%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU221+3 : 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 : n019.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 08:58:33 AM UTC 2026
% Result : Theorem 12.67s 13.00s
% Output : Proof 13.04s
% 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(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_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(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(t57_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t62_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
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] :
( ( ( one_to_one(A)
| ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) ) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(f_5_2,plain,
! [U_9] :
( ( ( one_to_one(U_9)
| ? [U_8,U_7] :
( U_8 != U_7
& apply(U_9,U_8) = apply(U_9,U_7)
& in(U_7,relation_dom(U_9))
& in(U_8,relation_dom(U_9)) ) )
& ( ! [U_6,U_5] :
( U_6 = U_5
| apply(U_9,U_6) != apply(U_9,U_5)
| ~ in(U_5,relation_dom(U_9))
| ~ in(U_6,relation_dom(U_9)) )
| ~ one_to_one(U_9) ) )
| ~ function(U_9)
| ~ relation(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_9] :
( ( ( one_to_one(U_9)
| ? [U_7] :
( sK1(U_9) != U_7
& apply(U_9,sK1(U_9)) = apply(U_9,U_7)
& in(U_7,relation_dom(U_9))
& in(sK1(U_9),relation_dom(U_9)) ) )
& ( ! [U_6,U_5] :
( U_6 = U_5
| apply(U_9,U_6) != apply(U_9,U_5)
| ~ in(U_5,relation_dom(U_9))
| ~ in(U_6,relation_dom(U_9)) )
| ~ one_to_one(U_9) ) )
| ~ function(U_9)
| ~ relation(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_9))],[f_5_2]) ).
fof(f_5_4,plain,
! [U_9] :
( ( ( one_to_one(U_9)
| ( sK1(U_9) != sK2(U_9)
& apply(U_9,sK1(U_9)) = apply(U_9,sK2(U_9))
& in(sK2(U_9),relation_dom(U_9))
& in(sK1(U_9),relation_dom(U_9)) ) )
& ( ! [U_6,U_5] :
( U_6 = U_5
| apply(U_9,U_6) != apply(U_9,U_5)
| ~ in(U_5,relation_dom(U_9))
| ~ in(U_6,relation_dom(U_9)) )
| ~ one_to_one(U_9) ) )
| ~ function(U_9)
| ~ relation(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_7,sK2(U_9))],[f_5_3]) ).
cnf(f_5_5,plain,
( U_6 = U_5
| apply(U_9,U_6) != apply(U_9,U_5)
| ~ in(U_5,relation_dom(U_9))
| ~ in(U_6,relation_dom(U_9))
| ~ one_to_one(U_9)
| ~ function(U_9)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( in(sK1(U_9),relation_dom(U_9))
| one_to_one(U_9)
| ~ function(U_9)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( in(sK2(U_9),relation_dom(U_9))
| one_to_one(U_9)
| ~ function(U_9)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_8,plain,
( apply(U_9,sK1(U_9)) = apply(U_9,sK2(U_9))
| one_to_one(U_9)
| ~ function(U_9)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_9,plain,
( sK1(U_9) != sK2(U_9)
| one_to_one(U_9)
| ~ function(U_9)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_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_6_2,plain,
! [U_10] :
( ( function(function_inverse(U_10))
& relation(function_inverse(U_10)) )
| ~ function(U_10)
| ~ relation(U_10) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( relation(function_inverse(U_10))
| ~ function(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( function(function_inverse(U_10))
| ~ function(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_7_2,plain,
! [U_12,U_11] :
( relation(relation_composition(U_12,U_11))
| ~ relation(U_11)
| ~ relation(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( relation(relation_composition(U_12,U_11))
| ~ relation(U_11)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_8_2,plain,
! [U_14] :
? [U_13] : element(U_13,U_14),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_14] : element(sK3(U_14),U_14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_13,sK3(U_14))],[f_8_2]) ).
cnf(f_8_4,plain,
element(sK3(U_14),U_14),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_9_2,plain,
! [U_16,U_15] :
( ( relation(relation_composition(U_15,U_16))
& empty(relation_composition(U_15,U_16)) )
| ~ relation(U_15)
| ~ empty(U_16) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( empty(relation_composition(U_15,U_16))
| ~ relation(U_15)
| ~ empty(U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( relation(relation_composition(U_15,U_16))
| ~ relation(U_15)
| ~ empty(U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_10_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
cnf(f_10_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_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_11_2,plain,
! [U_18,U_17] :
( ( function(relation_composition(U_18,U_17))
& relation(relation_composition(U_18,U_17)) )
| ~ function(U_17)
| ~ relation(U_17)
| ~ function(U_18)
| ~ relation(U_18) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(relation_composition(U_18,U_17))
| ~ function(U_17)
| ~ relation(U_17)
| ~ function(U_18)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( function(relation_composition(U_18,U_17))
| ~ function(U_17)
| ~ relation(U_17)
| ~ function(U_18)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_12_2,plain,
! [U_19] : ~ empty(powerset(U_19)),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
~ empty(powerset(U_19)),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_13_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_14_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_15_2,plain,
! [U_20] :
( ~ empty(relation_dom(U_20))
| ~ relation(U_20)
| empty(U_20) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( ~ empty(relation_dom(U_20))
| ~ relation(U_20)
| empty(U_20) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_16_2,plain,
! [U_21] :
( ~ empty(relation_rng(U_21))
| ~ relation(U_21)
| empty(U_21) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( ~ empty(relation_rng(U_21))
| ~ relation(U_21)
| empty(U_21) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_17_2,plain,
! [U_22] :
( ( relation(relation_dom(U_22))
& empty(relation_dom(U_22)) )
| ~ empty(U_22) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( empty(relation_dom(U_22))
| ~ empty(U_22) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( relation(relation_dom(U_22))
| ~ empty(U_22) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_18_2,plain,
! [U_23] :
( ( relation(relation_rng(U_23))
& empty(relation_rng(U_23)) )
| ~ empty(U_23) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( empty(relation_rng(U_23))
| ~ empty(U_23) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( relation(relation_rng(U_23))
| ~ empty(U_23) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_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_19_2,plain,
! [U_25,U_24] :
( ( relation(relation_composition(U_25,U_24))
& empty(relation_composition(U_25,U_24)) )
| ~ relation(U_24)
| ~ empty(U_25) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( empty(relation_composition(U_25,U_24))
| ~ relation(U_24)
| ~ empty(U_25) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( relation(relation_composition(U_25,U_24))
| ~ relation(U_24)
| ~ empty(U_25) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_20_2,plain,
? [U_26] :
( function(U_26)
& relation(U_26) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( function(sK4)
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4)],[f_20_2]) ).
cnf(f_20_4,plain,
relation(sK4),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
function(sK4),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_21_2,plain,
? [U_27] :
( relation(U_27)
& empty(U_27) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( relation(sK5)
& empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_27,sK5)],[f_21_2]) ).
cnf(f_21_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_22_2,plain,
! [U_29] :
( ? [U_28] :
( ~ empty(U_28)
& element(U_28,powerset(U_29)) )
| empty(U_29) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_29] :
( ( ~ empty(sK6(U_29))
& element(sK6(U_29),powerset(U_29)) )
| empty(U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_28,sK6(U_29))],[f_22_2]) ).
cnf(f_22_4,plain,
( element(sK6(U_29),powerset(U_29))
| empty(U_29) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( ~ empty(sK6(U_29))
| empty(U_29) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_23_2,plain,
? [U_30] : empty(U_30),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_30,sK7)],[f_23_2]) ).
cnf(f_23_4,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_24_2,plain,
? [U_31] :
( function(U_31)
& empty(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( function(sK8)
& empty(sK8)
& relation(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_31,sK8)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
function(sK8),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_25_2,plain,
? [U_32] :
( relation(U_32)
& ~ empty(U_32) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_32,sK9)],[f_25_2]) ).
cnf(f_25_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_26_2,plain,
! [U_34] :
? [U_33] :
( empty(U_33)
& element(U_33,powerset(U_34)) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_34] :
( empty(sK10(U_34))
& element(sK10(U_34),powerset(U_34)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_33,sK10(U_34))],[f_26_2]) ).
cnf(f_26_4,plain,
element(sK10(U_34),powerset(U_34)),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
empty(sK10(U_34)),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_27_2,plain,
? [U_35] : ~ empty(U_35),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
~ empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_35,sK11)],[f_27_2]) ).
cnf(f_27_4,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_28_2,plain,
? [U_36] :
( one_to_one(U_36)
& function(U_36)
& relation(U_36) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_36,sK12)],[f_28_2]) ).
cnf(f_28_4,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
function(sK12),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
one_to_one(sK12),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_29_2,plain,
? [U_37] :
( relation_empty_yielding(U_37)
& relation(U_37) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( relation_empty_yielding(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_37,sK13)],[f_29_2]) ).
cnf(f_29_4,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
relation_empty_yielding(sK13),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_30_2,plain,
! [U_39,U_38] : subset(U_39,U_39),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_39] : subset(U_39,U_39),
inference(miniscope,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
subset(U_39,U_39),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_31_2,plain,
! [U_41,U_40] :
( element(U_41,U_40)
| ~ in(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( element(U_41,U_40)
| ~ in(U_41,U_40) ),
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_43,U_42] :
( in(U_43,U_42)
| empty(U_42)
| ~ element(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( in(U_43,U_42)
| empty(U_42)
| ~ element(U_43,U_42) ),
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_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_33_1]) ).
fof(f_33_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_33_2]) ).
cnf(f_33_4,plain,
( subset(U_48,U_46)
| ~ element(U_48,powerset(U_46)) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( element(U_49,powerset(U_47))
| ~ subset(U_49,U_47) ),
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_52,U_51,U_50] :
( element(U_52,U_50)
| ~ element(U_51,powerset(U_50))
| ~ in(U_52,U_51) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( element(U_52,U_50)
| ~ element(U_51,powerset(U_50))
| ~ in(U_52,U_51) ),
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_58] :
( ! [U_57] :
( ( ( U_57 = function_inverse(U_58)
| ? [U_56,U_55] :
( ( ( U_55 != apply(U_57,U_56)
| ~ in(U_56,relation_rng(U_58)) )
& U_56 = apply(U_58,U_55)
& in(U_55,relation_dom(U_58)) )
| ( ( U_56 != apply(U_58,U_55)
| ~ in(U_55,relation_dom(U_58)) )
& U_55 = apply(U_57,U_56)
& in(U_56,relation_rng(U_58)) ) )
| relation_dom(U_57) != relation_rng(U_58) )
& ( ( ! [U_54,U_53] :
( ( ( U_53 = apply(U_57,U_54)
& in(U_54,relation_rng(U_58)) )
| U_54 != apply(U_58,U_53)
| ~ in(U_53,relation_dom(U_58)) )
& ( ( U_54 = apply(U_58,U_53)
& in(U_53,relation_dom(U_58)) )
| U_53 != apply(U_57,U_54)
| ~ in(U_54,relation_rng(U_58)) ) )
& relation_dom(U_57) = relation_rng(U_58) )
| U_57 != function_inverse(U_58) ) )
| ~ function(U_57)
| ~ relation(U_57) )
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_58] :
( ! [U_57] :
( ( ( U_57 = function_inverse(U_58)
| ? [U_66,U_64] :
( ( U_64 != apply(U_57,U_66)
| ~ in(U_66,relation_rng(U_58)) )
& U_66 = apply(U_58,U_64)
& in(U_64,relation_dom(U_58)) )
| ? [U_65,U_63] :
( ( U_65 != apply(U_58,U_63)
| ~ in(U_63,relation_dom(U_58)) )
& U_63 = apply(U_57,U_65)
& in(U_65,relation_rng(U_58)) )
| relation_dom(U_57) != relation_rng(U_58) )
& ( ( ! [U_62,U_60] :
( ( U_60 = apply(U_57,U_62)
& in(U_62,relation_rng(U_58)) )
| U_62 != apply(U_58,U_60)
| ~ in(U_60,relation_dom(U_58)) )
& ! [U_61,U_59] :
( ( U_61 = apply(U_58,U_59)
& in(U_59,relation_dom(U_58)) )
| U_59 != apply(U_57,U_61)
| ~ in(U_61,relation_rng(U_58)) )
& relation_dom(U_57) = relation_rng(U_58) )
| U_57 != function_inverse(U_58) ) )
| ~ function(U_57)
| ~ relation(U_57) )
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
! [U_58] :
( ! [U_57] :
( ( ( U_57 = function_inverse(U_58)
| ? [U_66,U_64] :
( ( U_64 != apply(U_57,U_66)
| ~ in(U_66,relation_rng(U_58)) )
& U_66 = apply(U_58,U_64)
& in(U_64,relation_dom(U_58)) )
| ? [U_63] :
( ( sK14(U_58,U_57) != apply(U_58,U_63)
| ~ in(U_63,relation_dom(U_58)) )
& U_63 = apply(U_57,sK14(U_58,U_57))
& in(sK14(U_58,U_57),relation_rng(U_58)) )
| relation_dom(U_57) != relation_rng(U_58) )
& ( ( ! [U_62,U_60] :
( ( U_60 = apply(U_57,U_62)
& in(U_62,relation_rng(U_58)) )
| U_62 != apply(U_58,U_60)
| ~ in(U_60,relation_dom(U_58)) )
& ! [U_61,U_59] :
( ( U_61 = apply(U_58,U_59)
& in(U_59,relation_dom(U_58)) )
| U_59 != apply(U_57,U_61)
| ~ in(U_61,relation_rng(U_58)) )
& relation_dom(U_57) = relation_rng(U_58) )
| U_57 != function_inverse(U_58) ) )
| ~ function(U_57)
| ~ relation(U_57) )
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_65,sK14(U_58,U_57))],[f_35_3]) ).
fof(f_35_5,plain,
! [U_58] :
( ! [U_57] :
( ( ( U_57 = function_inverse(U_58)
| ? [U_66,U_64] :
( ( U_64 != apply(U_57,U_66)
| ~ in(U_66,relation_rng(U_58)) )
& U_66 = apply(U_58,U_64)
& in(U_64,relation_dom(U_58)) )
| ( ( sK14(U_58,U_57) != apply(U_58,sK15(U_58,U_57))
| ~ in(sK15(U_58,U_57),relation_dom(U_58)) )
& sK15(U_58,U_57) = apply(U_57,sK14(U_58,U_57))
& in(sK14(U_58,U_57),relation_rng(U_58)) )
| relation_dom(U_57) != relation_rng(U_58) )
& ( ( ! [U_62,U_60] :
( ( U_60 = apply(U_57,U_62)
& in(U_62,relation_rng(U_58)) )
| U_62 != apply(U_58,U_60)
| ~ in(U_60,relation_dom(U_58)) )
& ! [U_61,U_59] :
( ( U_61 = apply(U_58,U_59)
& in(U_59,relation_dom(U_58)) )
| U_59 != apply(U_57,U_61)
| ~ in(U_61,relation_rng(U_58)) )
& relation_dom(U_57) = relation_rng(U_58) )
| U_57 != function_inverse(U_58) ) )
| ~ function(U_57)
| ~ relation(U_57) )
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_63,sK15(U_58,U_57))],[f_35_4]) ).
fof(f_35_6,plain,
! [U_58] :
( ! [U_57] :
( ( ( U_57 = function_inverse(U_58)
| ? [U_64] :
( ( U_64 != apply(U_57,sK16(U_58,U_57))
| ~ in(sK16(U_58,U_57),relation_rng(U_58)) )
& sK16(U_58,U_57) = apply(U_58,U_64)
& in(U_64,relation_dom(U_58)) )
| ( ( sK14(U_58,U_57) != apply(U_58,sK15(U_58,U_57))
| ~ in(sK15(U_58,U_57),relation_dom(U_58)) )
& sK15(U_58,U_57) = apply(U_57,sK14(U_58,U_57))
& in(sK14(U_58,U_57),relation_rng(U_58)) )
| relation_dom(U_57) != relation_rng(U_58) )
& ( ( ! [U_62,U_60] :
( ( U_60 = apply(U_57,U_62)
& in(U_62,relation_rng(U_58)) )
| U_62 != apply(U_58,U_60)
| ~ in(U_60,relation_dom(U_58)) )
& ! [U_61,U_59] :
( ( U_61 = apply(U_58,U_59)
& in(U_59,relation_dom(U_58)) )
| U_59 != apply(U_57,U_61)
| ~ in(U_61,relation_rng(U_58)) )
& relation_dom(U_57) = relation_rng(U_58) )
| U_57 != function_inverse(U_58) ) )
| ~ function(U_57)
| ~ relation(U_57) )
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_66,sK16(U_58,U_57))],[f_35_5]) ).
fof(f_35_7,plain,
! [U_58] :
( ! [U_57] :
( ( ( U_57 = function_inverse(U_58)
| ( ( sK17(U_58,U_57) != apply(U_57,sK16(U_58,U_57))
| ~ in(sK16(U_58,U_57),relation_rng(U_58)) )
& sK16(U_58,U_57) = apply(U_58,sK17(U_58,U_57))
& in(sK17(U_58,U_57),relation_dom(U_58)) )
| ( ( sK14(U_58,U_57) != apply(U_58,sK15(U_58,U_57))
| ~ in(sK15(U_58,U_57),relation_dom(U_58)) )
& sK15(U_58,U_57) = apply(U_57,sK14(U_58,U_57))
& in(sK14(U_58,U_57),relation_rng(U_58)) )
| relation_dom(U_57) != relation_rng(U_58) )
& ( ( ! [U_62,U_60] :
( ( U_60 = apply(U_57,U_62)
& in(U_62,relation_rng(U_58)) )
| U_62 != apply(U_58,U_60)
| ~ in(U_60,relation_dom(U_58)) )
& ! [U_61,U_59] :
( ( U_61 = apply(U_58,U_59)
& in(U_59,relation_dom(U_58)) )
| U_59 != apply(U_57,U_61)
| ~ in(U_61,relation_rng(U_58)) )
& relation_dom(U_57) = relation_rng(U_58) )
| U_57 != function_inverse(U_58) ) )
| ~ function(U_57)
| ~ relation(U_57) )
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_64,sK17(U_58,U_57))],[f_35_6]) ).
cnf(f_35_8,plain,
( relation_dom(U_57) = relation_rng(U_58)
| U_57 != function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_9,plain,
( in(U_59,relation_dom(U_58))
| U_59 != apply(U_57,U_61)
| ~ in(U_61,relation_rng(U_58))
| U_57 != function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_10,plain,
( U_61 = apply(U_58,U_59)
| U_59 != apply(U_57,U_61)
| ~ in(U_61,relation_rng(U_58))
| U_57 != function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_11,plain,
( in(U_62,relation_rng(U_58))
| U_62 != apply(U_58,U_60)
| ~ in(U_60,relation_dom(U_58))
| U_57 != function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_12,plain,
( U_60 = apply(U_57,U_62)
| U_62 != apply(U_58,U_60)
| ~ in(U_60,relation_dom(U_58))
| U_57 != function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_13,plain,
( in(sK17(U_58,U_57),relation_dom(U_58))
| in(sK14(U_58,U_57),relation_rng(U_58))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_14,plain,
( sK16(U_58,U_57) = apply(U_58,sK17(U_58,U_57))
| in(sK14(U_58,U_57),relation_rng(U_58))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_15,plain,
( in(sK17(U_58,U_57),relation_dom(U_58))
| sK15(U_58,U_57) = apply(U_57,sK14(U_58,U_57))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_16,plain,
( sK16(U_58,U_57) = apply(U_58,sK17(U_58,U_57))
| sK15(U_58,U_57) = apply(U_57,sK14(U_58,U_57))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_17,plain,
( in(sK14(U_58,U_57),relation_rng(U_58))
| sK17(U_58,U_57) != apply(U_57,sK16(U_58,U_57))
| ~ in(sK16(U_58,U_57),relation_rng(U_58))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_18,plain,
( sK15(U_58,U_57) = apply(U_57,sK14(U_58,U_57))
| sK17(U_58,U_57) != apply(U_57,sK16(U_58,U_57))
| ~ in(sK16(U_58,U_57),relation_rng(U_58))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_19,plain,
( in(sK17(U_58,U_57),relation_dom(U_58))
| sK14(U_58,U_57) != apply(U_58,sK15(U_58,U_57))
| ~ in(sK15(U_58,U_57),relation_dom(U_58))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_20,plain,
( sK16(U_58,U_57) = apply(U_58,sK17(U_58,U_57))
| sK14(U_58,U_57) != apply(U_58,sK15(U_58,U_57))
| ~ in(sK15(U_58,U_57),relation_dom(U_58))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_21,plain,
( sK17(U_58,U_57) != apply(U_57,sK16(U_58,U_57))
| ~ in(sK16(U_58,U_57),relation_rng(U_58))
| sK14(U_58,U_57) != apply(U_58,sK15(U_58,U_57))
| ~ in(sK15(U_58,U_57),relation_dom(U_58))
| relation_dom(U_57) != relation_rng(U_58)
| U_57 = function_inverse(U_58)
| ~ function(U_57)
| ~ relation(U_57)
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_35_7]) ).
fof(f_36_1,plain,
! [A,B] :
( ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) )
| ~ in(A,relation_rng(B))
| ~ one_to_one(B)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t57_funct_1]) ).
fof(f_36_2,plain,
! [U_68,U_67] :
( ( U_68 = apply(relation_composition(function_inverse(U_67),U_67),U_68)
& U_68 = apply(U_67,apply(function_inverse(U_67),U_68)) )
| ~ in(U_68,relation_rng(U_67))
| ~ one_to_one(U_67)
| ~ function(U_67)
| ~ relation(U_67) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( U_68 = apply(U_67,apply(function_inverse(U_67),U_68))
| ~ in(U_68,relation_rng(U_67))
| ~ one_to_one(U_67)
| ~ function(U_67)
| ~ relation(U_67) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( U_68 = apply(relation_composition(function_inverse(U_67),U_67),U_68)
| ~ in(U_68,relation_rng(U_67))
| ~ one_to_one(U_67)
| ~ function(U_67)
| ~ relation(U_67) ),
inference(clausify,[status(thm)],[f_36_2]) ).
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_71,U_70,U_69] :
( ~ empty(U_69)
| ~ element(U_70,powerset(U_69))
| ~ in(U_71,U_70) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_71,U_70] :
( ! [U_69] :
( ~ empty(U_69)
| ~ element(U_70,powerset(U_69)) )
| ~ in(U_71,U_70) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( ~ empty(U_69)
| ~ element(U_70,powerset(U_69))
| ~ in(U_71,U_70) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
inference(negate,[status(cth)],[t62_funct_1]) ).
fof(f_38_2,negated_conjecture,
? [A] :
( ~ one_to_one(function_inverse(A))
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_38_1]) ).
fof(f_38_3,negated_conjecture,
? [U_72] :
( ~ one_to_one(function_inverse(U_72))
& one_to_one(U_72)
& function(U_72)
& relation(U_72) ),
inference(variable_rename,[status(thm)],[f_38_2]) ).
fof(f_38_4,negated_conjecture,
( ~ one_to_one(function_inverse(sK18))
& one_to_one(sK18)
& function(sK18)
& relation(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_72,sK18)],[f_38_3]) ).
fof(f_38_5,negated_conjecture,
( ~ one_to_one(function_inverse(sK18))
& one_to_one(sK18)
& function(sK18)
& relation(sK18) ),
inference(definitional_conversion,[status(esa)],[f_38_4]) ).
cnf(f_38_6,negated_conjecture,
relation(sK18),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_7,negated_conjecture,
function(sK18),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_8,negated_conjecture,
one_to_one(sK18),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_9,negated_conjecture,
~ one_to_one(function_inverse(sK18)),
inference(clausify,[status(thm)],[f_38_5]) ).
fof(f_39_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_39_2,plain,
! [U_73] :
( U_73 = empty_set
| ~ empty(U_73) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( U_73 = empty_set
| ~ empty(U_73) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_40_2,plain,
! [U_75,U_74] :
( ~ empty(U_74)
| ~ in(U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( ~ empty(U_74)
| ~ in(U_75,U_74) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_41_2,plain,
! [U_77,U_76] :
( ~ empty(U_76)
| U_77 = U_76
| ~ empty(U_77) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_77] :
( ! [U_76] :
( ~ empty(U_76)
| U_77 = U_76 )
| ~ empty(U_77) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( ~ empty(U_76)
| U_77 = U_76
| ~ empty(U_77) ),
inference(clausify,[status(thm)],[f_41_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,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| 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,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| 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,
( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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_24,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_25,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_26,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 : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n019.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sat Sep 19 23:34:20 UTC 2026
% 0.08/0.33 % CPUTime :
% 12.67/13.00 % SZS status Theorem for theBenchmark
% 12.67/13.00 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------