%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU023+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 : n018.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 08:57:57 AM UTC 2026
% Result : Theorem 0.67s 0.94s
% Output : Proof 0.67s
% 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(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_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(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(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(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_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(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_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_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
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_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
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(t23_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_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(t54_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t56_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_dom(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(B,function_inverse(B)),A)
& A = apply(function_inverse(B),apply(B,A)) ) ) ),
file('theBenchmark.p',t56_funct_1) ).
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] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_4_2,plain,
! [U_4] :
( ( one_to_one(U_4)
& function(U_4)
& relation(U_4) )
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( function(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( one_to_one(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_5_2,plain,
! [U_5] :
( ( function(function_inverse(U_5))
& relation(function_inverse(U_5)) )
| ~ function(U_5)
| ~ relation(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(function_inverse(U_5))
| ~ function(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( function(function_inverse(U_5))
| ~ function(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_6_2,plain,
! [U_7,U_6] :
( relation(relation_composition(U_7,U_6))
| ~ relation(U_6)
| ~ relation(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( relation(relation_composition(U_7,U_6))
| ~ relation(U_6)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_7_2,plain,
! [U_9] :
? [U_8] : element(U_8,U_9),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_9] : element(sK1(U_9),U_9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_9))],[f_7_2]) ).
cnf(f_7_4,plain,
element(sK1(U_9),U_9),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_2,plain,
! [U_11,U_10] :
( ( relation(relation_composition(U_10,U_11))
& empty(relation_composition(U_10,U_11)) )
| ~ relation(U_10)
| ~ empty(U_11) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( empty(relation_composition(U_10,U_11))
| ~ relation(U_10)
| ~ empty(U_11) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( relation(relation_composition(U_10,U_11))
| ~ relation(U_10)
| ~ empty(U_11) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_9_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_9_1]) ).
cnf(f_9_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_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_10_2,plain,
! [U_13,U_12] :
( ( function(relation_composition(U_13,U_12))
& relation(relation_composition(U_13,U_12)) )
| ~ function(U_12)
| ~ relation(U_12)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( relation(relation_composition(U_13,U_12))
| ~ function(U_12)
| ~ relation(U_12)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( function(relation_composition(U_13,U_12))
| ~ function(U_12)
| ~ relation(U_12)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_11_2,plain,
! [U_14] : ~ empty(powerset(U_14)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
~ empty(powerset(U_14)),
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_15] :
( ~ empty(relation_dom(U_15))
| ~ relation(U_15)
| empty(U_15) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( ~ empty(relation_dom(U_15))
| ~ relation(U_15)
| empty(U_15) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_15_2,plain,
! [U_16] :
( ~ empty(relation_rng(U_16))
| ~ relation(U_16)
| empty(U_16) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( ~ empty(relation_rng(U_16))
| ~ relation(U_16)
| empty(U_16) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_16_2,plain,
! [U_17] :
( ( relation(relation_dom(U_17))
& empty(relation_dom(U_17)) )
| ~ empty(U_17) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( empty(relation_dom(U_17))
| ~ empty(U_17) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( relation(relation_dom(U_17))
| ~ empty(U_17) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_17_2,plain,
! [U_18] :
( ( relation(relation_rng(U_18))
& empty(relation_rng(U_18)) )
| ~ empty(U_18) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( empty(relation_rng(U_18))
| ~ empty(U_18) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( relation(relation_rng(U_18))
| ~ empty(U_18) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_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_18_1]) ).
cnf(f_18_3,plain,
( empty(relation_composition(U_20,U_19))
| ~ relation(U_19)
| ~ empty(U_20) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( relation(relation_composition(U_20,U_19))
| ~ relation(U_19)
| ~ empty(U_20) ),
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_21] :
( function(U_21)
& relation(U_21) ),
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_21,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] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_20_2,plain,
? [U_22] :
( relation(U_22)
& empty(U_22) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3)],[f_20_2]) ).
cnf(f_20_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_21_2,plain,
! [U_24] :
( ? [U_23] :
( ~ empty(U_23)
& element(U_23,powerset(U_24)) )
| empty(U_24) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_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_21_2]) ).
cnf(f_21_4,plain,
( element(sK4(U_24),powerset(U_24))
| empty(U_24) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( ~ empty(sK4(U_24))
| empty(U_24) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_22_2,plain,
? [U_25] : empty(U_25),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_25,sK5)],[f_22_2]) ).
cnf(f_22_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_23_2,plain,
? [U_26] :
( function(U_26)
& empty(U_26)
& relation(U_26) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( function(sK6)
& empty(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_26,sK6)],[f_23_2]) ).
cnf(f_23_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
function(sK6),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_24_2,plain,
? [U_27] :
( relation(U_27)
& ~ empty(U_27) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( relation(sK7)
& ~ empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_27,sK7)],[f_24_2]) ).
cnf(f_24_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_25_2,plain,
! [U_29] :
? [U_28] :
( empty(U_28)
& element(U_28,powerset(U_29)) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_29] :
( empty(sK8(U_29))
& element(sK8(U_29),powerset(U_29)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_28,sK8(U_29))],[f_25_2]) ).
cnf(f_25_4,plain,
element(sK8(U_29),powerset(U_29)),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
empty(sK8(U_29)),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_26_2,plain,
? [U_30] : ~ empty(U_30),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_30,sK9)],[f_26_2]) ).
cnf(f_26_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_27_2,plain,
? [U_31] :
( one_to_one(U_31)
& function(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_31,sK10)],[f_27_2]) ).
cnf(f_27_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
function(sK10),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_28_2,plain,
? [U_32] :
( relation_empty_yielding(U_32)
& relation(U_32) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( relation_empty_yielding(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_32,sK11)],[f_28_2]) ).
cnf(f_28_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
relation_empty_yielding(sK11),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_29_2,plain,
! [U_34,U_33] : subset(U_34,U_34),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_34] : subset(U_34,U_34),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
subset(U_34,U_34),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_30_2,plain,
! [U_36,U_35] :
( element(U_36,U_35)
| ~ in(U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( element(U_36,U_35)
| ~ in(U_36,U_35) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_funct_1]) ).
fof(f_31_2,plain,
! [U_39,U_38] :
( ! [U_37] :
( apply(relation_composition(U_38,U_37),U_39) = apply(U_37,apply(U_38,U_39))
| ~ in(U_39,relation_dom(U_38))
| ~ function(U_37)
| ~ relation(U_37) )
| ~ function(U_38)
| ~ relation(U_38) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( apply(relation_composition(U_38,U_37),U_39) = apply(U_37,apply(U_38,U_39))
| ~ in(U_39,relation_dom(U_38))
| ~ function(U_37)
| ~ relation(U_37)
| ~ function(U_38)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_32_2,plain,
! [U_41,U_40] :
( in(U_41,U_40)
| empty(U_40)
| ~ element(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( in(U_41,U_40)
| empty(U_40)
| ~ element(U_41,U_40) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_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_33_2,plain,
! [U_43,U_42] :
( ( element(U_43,powerset(U_42))
| ~ subset(U_43,U_42) )
& ( subset(U_43,U_42)
| ~ element(U_43,powerset(U_42)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_47,U_45] :
( element(U_47,powerset(U_45))
| ~ subset(U_47,U_45) )
& ! [U_46,U_44] :
( subset(U_46,U_44)
| ~ element(U_46,powerset(U_44)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( subset(U_46,U_44)
| ~ element(U_46,powerset(U_44)) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( element(U_47,powerset(U_45))
| ~ subset(U_47,U_45) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_34_2,plain,
! [U_50,U_49,U_48] :
( element(U_50,U_48)
| ~ element(U_49,powerset(U_48))
| ~ in(U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( element(U_50,U_48)
| ~ element(U_49,powerset(U_48))
| ~ in(U_50,U_49) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A] :
( ! [B] :
( ( ( B = function_inverse(A)
| ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ( ( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& D = apply(B,C)
& in(C,relation_rng(A)) ) )
| relation_dom(B) != relation_rng(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t54_funct_1]) ).
fof(f_35_2,plain,
! [U_56] :
( ! [U_55] :
( ( ( U_55 = function_inverse(U_56)
| ? [U_54,U_53] :
( ( ( U_53 != apply(U_55,U_54)
| ~ in(U_54,relation_rng(U_56)) )
& U_54 = apply(U_56,U_53)
& in(U_53,relation_dom(U_56)) )
| ( ( U_54 != apply(U_56,U_53)
| ~ in(U_53,relation_dom(U_56)) )
& U_53 = apply(U_55,U_54)
& in(U_54,relation_rng(U_56)) ) )
| relation_dom(U_55) != relation_rng(U_56) )
& ( ( ! [U_52,U_51] :
( ( ( U_51 = apply(U_55,U_52)
& in(U_52,relation_rng(U_56)) )
| U_52 != apply(U_56,U_51)
| ~ in(U_51,relation_dom(U_56)) )
& ( ( U_52 = apply(U_56,U_51)
& in(U_51,relation_dom(U_56)) )
| U_51 != apply(U_55,U_52)
| ~ in(U_52,relation_rng(U_56)) ) )
& relation_dom(U_55) = relation_rng(U_56) )
| U_55 != function_inverse(U_56) ) )
| ~ function(U_55)
| ~ relation(U_55) )
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_56] :
( ! [U_55] :
( ( ( U_55 = function_inverse(U_56)
| ? [U_64,U_62] :
( ( U_62 != apply(U_55,U_64)
| ~ in(U_64,relation_rng(U_56)) )
& U_64 = apply(U_56,U_62)
& in(U_62,relation_dom(U_56)) )
| ? [U_63,U_61] :
( ( U_63 != apply(U_56,U_61)
| ~ in(U_61,relation_dom(U_56)) )
& U_61 = apply(U_55,U_63)
& in(U_63,relation_rng(U_56)) )
| relation_dom(U_55) != relation_rng(U_56) )
& ( ( ! [U_60,U_58] :
( ( U_58 = apply(U_55,U_60)
& in(U_60,relation_rng(U_56)) )
| U_60 != apply(U_56,U_58)
| ~ in(U_58,relation_dom(U_56)) )
& ! [U_59,U_57] :
( ( U_59 = apply(U_56,U_57)
& in(U_57,relation_dom(U_56)) )
| U_57 != apply(U_55,U_59)
| ~ in(U_59,relation_rng(U_56)) )
& relation_dom(U_55) = relation_rng(U_56) )
| U_55 != function_inverse(U_56) ) )
| ~ function(U_55)
| ~ relation(U_55) )
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
! [U_56] :
( ! [U_55] :
( ( ( U_55 = function_inverse(U_56)
| ? [U_64,U_62] :
( ( U_62 != apply(U_55,U_64)
| ~ in(U_64,relation_rng(U_56)) )
& U_64 = apply(U_56,U_62)
& in(U_62,relation_dom(U_56)) )
| ? [U_61] :
( ( sK12(U_56,U_55) != apply(U_56,U_61)
| ~ in(U_61,relation_dom(U_56)) )
& U_61 = apply(U_55,sK12(U_56,U_55))
& in(sK12(U_56,U_55),relation_rng(U_56)) )
| relation_dom(U_55) != relation_rng(U_56) )
& ( ( ! [U_60,U_58] :
( ( U_58 = apply(U_55,U_60)
& in(U_60,relation_rng(U_56)) )
| U_60 != apply(U_56,U_58)
| ~ in(U_58,relation_dom(U_56)) )
& ! [U_59,U_57] :
( ( U_59 = apply(U_56,U_57)
& in(U_57,relation_dom(U_56)) )
| U_57 != apply(U_55,U_59)
| ~ in(U_59,relation_rng(U_56)) )
& relation_dom(U_55) = relation_rng(U_56) )
| U_55 != function_inverse(U_56) ) )
| ~ function(U_55)
| ~ relation(U_55) )
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_63,sK12(U_56,U_55))],[f_35_3]) ).
fof(f_35_5,plain,
! [U_56] :
( ! [U_55] :
( ( ( U_55 = function_inverse(U_56)
| ? [U_64,U_62] :
( ( U_62 != apply(U_55,U_64)
| ~ in(U_64,relation_rng(U_56)) )
& U_64 = apply(U_56,U_62)
& in(U_62,relation_dom(U_56)) )
| ( ( sK12(U_56,U_55) != apply(U_56,sK13(U_56,U_55))
| ~ in(sK13(U_56,U_55),relation_dom(U_56)) )
& sK13(U_56,U_55) = apply(U_55,sK12(U_56,U_55))
& in(sK12(U_56,U_55),relation_rng(U_56)) )
| relation_dom(U_55) != relation_rng(U_56) )
& ( ( ! [U_60,U_58] :
( ( U_58 = apply(U_55,U_60)
& in(U_60,relation_rng(U_56)) )
| U_60 != apply(U_56,U_58)
| ~ in(U_58,relation_dom(U_56)) )
& ! [U_59,U_57] :
( ( U_59 = apply(U_56,U_57)
& in(U_57,relation_dom(U_56)) )
| U_57 != apply(U_55,U_59)
| ~ in(U_59,relation_rng(U_56)) )
& relation_dom(U_55) = relation_rng(U_56) )
| U_55 != function_inverse(U_56) ) )
| ~ function(U_55)
| ~ relation(U_55) )
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_61,sK13(U_56,U_55))],[f_35_4]) ).
fof(f_35_6,plain,
! [U_56] :
( ! [U_55] :
( ( ( U_55 = function_inverse(U_56)
| ? [U_62] :
( ( U_62 != apply(U_55,sK14(U_56,U_55))
| ~ in(sK14(U_56,U_55),relation_rng(U_56)) )
& sK14(U_56,U_55) = apply(U_56,U_62)
& in(U_62,relation_dom(U_56)) )
| ( ( sK12(U_56,U_55) != apply(U_56,sK13(U_56,U_55))
| ~ in(sK13(U_56,U_55),relation_dom(U_56)) )
& sK13(U_56,U_55) = apply(U_55,sK12(U_56,U_55))
& in(sK12(U_56,U_55),relation_rng(U_56)) )
| relation_dom(U_55) != relation_rng(U_56) )
& ( ( ! [U_60,U_58] :
( ( U_58 = apply(U_55,U_60)
& in(U_60,relation_rng(U_56)) )
| U_60 != apply(U_56,U_58)
| ~ in(U_58,relation_dom(U_56)) )
& ! [U_59,U_57] :
( ( U_59 = apply(U_56,U_57)
& in(U_57,relation_dom(U_56)) )
| U_57 != apply(U_55,U_59)
| ~ in(U_59,relation_rng(U_56)) )
& relation_dom(U_55) = relation_rng(U_56) )
| U_55 != function_inverse(U_56) ) )
| ~ function(U_55)
| ~ relation(U_55) )
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_64,sK14(U_56,U_55))],[f_35_5]) ).
fof(f_35_7,plain,
! [U_56] :
( ! [U_55] :
( ( ( U_55 = function_inverse(U_56)
| ( ( sK15(U_56,U_55) != apply(U_55,sK14(U_56,U_55))
| ~ in(sK14(U_56,U_55),relation_rng(U_56)) )
& sK14(U_56,U_55) = apply(U_56,sK15(U_56,U_55))
& in(sK15(U_56,U_55),relation_dom(U_56)) )
| ( ( sK12(U_56,U_55) != apply(U_56,sK13(U_56,U_55))
| ~ in(sK13(U_56,U_55),relation_dom(U_56)) )
& sK13(U_56,U_55) = apply(U_55,sK12(U_56,U_55))
& in(sK12(U_56,U_55),relation_rng(U_56)) )
| relation_dom(U_55) != relation_rng(U_56) )
& ( ( ! [U_60,U_58] :
( ( U_58 = apply(U_55,U_60)
& in(U_60,relation_rng(U_56)) )
| U_60 != apply(U_56,U_58)
| ~ in(U_58,relation_dom(U_56)) )
& ! [U_59,U_57] :
( ( U_59 = apply(U_56,U_57)
& in(U_57,relation_dom(U_56)) )
| U_57 != apply(U_55,U_59)
| ~ in(U_59,relation_rng(U_56)) )
& relation_dom(U_55) = relation_rng(U_56) )
| U_55 != function_inverse(U_56) ) )
| ~ function(U_55)
| ~ relation(U_55) )
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_62,sK15(U_56,U_55))],[f_35_6]) ).
cnf(f_35_8,plain,
( relation_dom(U_55) = relation_rng(U_56)
| U_55 != function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_9,plain,
( in(U_57,relation_dom(U_56))
| U_57 != apply(U_55,U_59)
| ~ in(U_59,relation_rng(U_56))
| U_55 != function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_10,plain,
( U_59 = apply(U_56,U_57)
| U_57 != apply(U_55,U_59)
| ~ in(U_59,relation_rng(U_56))
| U_55 != function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_11,plain,
( in(U_60,relation_rng(U_56))
| U_60 != apply(U_56,U_58)
| ~ in(U_58,relation_dom(U_56))
| U_55 != function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_12,plain,
( U_58 = apply(U_55,U_60)
| U_60 != apply(U_56,U_58)
| ~ in(U_58,relation_dom(U_56))
| U_55 != function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_13,plain,
( in(sK15(U_56,U_55),relation_dom(U_56))
| in(sK12(U_56,U_55),relation_rng(U_56))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_14,plain,
( sK14(U_56,U_55) = apply(U_56,sK15(U_56,U_55))
| in(sK12(U_56,U_55),relation_rng(U_56))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_15,plain,
( in(sK15(U_56,U_55),relation_dom(U_56))
| sK13(U_56,U_55) = apply(U_55,sK12(U_56,U_55))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_16,plain,
( sK14(U_56,U_55) = apply(U_56,sK15(U_56,U_55))
| sK13(U_56,U_55) = apply(U_55,sK12(U_56,U_55))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_17,plain,
( in(sK12(U_56,U_55),relation_rng(U_56))
| sK15(U_56,U_55) != apply(U_55,sK14(U_56,U_55))
| ~ in(sK14(U_56,U_55),relation_rng(U_56))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_18,plain,
( sK13(U_56,U_55) = apply(U_55,sK12(U_56,U_55))
| sK15(U_56,U_55) != apply(U_55,sK14(U_56,U_55))
| ~ in(sK14(U_56,U_55),relation_rng(U_56))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_19,plain,
( in(sK15(U_56,U_55),relation_dom(U_56))
| sK12(U_56,U_55) != apply(U_56,sK13(U_56,U_55))
| ~ in(sK13(U_56,U_55),relation_dom(U_56))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_20,plain,
( sK14(U_56,U_55) = apply(U_56,sK15(U_56,U_55))
| sK12(U_56,U_55) != apply(U_56,sK13(U_56,U_55))
| ~ in(sK13(U_56,U_55),relation_dom(U_56))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_21,plain,
( sK15(U_56,U_55) != apply(U_55,sK14(U_56,U_55))
| ~ in(sK14(U_56,U_55),relation_rng(U_56))
| sK12(U_56,U_55) != apply(U_56,sK13(U_56,U_55))
| ~ in(sK13(U_56,U_55),relation_dom(U_56))
| relation_dom(U_55) != relation_rng(U_56)
| U_55 = function_inverse(U_56)
| ~ function(U_55)
| ~ relation(U_55)
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_35_7]) ).
fof(f_36_1,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_dom(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(B,function_inverse(B)),A)
& A = apply(function_inverse(B),apply(B,A)) ) ) ),
inference(negate,[status(cth)],[t56_funct_1]) ).
fof(f_36_2,negated_conjecture,
? [A,B] :
( ( A != apply(relation_composition(B,function_inverse(B)),A)
| A != apply(function_inverse(B),apply(B,A)) )
& in(A,relation_dom(B))
& one_to_one(B)
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_36_1]) ).
fof(f_36_3,negated_conjecture,
? [U_66,U_65] :
( ( U_66 != apply(relation_composition(U_65,function_inverse(U_65)),U_66)
| U_66 != apply(function_inverse(U_65),apply(U_65,U_66)) )
& in(U_66,relation_dom(U_65))
& one_to_one(U_65)
& function(U_65)
& relation(U_65) ),
inference(variable_rename,[status(thm)],[f_36_2]) ).
fof(f_36_4,negated_conjecture,
? [U_65] :
( ( sK16 != apply(relation_composition(U_65,function_inverse(U_65)),sK16)
| sK16 != apply(function_inverse(U_65),apply(U_65,sK16)) )
& in(sK16,relation_dom(U_65))
& one_to_one(U_65)
& function(U_65)
& relation(U_65) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_66,sK16)],[f_36_3]) ).
fof(f_36_5,negated_conjecture,
( ( sK16 != apply(relation_composition(sK17,function_inverse(sK17)),sK16)
| sK16 != apply(function_inverse(sK17),apply(sK17,sK16)) )
& in(sK16,relation_dom(sK17))
& one_to_one(sK17)
& function(sK17)
& relation(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_65,sK17)],[f_36_4]) ).
fof(f_36_6,negated_conjecture,
( ( sK16 != apply(relation_composition(sK17,function_inverse(sK17)),sK16)
| sK16 != apply(function_inverse(sK17),apply(sK17,sK16)) )
& in(sK16,relation_dom(sK17))
& one_to_one(sK17)
& function(sK17)
& relation(sK17) ),
inference(definitional_conversion,[status(esa)],[f_36_5]) ).
cnf(f_36_7,negated_conjecture,
relation(sK17),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_8,negated_conjecture,
function(sK17),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_9,negated_conjecture,
one_to_one(sK17),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_10,negated_conjecture,
in(sK16,relation_dom(sK17)),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_11,negated_conjecture,
( sK16 != apply(relation_composition(sK17,function_inverse(sK17)),sK16)
| sK16 != apply(function_inverse(sK17),apply(sK17,sK16)) ),
inference(clausify,[status(thm)],[f_36_6]) ).
fof(f_37_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_37_2,plain,
! [U_69,U_68,U_67] :
( ~ empty(U_67)
| ~ element(U_68,powerset(U_67))
| ~ in(U_69,U_68) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_69,U_68] :
( ! [U_67] :
( ~ empty(U_67)
| ~ element(U_68,powerset(U_67)) )
| ~ in(U_69,U_68) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( ~ empty(U_67)
| ~ element(U_68,powerset(U_67))
| ~ in(U_69,U_68) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_38_2,plain,
! [U_70] :
( U_70 = empty_set
| ~ empty(U_70) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( U_70 = empty_set
| ~ empty(U_70) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_39_2,plain,
! [U_72,U_71] :
( ~ empty(U_71)
| ~ in(U_72,U_71) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( ~ empty(U_71)
| ~ in(U_72,U_71) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_40_2,plain,
! [U_74,U_73] :
( ~ empty(U_73)
| U_74 = U_73
| ~ empty(U_74) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_74] :
( ! [U_73] :
( ~ empty(U_73)
| U_74 = U_73 )
| ~ empty(U_74) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( ~ empty(U_73)
| U_74 = U_73
| ~ empty(U_74) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
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,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_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,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,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_10,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(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,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(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,
( 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_18,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,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_23,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_24,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
% 0.00/0.03 % Problem : SEU023+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
% 0.08/0.35 % Computer : n018.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 23:15:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.67/0.94 % SZS status Theorem for theBenchmark
% 0.67/0.94 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------