U_5),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_7_2,plain,
! [U_6] :
( function(U_6)
| ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( function(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_8_2,plain,
! [U_7] : ~ empty(powerset(U_7)),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
~ empty(powerset(U_7)),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_9_2,plain,
! [U_8] : ~ empty(singleton(U_8)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
~ empty(singleton(U_8)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_10_2,plain,
! [U_10,U_9] : ~ empty(unordered_pair(U_10,U_9)),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
~ empty(unordered_pair(U_10,U_9)),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_11_2,plain,
! [U_11] :
( relation(U_11)
| ~ empty(U_11) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(U_11)
| ~ empty(U_11) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_12_2,plain,
! [U_13,U_12] :
( in(U_13,U_12)
| empty(U_12)
| ~ element(U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( in(U_13,U_12)
| empty(U_12)
| ~ element(U_13,U_12) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_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_13_2,plain,
! [U_15,U_14] :
( ( element(U_15,powerset(U_14))
| ~ subset(U_15,U_14) )
& ( subset(U_15,U_14)
| ~ element(U_15,powerset(U_14)) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_19,U_17] :
( element(U_19,powerset(U_17))
| ~ subset(U_19,U_17) )
& ! [U_18,U_16] :
( subset(U_18,U_16)
| ~ element(U_18,powerset(U_16)) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( subset(U_18,U_16)
| ~ element(U_18,powerset(U_16)) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( element(U_19,powerset(U_17))
| ~ subset(U_19,U_17) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_14_2,plain,
! [U_22,U_21,U_20] :
( element(U_22,U_20)
| ~ element(U_21,powerset(U_20))
| ~ in(U_22,U_21) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( element(U_22,U_20)
| ~ element(U_21,powerset(U_20))
| ~ in(U_22,U_21) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_15_2,plain,
! [U_25,U_24,U_23] :
( ~ empty(U_23)
| ~ element(U_24,powerset(U_23))
| ~ in(U_25,U_24) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_25,U_24] :
( ! [U_23] :
( ~ empty(U_23)
| ~ element(U_24,powerset(U_23)) )
| ~ in(U_25,U_24) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( ~ empty(U_23)
| ~ element(U_24,powerset(U_23))
| ~ in(U_25,U_24) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_16_2,plain,
! [U_26] :
( U_26 = empty_set
| ~ empty(U_26) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( U_26 = empty_set
| ~ empty(U_26) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_17_2,plain,
! [U_28,U_27] :
( ~ empty(U_27)
| U_28 = U_27
| ~ empty(U_28) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_28] :
( ! [U_27] :
( ~ empty(U_27)
| U_28 = U_27 )
| ~ empty(U_28) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( ~ empty(U_27)
| U_28 = U_27
| ~ empty(U_28) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_18_2,plain,
! [U_30,U_29] :
( ~ in(U_29,U_30)
| ~ in(U_30,U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ~ in(U_29,U_30)
| ~ in(U_30,U_29) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_19_2,plain,
? [U_31] :
( function(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_31,sK2)],[f_19_2]) ).
cnf(f_19_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_20_2,plain,
! [U_33] :
( ? [U_32] :
( ~ empty(U_32)
& element(U_32,powerset(U_33)) )
| empty(U_33) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_33] :
( ( ~ empty(sK3(U_33))
& element(sK3(U_33),powerset(U_33)) )
| empty(U_33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_32,sK3(U_33))],[f_20_2]) ).
cnf(f_20_4,plain,
( element(sK3(U_33),powerset(U_33))
| empty(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( ~ empty(sK3(U_33))
| empty(U_33) ),
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_35] :
? [U_34] :
( empty(U_34)
& element(U_34,powerset(U_35)) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_35] :
( empty(sK4(U_35))
& element(sK4(U_35),powerset(U_35)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_34,sK4(U_35))],[f_21_2]) ).
cnf(f_21_4,plain,
element(sK4(U_35),powerset(U_35)),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
empty(sK4(U_35)),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_22_2,plain,
? [U_36] :
( relation(U_36)
& empty(U_36) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( relation(sK5)
& empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_36,sK5)],[f_22_2]) ).
cnf(f_22_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_23_2,plain,
? [U_37] :
( relation(U_37)
& ~ empty(U_37) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_37,sK6)],[f_23_2]) ).
cnf(f_23_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_24_2,plain,
? [U_38] :
( relation_empty_yielding(U_38)
& relation(U_38) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( relation_empty_yielding(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_38,sK7)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
relation_empty_yielding(sK7),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_25_2,plain,
! [U_40,U_39] : ~ empty(ordered_pair(U_40,U_39)),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
~ empty(ordered_pair(U_40,U_39)),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_26_2,plain,
? [U_41] : empty(U_41),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_41,sK8)],[f_26_2]) ).
cnf(f_26_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_27_2,plain,
? [U_42] : ~ empty(U_42),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_42,sK9)],[f_27_2]) ).
cnf(f_27_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_28_2,plain,
! [U_44,U_43] :
( element(U_44,U_43)
| ~ in(U_44,U_43) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( element(U_44,U_43)
| ~ in(U_44,U_43) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_29_2,plain,
! [U_46,U_45] :
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_48,U_47] : ordered_pair(U_48,U_47) = unordered_pair(unordered_pair(U_48,U_47),singleton(U_48)),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
ordered_pair(U_48,U_47) = unordered_pair(unordered_pair(U_48,U_47),singleton(U_48)),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,negated_conjecture,
~ ! [A] :
( ( ! [B,C,D] :
( ( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
=> C = D )
& ! [B] :
~ ( ! [C,D] : ordered_pair(C,D) != B
& in(B,A) ) )
=> ( function(A)
& relation(A) ) ),
inference(negate,[status(cth)],[t2_funct_1]) ).
fof(f_31_2,negated_conjecture,
? [A] :
( ( ~ function(A)
| ~ relation(A) )
& ! [B,C,D] :
( C = D
| ~ in(ordered_pair(B,D),A)
| ~ in(ordered_pair(B,C),A) )
& ! [B] :
( ? [C,D] : ordered_pair(C,D) = B
| ~ in(B,A) ) ),
inference(fof_nnf,[status(thm)],[f_31_1]) ).
fof(f_31_3,negated_conjecture,
? [U_55] :
( ( ~ function(U_55)
| ~ relation(U_55) )
& ! [U_54,U_53,U_52] :
( U_53 = U_52
| ~ in(ordered_pair(U_54,U_52),U_55)
| ~ in(ordered_pair(U_54,U_53),U_55) )
& ! [U_51] :
( ? [U_50,U_49] : ordered_pair(U_50,U_49) = U_51
| ~ in(U_51,U_55) ) ),
inference(variable_rename,[status(thm)],[f_31_2]) ).
fof(f_31_4,negated_conjecture,
( ( ~ function(sK10)
| ~ relation(sK10) )
& ! [U_54,U_53,U_52] :
( U_53 = U_52
| ~ in(ordered_pair(U_54,U_52),sK10)
| ~ in(ordered_pair(U_54,U_53),sK10) )
& ! [U_51] :
( ? [U_50,U_49] : ordered_pair(U_50,U_49) = U_51
| ~ in(U_51,sK10) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_55,sK10)],[f_31_3]) ).
fof(f_31_5,negated_conjecture,
( ( ~ function(sK10)
| ~ relation(sK10) )
& ! [U_54,U_53,U_52] :
( U_53 = U_52
| ~ in(ordered_pair(U_54,U_52),sK10)
| ~ in(ordered_pair(U_54,U_53),sK10) )
& ! [U_51] :
( ? [U_49] : ordered_pair(sK11(U_51),U_49) = U_51
| ~ in(U_51,sK10) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_50,sK11(U_51))],[f_31_4]) ).
fof(f_31_6,negated_conjecture,
( ( ~ function(sK10)
| ~ relation(sK10) )
& ! [U_54,U_53,U_52] :
( U_53 = U_52
| ~ in(ordered_pair(U_54,U_52),sK10)
| ~ in(ordered_pair(U_54,U_53),sK10) )
& ! [U_51] :
( ordered_pair(sK11(U_51),sK12(U_51)) = U_51
| ~ in(U_51,sK10) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_49,sK12(U_51))],[f_31_5]) ).
fof(f_31_7,negated_conjecture,
( ( ~ function(sK10)
| ~ relation(sK10) )
& ! [U_52,U_53,U_54] :
( U_53 = U_52
| ~ in(ordered_pair(U_54,U_52),sK10)
| ~ in(ordered_pair(U_54,U_53),sK10) )
& ! [U_51] :
( ordered_pair(sK11(U_51),sK12(U_51)) = U_51
| ~ in(U_51,sK10) ) ),
inference(definitional_conversion,[status(esa)],[f_31_6]) ).
cnf(f_31_8,negated_conjecture,
( ordered_pair(sK11(U_51),sK12(U_51)) = U_51
| ~ in(U_51,sK10) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_9,negated_conjecture,
( U_53 = U_52
| ~ in(ordered_pair(U_54,U_52),sK10)
| ~ in(ordered_pair(U_54,U_53),sK10) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_10,negated_conjecture,
( ~ function(sK10)
| ~ relation(sK10) ),
inference(clausify,[status(thm)],[f_31_7]) ).
fof(f_32_1,plain,
! [A] :
( ( function(A)
| ? [B,C,D] :
( C != D
& in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) ) )
& ( ! [B,C,D] :
( C = D
| ~ in(ordered_pair(B,D),A)
| ~ in(ordered_pair(B,C),A) )
| ~ function(A) ) ),
inference(fof_nnf,[status(thm)],[d1_funct_1]) ).
fof(f_32_2,plain,
! [U_62] :
( ( function(U_62)
| ? [U_61,U_60,U_59] :
( U_60 != U_59
& in(ordered_pair(U_61,U_59),U_62)
& in(ordered_pair(U_61,U_60),U_62) ) )
& ( ! [U_58,U_57,U_56] :
( U_57 = U_56
| ~ in(ordered_pair(U_58,U_56),U_62)
| ~ in(ordered_pair(U_58,U_57),U_62) )
| ~ function(U_62) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_64] :
( function(U_64)
| ? [U_61,U_60,U_59] :
( U_60 != U_59
& in(ordered_pair(U_61,U_59),U_64)
& in(ordered_pair(U_61,U_60),U_64) ) )
& ! [U_63] :
( ! [U_58,U_57,U_56] :
( U_57 = U_56
| ~ in(ordered_pair(U_58,U_56),U_63)
| ~ in(ordered_pair(U_58,U_57),U_63) )
| ~ function(U_63) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_64] :
( function(U_64)
| ? [U_60,U_59] :
( U_60 != U_59
& in(ordered_pair(sK13(U_64),U_59),U_64)
& in(ordered_pair(sK13(U_64),U_60),U_64) ) )
& ! [U_63] :
( ! [U_58,U_57,U_56] :
( U_57 = U_56
| ~ in(ordered_pair(U_58,U_56),U_63)
| ~ in(ordered_pair(U_58,U_57),U_63) )
| ~ function(U_63) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_61,sK13(U_64))],[f_32_3]) ).
fof(f_32_5,plain,
( ! [U_64] :
( function(U_64)
| ? [U_59] :
( sK14(U_64) != U_59
& in(ordered_pair(sK13(U_64),U_59),U_64)
& in(ordered_pair(sK13(U_64),sK14(U_64)),U_64) ) )
& ! [U_63] :
( ! [U_58,U_57,U_56] :
( U_57 = U_56
| ~ in(ordered_pair(U_58,U_56),U_63)
| ~ in(ordered_pair(U_58,U_57),U_63) )
| ~ function(U_63) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_60,sK14(U_64))],[f_32_4]) ).
fof(f_32_6,plain,
( ! [U_64] :
( function(U_64)
| ( sK14(U_64) != sK15(U_64)
& in(ordered_pair(sK13(U_64),sK15(U_64)),U_64)
& in(ordered_pair(sK13(U_64),sK14(U_64)),U_64) ) )
& ! [U_63] :
( ! [U_58,U_57,U_56] :
( U_57 = U_56
| ~ in(ordered_pair(U_58,U_56),U_63)
| ~ in(ordered_pair(U_58,U_57),U_63) )
| ~ function(U_63) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_59,sK15(U_64))],[f_32_5]) ).
cnf(f_32_7,plain,
( U_57 = U_56
| ~ in(ordered_pair(U_58,U_56),U_63)
| ~ in(ordered_pair(U_58,U_57),U_63)
| ~ function(U_63) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_8,plain,
( in(ordered_pair(sK13(U_64),sK14(U_64)),U_64)
| function(U_64) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_9,plain,
( in(ordered_pair(sK13(U_64),sK15(U_64)),U_64)
| function(U_64) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_10,plain,
( sK14(U_64) != sK15(U_64)
| function(U_64) ),
inference(clausify,[status(thm)],[f_32_6]) ).
fof(f_33_1,plain,
! [A] :
( ( relation(A)
| ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(fof_nnf,[status(thm)],[d1_relat_1]) ).
fof(f_33_2,plain,
! [U_71] :
( ( relation(U_71)
| ? [U_70] :
( ! [U_69,U_68] : U_70 != ordered_pair(U_69,U_68)
& in(U_70,U_71) ) )
& ( ! [U_67] :
( ? [U_66,U_65] : U_67 = ordered_pair(U_66,U_65)
| ~ in(U_67,U_71) )
| ~ relation(U_71) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_73] :
( relation(U_73)
| ? [U_70] :
( ! [U_69,U_68] : U_70 != ordered_pair(U_69,U_68)
& in(U_70,U_73) ) )
& ! [U_72] :
( ! [U_67] :
( ? [U_66,U_65] : U_67 = ordered_pair(U_66,U_65)
| ~ in(U_67,U_72) )
| ~ relation(U_72) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_73] :
( relation(U_73)
| ? [U_70] :
( ! [U_69,U_68] : U_70 != ordered_pair(U_69,U_68)
& in(U_70,U_73) ) )
& ! [U_72] :
( ! [U_67] :
( ? [U_65] : U_67 = ordered_pair(sK16(U_72,U_67),U_65)
| ~ in(U_67,U_72) )
| ~ relation(U_72) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_66,sK16(U_72,U_67))],[f_33_3]) ).
fof(f_33_5,plain,
( ! [U_73] :
( relation(U_73)
| ? [U_70] :
( ! [U_69,U_68] : U_70 != ordered_pair(U_69,U_68)
& in(U_70,U_73) ) )
& ! [U_72] :
( ! [U_67] :
( U_67 = ordered_pair(sK16(U_72,U_67),sK17(U_72,U_67))
| ~ in(U_67,U_72) )
| ~ relation(U_72) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_65,sK17(U_72,U_67))],[f_33_4]) ).
fof(f_33_6,plain,
( ! [U_73] :
( relation(U_73)
| ( ! [U_69,U_68] : sK18(U_73) != ordered_pair(U_69,U_68)
& in(sK18(U_73),U_73) ) )
& ! [U_72] :
( ! [U_67] :
( U_67 = ordered_pair(sK16(U_72,U_67),sK17(U_72,U_67))
| ~ in(U_67,U_72) )
| ~ relation(U_72) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_70,sK18(U_73))],[f_33_5]) ).
cnf(f_33_7,plain,
( U_67 = ordered_pair(sK16(U_72,U_67),sK17(U_72,U_67))
| ~ in(U_67,U_72)
| ~ relation(U_72) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_8,plain,
( in(sK18(U_73),U_73)
| relation(U_73) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_9,plain,
( sK18(U_73) != ordered_pair(U_69,U_68)
| relation(U_73) ),
inference(clausify,[status(thm)],[f_33_6]) ).
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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| 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,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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_24,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:15:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 3.79/4.10 % SZS status Theorem for theBenchmark
% 3.79/4.10 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------