%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU221+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 0.65s 1.00s
% Output : Proof 0.76s
% 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_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_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_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_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_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(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_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_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_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(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(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(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,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_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_9_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_9_1]) ).
cnf(f_9_3,plain,
( relation(function_inverse(U_10))
| ~ function(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( function(function_inverse(U_10))
| ~ function(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_11_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_11_1]) ).
cnf(f_11_3,plain,
( relation(relation_composition(U_12,U_11))
| ~ relation(U_11)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_13_2,plain,
! [U_14] :
? [U_13] : element(U_13,U_14),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_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_13_2]) ).
cnf(f_13_4,plain,
element(sK3(U_14),U_14),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_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_14_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_14_1]) ).
cnf(f_14_3,plain,
( empty(relation_composition(U_15,U_16))
| ~ relation(U_15)
| ~ empty(U_16) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( relation(relation_composition(U_15,U_16))
| ~ relation(U_15)
| ~ empty(U_16) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_15_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_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_16_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_16_1]) ).
cnf(f_16_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_16_2]) ).
cnf(f_16_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_16_2]) ).
fof(f_17_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_17_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_18_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_19_2,plain,
! [U_19] :
( ~ empty(relation_dom(U_19))
| ~ relation(U_19)
| empty(U_19) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( ~ empty(relation_dom(U_19))
| ~ relation(U_19)
| empty(U_19) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_20_2,plain,
! [U_20] :
( ~ empty(relation_rng(U_20))
| ~ relation(U_20)
| empty(U_20) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ~ empty(relation_rng(U_20))
| ~ relation(U_20)
| empty(U_20) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_21_2,plain,
! [U_21] :
( ( relation(relation_dom(U_21))
& empty(relation_dom(U_21)) )
| ~ empty(U_21) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( empty(relation_dom(U_21))
| ~ empty(U_21) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( relation(relation_dom(U_21))
| ~ empty(U_21) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_22_2,plain,
! [U_22] :
( ( relation(relation_rng(U_22))
& empty(relation_rng(U_22)) )
| ~ empty(U_22) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( empty(relation_rng(U_22))
| ~ empty(U_22) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( relation(relation_rng(U_22))
| ~ empty(U_22) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_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_23_2,plain,
! [U_24,U_23] :
( ( relation(relation_composition(U_24,U_23))
& empty(relation_composition(U_24,U_23)) )
| ~ relation(U_23)
| ~ empty(U_24) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( empty(relation_composition(U_24,U_23))
| ~ relation(U_23)
| ~ empty(U_24) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( relation(relation_composition(U_24,U_23))
| ~ relation(U_23)
| ~ empty(U_24) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_24_2,plain,
? [U_25] :
( function(U_25)
& relation(U_25) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( function(sK4)
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_25,sK4)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK4),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
function(sK4),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_25_2,plain,
? [U_26] :
( relation(U_26)
& empty(U_26) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation(sK5)
& empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_26,sK5)],[f_25_2]) ).
cnf(f_25_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_26_2,plain,
? [U_27] : empty(U_27),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_27,sK6)],[f_26_2]) ).
cnf(f_26_4,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_27_2,plain,
? [U_28] :
( function(U_28)
& empty(U_28)
& relation(U_28) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( function(sK7)
& empty(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_28,sK7)],[f_27_2]) ).
cnf(f_27_4,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
function(sK7),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_28_2,plain,
? [U_29] :
( relation(U_29)
& ~ empty(U_29) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( relation(sK8)
& ~ empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_29,sK8)],[f_28_2]) ).
cnf(f_28_4,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_29_2,plain,
? [U_30] : ~ empty(U_30),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_30,sK9)],[f_29_2]) ).
cnf(f_29_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_30_2,plain,
? [U_31] :
( one_to_one(U_31)
& function(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_31,sK10)],[f_30_2]) ).
cnf(f_30_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
function(sK10),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_31_2,plain,
? [U_32] :
( relation_empty_yielding(U_32)
& relation(U_32) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( relation_empty_yielding(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_32,sK11)],[f_31_2]) ).
cnf(f_31_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
relation_empty_yielding(sK11),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_32_2,plain,
! [U_34,U_33] :
( element(U_34,U_33)
| ~ in(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( element(U_34,U_33)
| ~ in(U_34,U_33) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_33_2,plain,
! [U_36,U_35] :
( in(U_36,U_35)
| empty(U_35)
| ~ element(U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( in(U_36,U_35)
| empty(U_35)
| ~ element(U_36,U_35) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
! [U_42] :
( ! [U_41] :
( ( ( U_41 = function_inverse(U_42)
| ? [U_40,U_39] :
( ( ( U_39 != apply(U_41,U_40)
| ~ in(U_40,relation_rng(U_42)) )
& U_40 = apply(U_42,U_39)
& in(U_39,relation_dom(U_42)) )
| ( ( U_40 != apply(U_42,U_39)
| ~ in(U_39,relation_dom(U_42)) )
& U_39 = apply(U_41,U_40)
& in(U_40,relation_rng(U_42)) ) )
| relation_dom(U_41) != relation_rng(U_42) )
& ( ( ! [U_38,U_37] :
( ( ( U_37 = apply(U_41,U_38)
& in(U_38,relation_rng(U_42)) )
| U_38 != apply(U_42,U_37)
| ~ in(U_37,relation_dom(U_42)) )
& ( ( U_38 = apply(U_42,U_37)
& in(U_37,relation_dom(U_42)) )
| U_37 != apply(U_41,U_38)
| ~ in(U_38,relation_rng(U_42)) ) )
& relation_dom(U_41) = relation_rng(U_42) )
| U_41 != function_inverse(U_42) ) )
| ~ function(U_41)
| ~ relation(U_41) )
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_42] :
( ! [U_41] :
( ( ( U_41 = function_inverse(U_42)
| ? [U_50,U_48] :
( ( U_48 != apply(U_41,U_50)
| ~ in(U_50,relation_rng(U_42)) )
& U_50 = apply(U_42,U_48)
& in(U_48,relation_dom(U_42)) )
| ? [U_49,U_47] :
( ( U_49 != apply(U_42,U_47)
| ~ in(U_47,relation_dom(U_42)) )
& U_47 = apply(U_41,U_49)
& in(U_49,relation_rng(U_42)) )
| relation_dom(U_41) != relation_rng(U_42) )
& ( ( ! [U_46,U_44] :
( ( U_44 = apply(U_41,U_46)
& in(U_46,relation_rng(U_42)) )
| U_46 != apply(U_42,U_44)
| ~ in(U_44,relation_dom(U_42)) )
& ! [U_45,U_43] :
( ( U_45 = apply(U_42,U_43)
& in(U_43,relation_dom(U_42)) )
| U_43 != apply(U_41,U_45)
| ~ in(U_45,relation_rng(U_42)) )
& relation_dom(U_41) = relation_rng(U_42) )
| U_41 != function_inverse(U_42) ) )
| ~ function(U_41)
| ~ relation(U_41) )
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
! [U_42] :
( ! [U_41] :
( ( ( U_41 = function_inverse(U_42)
| ? [U_50,U_48] :
( ( U_48 != apply(U_41,U_50)
| ~ in(U_50,relation_rng(U_42)) )
& U_50 = apply(U_42,U_48)
& in(U_48,relation_dom(U_42)) )
| ? [U_47] :
( ( sK12(U_42,U_41) != apply(U_42,U_47)
| ~ in(U_47,relation_dom(U_42)) )
& U_47 = apply(U_41,sK12(U_42,U_41))
& in(sK12(U_42,U_41),relation_rng(U_42)) )
| relation_dom(U_41) != relation_rng(U_42) )
& ( ( ! [U_46,U_44] :
( ( U_44 = apply(U_41,U_46)
& in(U_46,relation_rng(U_42)) )
| U_46 != apply(U_42,U_44)
| ~ in(U_44,relation_dom(U_42)) )
& ! [U_45,U_43] :
( ( U_45 = apply(U_42,U_43)
& in(U_43,relation_dom(U_42)) )
| U_43 != apply(U_41,U_45)
| ~ in(U_45,relation_rng(U_42)) )
& relation_dom(U_41) = relation_rng(U_42) )
| U_41 != function_inverse(U_42) ) )
| ~ function(U_41)
| ~ relation(U_41) )
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_49,sK12(U_42,U_41))],[f_34_3]) ).
fof(f_34_5,plain,
! [U_42] :
( ! [U_41] :
( ( ( U_41 = function_inverse(U_42)
| ? [U_50,U_48] :
( ( U_48 != apply(U_41,U_50)
| ~ in(U_50,relation_rng(U_42)) )
& U_50 = apply(U_42,U_48)
& in(U_48,relation_dom(U_42)) )
| ( ( sK12(U_42,U_41) != apply(U_42,sK13(U_42,U_41))
| ~ in(sK13(U_42,U_41),relation_dom(U_42)) )
& sK13(U_42,U_41) = apply(U_41,sK12(U_42,U_41))
& in(sK12(U_42,U_41),relation_rng(U_42)) )
| relation_dom(U_41) != relation_rng(U_42) )
& ( ( ! [U_46,U_44] :
( ( U_44 = apply(U_41,U_46)
& in(U_46,relation_rng(U_42)) )
| U_46 != apply(U_42,U_44)
| ~ in(U_44,relation_dom(U_42)) )
& ! [U_45,U_43] :
( ( U_45 = apply(U_42,U_43)
& in(U_43,relation_dom(U_42)) )
| U_43 != apply(U_41,U_45)
| ~ in(U_45,relation_rng(U_42)) )
& relation_dom(U_41) = relation_rng(U_42) )
| U_41 != function_inverse(U_42) ) )
| ~ function(U_41)
| ~ relation(U_41) )
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_47,sK13(U_42,U_41))],[f_34_4]) ).
fof(f_34_6,plain,
! [U_42] :
( ! [U_41] :
( ( ( U_41 = function_inverse(U_42)
| ? [U_48] :
( ( U_48 != apply(U_41,sK14(U_42,U_41))
| ~ in(sK14(U_42,U_41),relation_rng(U_42)) )
& sK14(U_42,U_41) = apply(U_42,U_48)
& in(U_48,relation_dom(U_42)) )
| ( ( sK12(U_42,U_41) != apply(U_42,sK13(U_42,U_41))
| ~ in(sK13(U_42,U_41),relation_dom(U_42)) )
& sK13(U_42,U_41) = apply(U_41,sK12(U_42,U_41))
& in(sK12(U_42,U_41),relation_rng(U_42)) )
| relation_dom(U_41) != relation_rng(U_42) )
& ( ( ! [U_46,U_44] :
( ( U_44 = apply(U_41,U_46)
& in(U_46,relation_rng(U_42)) )
| U_46 != apply(U_42,U_44)
| ~ in(U_44,relation_dom(U_42)) )
& ! [U_45,U_43] :
( ( U_45 = apply(U_42,U_43)
& in(U_43,relation_dom(U_42)) )
| U_43 != apply(U_41,U_45)
| ~ in(U_45,relation_rng(U_42)) )
& relation_dom(U_41) = relation_rng(U_42) )
| U_41 != function_inverse(U_42) ) )
| ~ function(U_41)
| ~ relation(U_41) )
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_50,sK14(U_42,U_41))],[f_34_5]) ).
fof(f_34_7,plain,
! [U_42] :
( ! [U_41] :
( ( ( U_41 = function_inverse(U_42)
| ( ( sK15(U_42,U_41) != apply(U_41,sK14(U_42,U_41))
| ~ in(sK14(U_42,U_41),relation_rng(U_42)) )
& sK14(U_42,U_41) = apply(U_42,sK15(U_42,U_41))
& in(sK15(U_42,U_41),relation_dom(U_42)) )
| ( ( sK12(U_42,U_41) != apply(U_42,sK13(U_42,U_41))
| ~ in(sK13(U_42,U_41),relation_dom(U_42)) )
& sK13(U_42,U_41) = apply(U_41,sK12(U_42,U_41))
& in(sK12(U_42,U_41),relation_rng(U_42)) )
| relation_dom(U_41) != relation_rng(U_42) )
& ( ( ! [U_46,U_44] :
( ( U_44 = apply(U_41,U_46)
& in(U_46,relation_rng(U_42)) )
| U_46 != apply(U_42,U_44)
| ~ in(U_44,relation_dom(U_42)) )
& ! [U_45,U_43] :
( ( U_45 = apply(U_42,U_43)
& in(U_43,relation_dom(U_42)) )
| U_43 != apply(U_41,U_45)
| ~ in(U_45,relation_rng(U_42)) )
& relation_dom(U_41) = relation_rng(U_42) )
| U_41 != function_inverse(U_42) ) )
| ~ function(U_41)
| ~ relation(U_41) )
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_48,sK15(U_42,U_41))],[f_34_6]) ).
cnf(f_34_8,plain,
( relation_dom(U_41) = relation_rng(U_42)
| U_41 != function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_9,plain,
( in(U_43,relation_dom(U_42))
| U_43 != apply(U_41,U_45)
| ~ in(U_45,relation_rng(U_42))
| U_41 != function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_10,plain,
( U_45 = apply(U_42,U_43)
| U_43 != apply(U_41,U_45)
| ~ in(U_45,relation_rng(U_42))
| U_41 != function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_11,plain,
( in(U_46,relation_rng(U_42))
| U_46 != apply(U_42,U_44)
| ~ in(U_44,relation_dom(U_42))
| U_41 != function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_12,plain,
( U_44 = apply(U_41,U_46)
| U_46 != apply(U_42,U_44)
| ~ in(U_44,relation_dom(U_42))
| U_41 != function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_13,plain,
( in(sK15(U_42,U_41),relation_dom(U_42))
| in(sK12(U_42,U_41),relation_rng(U_42))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_14,plain,
( sK14(U_42,U_41) = apply(U_42,sK15(U_42,U_41))
| in(sK12(U_42,U_41),relation_rng(U_42))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_15,plain,
( in(sK15(U_42,U_41),relation_dom(U_42))
| sK13(U_42,U_41) = apply(U_41,sK12(U_42,U_41))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_16,plain,
( sK14(U_42,U_41) = apply(U_42,sK15(U_42,U_41))
| sK13(U_42,U_41) = apply(U_41,sK12(U_42,U_41))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_17,plain,
( in(sK12(U_42,U_41),relation_rng(U_42))
| sK15(U_42,U_41) != apply(U_41,sK14(U_42,U_41))
| ~ in(sK14(U_42,U_41),relation_rng(U_42))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_18,plain,
( sK13(U_42,U_41) = apply(U_41,sK12(U_42,U_41))
| sK15(U_42,U_41) != apply(U_41,sK14(U_42,U_41))
| ~ in(sK14(U_42,U_41),relation_rng(U_42))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_19,plain,
( in(sK15(U_42,U_41),relation_dom(U_42))
| sK12(U_42,U_41) != apply(U_42,sK13(U_42,U_41))
| ~ in(sK13(U_42,U_41),relation_dom(U_42))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_20,plain,
( sK14(U_42,U_41) = apply(U_42,sK15(U_42,U_41))
| sK12(U_42,U_41) != apply(U_42,sK13(U_42,U_41))
| ~ in(sK13(U_42,U_41),relation_dom(U_42))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_21,plain,
( sK15(U_42,U_41) != apply(U_41,sK14(U_42,U_41))
| ~ in(sK14(U_42,U_41),relation_rng(U_42))
| sK12(U_42,U_41) != apply(U_42,sK13(U_42,U_41))
| ~ in(sK13(U_42,U_41),relation_dom(U_42))
| relation_dom(U_41) != relation_rng(U_42)
| U_41 = function_inverse(U_42)
| ~ function(U_41)
| ~ relation(U_41)
| ~ one_to_one(U_42)
| ~ function(U_42)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_34_7]) ).
fof(f_35_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_35_2,plain,
! [U_52,U_51] :
( ( U_52 = apply(relation_composition(function_inverse(U_51),U_51),U_52)
& U_52 = apply(U_51,apply(function_inverse(U_51),U_52)) )
| ~ in(U_52,relation_rng(U_51))
| ~ one_to_one(U_51)
| ~ function(U_51)
| ~ relation(U_51) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( U_52 = apply(U_51,apply(function_inverse(U_51),U_52))
| ~ in(U_52,relation_rng(U_51))
| ~ one_to_one(U_51)
| ~ function(U_51)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( U_52 = apply(relation_composition(function_inverse(U_51),U_51),U_52)
| ~ in(U_52,relation_rng(U_51))
| ~ one_to_one(U_51)
| ~ function(U_51)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_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_36_2,negated_conjecture,
? [A] :
( ~ one_to_one(function_inverse(A))
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_36_1]) ).
fof(f_36_3,negated_conjecture,
? [U_53] :
( ~ one_to_one(function_inverse(U_53))
& one_to_one(U_53)
& function(U_53)
& relation(U_53) ),
inference(variable_rename,[status(thm)],[f_36_2]) ).
fof(f_36_4,negated_conjecture,
( ~ one_to_one(function_inverse(sK16))
& one_to_one(sK16)
& function(sK16)
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_53,sK16)],[f_36_3]) ).
fof(f_36_5,negated_conjecture,
( ~ one_to_one(function_inverse(sK16))
& one_to_one(sK16)
& function(sK16)
& relation(sK16) ),
inference(definitional_conversion,[status(esa)],[f_36_4]) ).
cnf(f_36_6,negated_conjecture,
relation(sK16),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_7,negated_conjecture,
function(sK16),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_8,negated_conjecture,
one_to_one(sK16),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_9,negated_conjecture,
~ one_to_one(function_inverse(sK16)),
inference(clausify,[status(thm)],[f_36_5]) ).
fof(f_37_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_37_2,plain,
! [U_54] :
( U_54 = empty_set
| ~ empty(U_54) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_54 = empty_set
| ~ empty(U_54) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_38_2,plain,
! [U_56,U_55] :
( ~ empty(U_55)
| ~ in(U_56,U_55) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( ~ empty(U_55)
| ~ in(U_56,U_55) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_39_2,plain,
! [U_58,U_57] :
( ~ empty(U_57)
| U_58 = U_57
| ~ empty(U_58) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_58] :
( ! [U_57] :
( ~ empty(U_57)
| U_58 = U_57 )
| ~ empty(U_58) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( ~ empty(U_57)
| U_58 = U_57
| ~ empty(U_58) ),
inference(clausify,[status(thm)],[f_39_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(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_2]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( 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,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| 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,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,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_14,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_15,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_16,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_17,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,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_21,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_22,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU221+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 23:34:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.65/1.00 % SZS status Theorem for theBenchmark
% 0.65/1.00 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------