%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU194+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:58:25 AM UTC 2026
% Result : Theorem 0.54s 0.82s
% Output : Proof 0.54s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
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_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_intersection2(A,B)) ),
file('theBenchmark.p',fc1_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
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(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
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(t86_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t90_relat_1,conjecture,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('theBenchmark.p',t90_relat_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] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_2_2,plain,
! [U_2] :
( relation(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( relation(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_3_2,plain,
! [U_4,U_3] : set_intersection2(U_4,U_3) = set_intersection2(U_3,U_4),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
set_intersection2(U_4,U_3) = set_intersection2(U_3,U_4),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( C = set_intersection2(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_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_4_2,plain,
! [U_9,U_8,U_7] :
( ( U_7 = set_intersection2(U_9,U_8)
| ? [U_6] :
( ( ~ in(U_6,U_7)
& in(U_6,U_8)
& in(U_6,U_9) )
| ( ( ~ in(U_6,U_8)
| ~ in(U_6,U_9) )
& in(U_6,U_7) ) ) )
& ( ! [U_5] :
( ( in(U_5,U_7)
| ~ in(U_5,U_8)
| ~ in(U_5,U_9) )
& ( ( in(U_5,U_8)
& in(U_5,U_9) )
| ~ in(U_5,U_7) ) )
| U_7 != set_intersection2(U_9,U_8) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_19,U_17,U_15] :
( U_15 = set_intersection2(U_19,U_17)
| ? [U_13] :
( ~ in(U_13,U_15)
& in(U_13,U_17)
& in(U_13,U_19) )
| ? [U_12] :
( ( ~ in(U_12,U_17)
| ~ in(U_12,U_19) )
& in(U_12,U_15) ) )
& ! [U_18,U_16,U_14] :
( ( ! [U_11] :
( in(U_11,U_14)
| ~ in(U_11,U_16)
| ~ in(U_11,U_18) )
& ! [U_10] :
( ( in(U_10,U_16)
& in(U_10,U_18) )
| ~ in(U_10,U_14) ) )
| U_14 != set_intersection2(U_18,U_16) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_19,U_17,U_15] :
( U_15 = set_intersection2(U_19,U_17)
| ? [U_13] :
( ~ in(U_13,U_15)
& in(U_13,U_17)
& in(U_13,U_19) )
| ( ( ~ in(sK1(U_19,U_17,U_15),U_17)
| ~ in(sK1(U_19,U_17,U_15),U_19) )
& in(sK1(U_19,U_17,U_15),U_15) ) )
& ! [U_18,U_16,U_14] :
( ( ! [U_11] :
( in(U_11,U_14)
| ~ in(U_11,U_16)
| ~ in(U_11,U_18) )
& ! [U_10] :
( ( in(U_10,U_16)
& in(U_10,U_18) )
| ~ in(U_10,U_14) ) )
| U_14 != set_intersection2(U_18,U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1(U_19,U_17,U_15))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_19,U_17,U_15] :
( U_15 = set_intersection2(U_19,U_17)
| ( ~ in(sK2(U_19,U_17,U_15),U_15)
& in(sK2(U_19,U_17,U_15),U_17)
& in(sK2(U_19,U_17,U_15),U_19) )
| ( ( ~ in(sK1(U_19,U_17,U_15),U_17)
| ~ in(sK1(U_19,U_17,U_15),U_19) )
& in(sK1(U_19,U_17,U_15),U_15) ) )
& ! [U_18,U_16,U_14] :
( ( ! [U_11] :
( in(U_11,U_14)
| ~ in(U_11,U_16)
| ~ in(U_11,U_18) )
& ! [U_10] :
( ( in(U_10,U_16)
& in(U_10,U_18) )
| ~ in(U_10,U_14) ) )
| U_14 != set_intersection2(U_18,U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_13,sK2(U_19,U_17,U_15))],[f_4_4]) ).
cnf(f_4_6,plain,
( in(U_10,U_18)
| ~ in(U_10,U_14)
| U_14 != set_intersection2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( in(U_10,U_16)
| ~ in(U_10,U_14)
| U_14 != set_intersection2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( in(U_11,U_14)
| ~ in(U_11,U_16)
| ~ in(U_11,U_18)
| U_14 != set_intersection2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( in(sK2(U_19,U_17,U_15),U_19)
| in(sK1(U_19,U_17,U_15),U_15)
| U_15 = set_intersection2(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_10,plain,
( in(sK2(U_19,U_17,U_15),U_17)
| in(sK1(U_19,U_17,U_15),U_15)
| U_15 = set_intersection2(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_11,plain,
( ~ in(sK2(U_19,U_17,U_15),U_15)
| in(sK1(U_19,U_17,U_15),U_15)
| U_15 = set_intersection2(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_12,plain,
( in(sK2(U_19,U_17,U_15),U_19)
| ~ in(sK1(U_19,U_17,U_15),U_17)
| ~ in(sK1(U_19,U_17,U_15),U_19)
| U_15 = set_intersection2(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_13,plain,
( in(sK2(U_19,U_17,U_15),U_17)
| ~ in(sK1(U_19,U_17,U_15),U_17)
| ~ in(sK1(U_19,U_17,U_15),U_19)
| U_15 = set_intersection2(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_14,plain,
( ~ in(sK2(U_19,U_17,U_15),U_15)
| ~ in(sK1(U_19,U_17,U_15),U_17)
| ~ in(sK1(U_19,U_17,U_15),U_19)
| U_15 = set_intersection2(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_8_2,plain,
! [U_21,U_20] :
( relation(relation_dom_restriction(U_21,U_20))
| ~ relation(U_21) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_21] :
( ! [U_20] : relation(relation_dom_restriction(U_21,U_20))
| ~ relation(U_21) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( relation(relation_dom_restriction(U_21,U_20))
| ~ relation(U_21) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
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_23] :
? [U_22] : element(U_22,U_23),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_23] : element(sK3(U_23),U_23),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3(U_23))],[f_10_2]) ).
cnf(f_10_4,plain,
element(sK3(U_23),U_23),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_11_2,plain,
! [U_25,U_24] :
( relation(set_intersection2(U_25,U_24))
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(set_intersection2(U_25,U_24))
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_12_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_13_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_14_2,plain,
! [U_26] :
( ~ empty(relation_dom(U_26))
| ~ relation(U_26)
| empty(U_26) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( ~ empty(relation_dom(U_26))
| ~ relation(U_26)
| empty(U_26) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_15_2,plain,
! [U_27] :
( ( relation(relation_dom(U_27))
& empty(relation_dom(U_27)) )
| ~ empty(U_27) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( empty(relation_dom(U_27))
| ~ empty(U_27) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( relation(relation_dom(U_27))
| ~ empty(U_27) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_16_2,plain,
! [U_29,U_28] : set_intersection2(U_29,U_29) = U_29,
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_29] : set_intersection2(U_29,U_29) = U_29,
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
set_intersection2(U_29,U_29) = U_29,
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_17_2,plain,
? [U_30] :
( relation(U_30)
& empty(U_30) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( relation(sK4)
& empty(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_30,sK4)],[f_17_2]) ).
cnf(f_17_4,plain,
empty(sK4),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
relation(sK4),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_18_2,plain,
? [U_31] : empty(U_31),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_31,sK5)],[f_18_2]) ).
cnf(f_18_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_19_2,plain,
? [U_32] :
( relation(U_32)
& ~ empty(U_32) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_32,sK6)],[f_19_2]) ).
cnf(f_19_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_20_2,plain,
? [U_33] : ~ empty(U_33),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_33,sK7)],[f_20_2]) ).
cnf(f_20_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_21_2,plain,
! [U_35,U_34] :
( element(U_35,U_34)
| ~ in(U_35,U_34) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( element(U_35,U_34)
| ~ in(U_35,U_34) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_22_2,plain,
! [U_36] : set_intersection2(U_36,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
set_intersection2(U_36,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_23_2,plain,
! [U_38,U_37] :
( in(U_38,U_37)
| empty(U_37)
| ~ element(U_38,U_37) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( in(U_38,U_37)
| empty(U_37)
| ~ element(U_38,U_37) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_24_2,plain,
! [U_41,U_40] :
( U_41 = U_40
| ? [U_39] :
( ( ~ in(U_39,U_41)
& in(U_39,U_40) )
| ( ~ in(U_39,U_40)
& in(U_39,U_41) ) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_41,U_40] :
( U_41 = U_40
| ? [U_43] :
( ~ in(U_43,U_41)
& in(U_43,U_40) )
| ? [U_42] :
( ~ in(U_42,U_40)
& in(U_42,U_41) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
! [U_41,U_40] :
( U_41 = U_40
| ? [U_43] :
( ~ in(U_43,U_41)
& in(U_43,U_40) )
| ( ~ in(sK8(U_41,U_40),U_40)
& in(sK8(U_41,U_40),U_41) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_42,sK8(U_41,U_40))],[f_24_3]) ).
fof(f_24_5,plain,
! [U_41,U_40] :
( U_41 = U_40
| ( ~ in(sK9(U_41,U_40),U_41)
& in(sK9(U_41,U_40),U_40) )
| ( ~ in(sK8(U_41,U_40),U_40)
& in(sK8(U_41,U_40),U_41) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_43,sK9(U_41,U_40))],[f_24_4]) ).
cnf(f_24_6,plain,
( in(sK9(U_41,U_40),U_40)
| in(sK8(U_41,U_40),U_41)
| U_41 = U_40 ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_7,plain,
( ~ in(sK9(U_41,U_40),U_41)
| in(sK8(U_41,U_40),U_41)
| U_41 = U_40 ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_8,plain,
( in(sK9(U_41,U_40),U_40)
| ~ in(sK8(U_41,U_40),U_40)
| U_41 = U_40 ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_9,plain,
( ~ in(sK9(U_41,U_40),U_41)
| ~ in(sK8(U_41,U_40),U_40)
| U_41 = U_40 ),
inference(clausify,[status(thm)],[f_24_5]) ).
fof(f_25_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_25_2,plain,
! [U_44] :
( U_44 = empty_set
| ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( U_44 = empty_set
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_25_2]) ).
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_46,U_45] :
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B,C] :
( ( ( in(A,relation_dom(relation_dom_restriction(C,B)))
| ~ in(A,relation_dom(C))
| ~ in(A,B) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t86_relat_1]) ).
fof(f_27_2,plain,
! [U_49,U_48,U_47] :
( ( ( in(U_49,relation_dom(relation_dom_restriction(U_47,U_48)))
| ~ in(U_49,relation_dom(U_47))
| ~ in(U_49,U_48) )
& ( ( in(U_49,relation_dom(U_47))
& in(U_49,U_48) )
| ~ in(U_49,relation_dom(relation_dom_restriction(U_47,U_48))) ) )
| ~ relation(U_47) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( in(U_49,U_48)
| ~ in(U_49,relation_dom(relation_dom_restriction(U_47,U_48)))
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( in(U_49,relation_dom(U_47))
| ~ in(U_49,relation_dom(relation_dom_restriction(U_47,U_48)))
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_5,plain,
( in(U_49,relation_dom(relation_dom_restriction(U_47,U_48)))
| ~ in(U_49,relation_dom(U_47))
| ~ in(U_49,U_48)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_28_2,plain,
! [U_51,U_50] :
( ~ empty(U_50)
| U_51 = U_50
| ~ empty(U_51) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_51] :
( ! [U_50] :
( ~ empty(U_50)
| U_51 = U_50 )
| ~ empty(U_51) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( ~ empty(U_50)
| U_51 = U_50
| ~ empty(U_51) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
inference(negate,[status(cth)],[t90_relat_1]) ).
fof(f_29_2,negated_conjecture,
? [A,B] :
( relation_dom(relation_dom_restriction(B,A)) != set_intersection2(relation_dom(B),A)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_29_1]) ).
fof(f_29_3,negated_conjecture,
? [U_53,U_52] :
( relation_dom(relation_dom_restriction(U_52,U_53)) != set_intersection2(relation_dom(U_52),U_53)
& relation(U_52) ),
inference(variable_rename,[status(thm)],[f_29_2]) ).
fof(f_29_4,negated_conjecture,
? [U_52] :
( relation_dom(relation_dom_restriction(U_52,sK10)) != set_intersection2(relation_dom(U_52),sK10)
& relation(U_52) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_53,sK10)],[f_29_3]) ).
fof(f_29_5,negated_conjecture,
( relation_dom(relation_dom_restriction(sK11,sK10)) != set_intersection2(relation_dom(sK11),sK10)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_52,sK11)],[f_29_4]) ).
fof(f_29_6,negated_conjecture,
( relation_dom(relation_dom_restriction(sK11,sK10)) != set_intersection2(relation_dom(sK11),sK10)
& relation(sK11) ),
inference(definitional_conversion,[status(esa)],[f_29_5]) ).
cnf(f_29_7,negated_conjecture,
relation(sK11),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_8,negated_conjecture,
relation_dom(relation_dom_restriction(sK11,sK10)) != set_intersection2(relation_dom(sK11),sK10),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_2]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
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_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(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,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(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,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_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) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(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,
( 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_12,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_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU194+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:31:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.54/0.82 % SZS status Theorem for theBenchmark
% 0.54/0.82 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------