%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU009+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : 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 08:57:56 AM UTC 2026
% Result : Theorem 18.94s 19.22s
% Output : Proof 19.29s
% 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_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_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_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
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(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t21_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('theBenchmark.p',t21_funct_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t34_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t40_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_composition(C,identity_relation(A))))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',t40_funct_1) ).
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(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
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] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_3)
| ~ empty(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_4_2,plain,
! [U_5,U_4] :
( relation(relation_composition(U_5,U_4))
| ~ relation(U_4)
| ~ relation(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(relation_composition(U_5,U_4))
| ~ relation(U_4)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_5_2,plain,
! [U_6] : relation(identity_relation(U_6)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
relation(identity_relation(U_6)),
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_8] :
? [U_7] : element(U_7,U_8),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_8] : element(sK1(U_8),U_8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_7,sK1(U_8))],[f_6_2]) ).
cnf(f_6_4,plain,
element(sK1(U_8),U_8),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B] :
( ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc10_relat_1]) ).
fof(f_7_2,plain,
! [U_10,U_9] :
( ( relation(relation_composition(U_9,U_10))
& empty(relation_composition(U_9,U_10)) )
| ~ relation(U_9)
| ~ empty(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( empty(relation_composition(U_9,U_10))
| ~ relation(U_9)
| ~ empty(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( relation(relation_composition(U_9,U_10))
| ~ relation(U_9)
| ~ empty(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_8_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
cnf(f_8_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_funct_1]) ).
fof(f_9_2,plain,
! [U_12,U_11] :
( ( function(relation_composition(U_12,U_11))
& relation(relation_composition(U_12,U_11)) )
| ~ function(U_11)
| ~ relation(U_11)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( relation(relation_composition(U_12,U_11))
| ~ function(U_11)
| ~ relation(U_11)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( function(relation_composition(U_12,U_11))
| ~ function(U_11)
| ~ relation(U_11)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_10_2,plain,
! [U_13] : ~ empty(powerset(U_13)),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
~ empty(powerset(U_13)),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_11_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_12_2,plain,
! [U_14] :
( function(identity_relation(U_14))
& relation(identity_relation(U_14)) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_16] : function(identity_relation(U_16))
& ! [U_15] : relation(identity_relation(U_15)) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
relation(identity_relation(U_15)),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
function(identity_relation(U_16)),
inference(clausify,[status(thm)],[f_12_3]) ).
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_17] :
( ~ empty(relation_dom(U_17))
| ~ relation(U_17)
| empty(U_17) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( ~ empty(relation_dom(U_17))
| ~ relation(U_17)
| empty(U_17) ),
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_18] :
( ( relation(relation_dom(U_18))
& empty(relation_dom(U_18)) )
| ~ empty(U_18) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( empty(relation_dom(U_18))
| ~ empty(U_18) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( relation(relation_dom(U_18))
| ~ empty(U_18) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B] :
( ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc9_relat_1]) ).
fof(f_16_2,plain,
! [U_20,U_19] :
( ( relation(relation_composition(U_20,U_19))
& empty(relation_composition(U_20,U_19)) )
| ~ relation(U_19)
| ~ empty(U_20) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( empty(relation_composition(U_20,U_19))
| ~ relation(U_19)
| ~ empty(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( relation(relation_composition(U_20,U_19))
| ~ relation(U_19)
| ~ empty(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_17_2,plain,
? [U_21] :
( function(U_21)
& relation(U_21) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_21,sK2)],[f_17_2]) ).
cnf(f_17_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_18_2,plain,
? [U_22] :
( relation(U_22)
& empty(U_22) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3)],[f_18_2]) ).
cnf(f_18_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_19_2,plain,
! [U_24] :
( ? [U_23] :
( ~ empty(U_23)
& element(U_23,powerset(U_24)) )
| empty(U_24) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_24] :
( ( ~ empty(sK4(U_24))
& element(sK4(U_24),powerset(U_24)) )
| empty(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_23,sK4(U_24))],[f_19_2]) ).
cnf(f_19_4,plain,
( element(sK4(U_24),powerset(U_24))
| empty(U_24) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( ~ empty(sK4(U_24))
| empty(U_24) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_20_2,plain,
? [U_25] : empty(U_25),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_25,sK5)],[f_20_2]) ).
cnf(f_20_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_21_2,plain,
? [U_26] :
( relation(U_26)
& ~ empty(U_26) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_26,sK6)],[f_21_2]) ).
cnf(f_21_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_22_2,plain,
! [U_28] :
? [U_27] :
( empty(U_27)
& element(U_27,powerset(U_28)) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_28] :
( empty(sK7(U_28))
& element(sK7(U_28),powerset(U_28)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_27,sK7(U_28))],[f_22_2]) ).
cnf(f_22_4,plain,
element(sK7(U_28),powerset(U_28)),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
empty(sK7(U_28)),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_23_2,plain,
? [U_29] : ~ empty(U_29),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_29,sK8)],[f_23_2]) ).
cnf(f_23_4,plain,
~ empty(sK8),
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_30] :
( relation_empty_yielding(U_30)
& relation(U_30) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( relation_empty_yielding(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_30,sK9)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
relation_empty_yielding(sK9),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_25_2,plain,
! [U_32,U_31] : subset(U_32,U_32),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_32] : subset(U_32,U_32),
inference(miniscope,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
subset(U_32,U_32),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_26_2,plain,
! [U_34,U_33] :
( element(U_34,U_33)
| ~ in(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( element(U_34,U_33)
| ~ in(U_34,U_33) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B] :
( ! [C] :
( ( ( in(A,relation_dom(relation_composition(C,B)))
| ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C)) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t21_funct_1]) ).
fof(f_27_2,plain,
! [U_37,U_36] :
( ! [U_35] :
( ( ( in(U_37,relation_dom(relation_composition(U_35,U_36)))
| ~ in(apply(U_35,U_37),relation_dom(U_36))
| ~ in(U_37,relation_dom(U_35)) )
& ( ( in(apply(U_35,U_37),relation_dom(U_36))
& in(U_37,relation_dom(U_35)) )
| ~ in(U_37,relation_dom(relation_composition(U_35,U_36))) ) )
| ~ function(U_35)
| ~ relation(U_35) )
| ~ function(U_36)
| ~ relation(U_36) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( in(U_37,relation_dom(U_35))
| ~ in(U_37,relation_dom(relation_composition(U_35,U_36)))
| ~ function(U_35)
| ~ relation(U_35)
| ~ function(U_36)
| ~ relation(U_36) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( in(apply(U_35,U_37),relation_dom(U_36))
| ~ in(U_37,relation_dom(relation_composition(U_35,U_36)))
| ~ function(U_35)
| ~ relation(U_35)
| ~ function(U_36)
| ~ relation(U_36) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_5,plain,
( in(U_37,relation_dom(relation_composition(U_35,U_36)))
| ~ in(apply(U_35,U_37),relation_dom(U_36))
| ~ in(U_37,relation_dom(U_35))
| ~ function(U_35)
| ~ relation(U_35)
| ~ function(U_36)
| ~ relation(U_36) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_28_2,plain,
! [U_39,U_38] :
( in(U_39,U_38)
| empty(U_38)
| ~ element(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( in(U_39,U_38)
| empty(U_38)
| ~ element(U_39,U_38) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t34_funct_1]) ).
fof(f_29_2,plain,
! [U_43,U_42] :
( ( ( U_42 = identity_relation(U_43)
| ? [U_41] :
( apply(U_42,U_41) != U_41
& in(U_41,U_43) )
| relation_dom(U_42) != U_43 )
& ( ( ! [U_40] :
( apply(U_42,U_40) = U_40
| ~ in(U_40,U_43) )
& relation_dom(U_42) = U_43 )
| U_42 != identity_relation(U_43) ) )
| ~ function(U_42)
| ~ relation(U_42) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_43,U_42] :
( ( ( U_42 = identity_relation(U_43)
| ( apply(U_42,sK10(U_43,U_42)) != sK10(U_43,U_42)
& in(sK10(U_43,U_42),U_43) )
| relation_dom(U_42) != U_43 )
& ( ( ! [U_40] :
( apply(U_42,U_40) = U_40
| ~ in(U_40,U_43) )
& relation_dom(U_42) = U_43 )
| U_42 != identity_relation(U_43) ) )
| ~ function(U_42)
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_41,sK10(U_43,U_42))],[f_29_2]) ).
cnf(f_29_4,plain,
( relation_dom(U_42) = U_43
| U_42 != identity_relation(U_43)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
( apply(U_42,U_40) = U_40
| ~ in(U_40,U_43)
| U_42 != identity_relation(U_43)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
( in(sK10(U_43,U_42),U_43)
| relation_dom(U_42) != U_43
| U_42 = identity_relation(U_43)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_7,plain,
( apply(U_42,sK10(U_43,U_42)) != sK10(U_43,U_42)
| relation_dom(U_42) != U_43
| U_42 = identity_relation(U_43)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_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_30_2,plain,
! [U_45,U_44] :
( ( element(U_45,powerset(U_44))
| ~ subset(U_45,U_44) )
& ( subset(U_45,U_44)
| ~ element(U_45,powerset(U_44)) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_49,U_47] :
( element(U_49,powerset(U_47))
| ~ subset(U_49,U_47) )
& ! [U_48,U_46] :
( subset(U_48,U_46)
| ~ element(U_48,powerset(U_46)) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
( subset(U_48,U_46)
| ~ element(U_48,powerset(U_46)) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( element(U_49,powerset(U_47))
| ~ subset(U_49,U_47) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_composition(C,identity_relation(A))))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
inference(negate,[status(cth)],[t40_funct_1]) ).
fof(f_31_2,negated_conjecture,
? [A,B,C] :
( ( ( ~ in(B,relation_dom(relation_composition(C,identity_relation(A))))
& in(apply(C,B),A)
& in(B,relation_dom(C)) )
| ( ( ~ in(apply(C,B),A)
| ~ in(B,relation_dom(C)) )
& in(B,relation_dom(relation_composition(C,identity_relation(A)))) ) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_31_1]) ).
fof(f_31_3,negated_conjecture,
? [U_52,U_51,U_50] :
( ( ( ~ in(U_51,relation_dom(relation_composition(U_50,identity_relation(U_52))))
& in(apply(U_50,U_51),U_52)
& in(U_51,relation_dom(U_50)) )
| ( ( ~ in(apply(U_50,U_51),U_52)
| ~ in(U_51,relation_dom(U_50)) )
& in(U_51,relation_dom(relation_composition(U_50,identity_relation(U_52)))) ) )
& function(U_50)
& relation(U_50) ),
inference(variable_rename,[status(thm)],[f_31_2]) ).
fof(f_31_4,negated_conjecture,
? [U_51,U_50] :
( ( ( ~ in(U_51,relation_dom(relation_composition(U_50,identity_relation(sK11))))
& in(apply(U_50,U_51),sK11)
& in(U_51,relation_dom(U_50)) )
| ( ( ~ in(apply(U_50,U_51),sK11)
| ~ in(U_51,relation_dom(U_50)) )
& in(U_51,relation_dom(relation_composition(U_50,identity_relation(sK11)))) ) )
& function(U_50)
& relation(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_52,sK11)],[f_31_3]) ).
fof(f_31_5,negated_conjecture,
? [U_50] :
( ( ( ~ in(sK12,relation_dom(relation_composition(U_50,identity_relation(sK11))))
& in(apply(U_50,sK12),sK11)
& in(sK12,relation_dom(U_50)) )
| ( ( ~ in(apply(U_50,sK12),sK11)
| ~ in(sK12,relation_dom(U_50)) )
& in(sK12,relation_dom(relation_composition(U_50,identity_relation(sK11)))) ) )
& function(U_50)
& relation(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_51,sK12)],[f_31_4]) ).
fof(f_31_6,negated_conjecture,
( ( ( ~ in(sK12,relation_dom(relation_composition(sK13,identity_relation(sK11))))
& in(apply(sK13,sK12),sK11)
& in(sK12,relation_dom(sK13)) )
| ( ( ~ in(apply(sK13,sK12),sK11)
| ~ in(sK12,relation_dom(sK13)) )
& in(sK12,relation_dom(relation_composition(sK13,identity_relation(sK11)))) ) )
& function(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_50,sK13)],[f_31_5]) ).
fof(f_31_7,negated_conjecture,
( ( ~ in(sK12,relation_dom(relation_composition(sK13,identity_relation(sK11))))
| ~ sP1 )
& ( in(apply(sK13,sK12),sK11)
| ~ sP1 )
& ( in(sK12,relation_dom(sK13))
| ~ sP1 )
& ( ~ in(apply(sK13,sK12),sK11)
| ~ in(sK12,relation_dom(sK13))
| ~ sP0 )
& ( in(sK12,relation_dom(relation_composition(sK13,identity_relation(sK11))))
| ~ sP0 )
& ( sP1
| sP0 )
& function(sK13)
& relation(sK13) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_31_6]) ).
cnf(f_31_8,negated_conjecture,
relation(sK13),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_9,negated_conjecture,
function(sK13),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_11,negated_conjecture,
( in(sK12,relation_dom(relation_composition(sK13,identity_relation(sK11))))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_12,negated_conjecture,
( ~ in(apply(sK13,sK12),sK11)
| ~ in(sK12,relation_dom(sK13))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_13,negated_conjecture,
( in(sK12,relation_dom(sK13))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_14,negated_conjecture,
( in(apply(sK13,sK12),sK11)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_15,negated_conjecture,
( ~ in(sK12,relation_dom(relation_composition(sK13,identity_relation(sK11))))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_31_7]) ).
fof(f_32_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_32_2,plain,
! [U_55,U_54,U_53] :
( element(U_55,U_53)
| ~ element(U_54,powerset(U_53))
| ~ in(U_55,U_54) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( element(U_55,U_53)
| ~ element(U_54,powerset(U_53))
| ~ in(U_55,U_54) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_33_2,plain,
! [U_58,U_57,U_56] :
( ~ empty(U_56)
| ~ element(U_57,powerset(U_56))
| ~ in(U_58,U_57) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_58,U_57] :
( ! [U_56] :
( ~ empty(U_56)
| ~ element(U_57,powerset(U_56)) )
| ~ in(U_58,U_57) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( ~ empty(U_56)
| ~ element(U_57,powerset(U_56))
| ~ in(U_58,U_57) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_34_2,plain,
! [U_59] :
( U_59 = empty_set
| ~ empty(U_59) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( U_59 = empty_set
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_35_2,plain,
! [U_61,U_60] :
( ~ empty(U_60)
| ~ in(U_61,U_60) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ empty(U_60)
| ~ in(U_61,U_60) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_63,U_62] :
( ~ empty(U_62)
| U_63 = U_62
| ~ empty(U_63) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_63] :
( ! [U_62] :
( ~ empty(U_62)
| U_63 = U_62 )
| ~ empty(U_63) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_62)
| U_63 = U_62
| ~ empty(U_63) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( relation_composition(Eq_x_0,Eq_x_1) = relation_composition(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,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( apply(Eq_x_0,Eq_x_1) = apply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK1(Eq_x_0) = sK1(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,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,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_18,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_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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU009+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n001.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 23:18:41 UTC 2026
% 0.07/0.34 % CPUTime :
% 18.94/19.22 % SZS status Theorem for theBenchmark
% 18.94/19.22 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------