%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU028+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:57:57 AM UTC 2026
% Result : Theorem 257.64s 257.92s
% Output : Proof 259.70s
% 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(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(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(t34_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t56_funct_1,axiom,
! [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(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(t58_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_rng(relation_composition(A,function_inverse(A))) = relation_dom(A)
& relation_dom(relation_composition(A,function_inverse(A))) = relation_dom(A) ) ) ),
file('theBenchmark.p',t58_funct_1) ).
fof(t59_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_rng(relation_composition(function_inverse(A),A)) = relation_rng(A)
& relation_dom(relation_composition(function_inverse(A),A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t59_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t61_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A))
& relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A)) ) ) ),
file('theBenchmark.p',t61_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] :
( ( 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] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_7_2,plain,
! [U_8] : relation(identity_relation(U_8)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
relation(identity_relation(U_8)),
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_10] :
? [U_9] : element(U_9,U_10),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_10] : element(sK1(U_10),U_10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1(U_10))],[f_8_2]) ).
cnf(f_8_4,plain,
element(sK1(U_10),U_10),
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_12,U_11] :
( ( relation(relation_composition(U_11,U_12))
& empty(relation_composition(U_11,U_12)) )
| ~ relation(U_11)
| ~ empty(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( empty(relation_composition(U_11,U_12))
| ~ relation(U_11)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( relation(relation_composition(U_11,U_12))
| ~ relation(U_11)
| ~ empty(U_12) ),
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_14,U_13] :
( ( function(relation_composition(U_14,U_13))
& relation(relation_composition(U_14,U_13)) )
| ~ function(U_13)
| ~ relation(U_13)
| ~ function(U_14)
| ~ relation(U_14) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(relation_composition(U_14,U_13))
| ~ function(U_13)
| ~ relation(U_13)
| ~ function(U_14)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( function(relation_composition(U_14,U_13))
| ~ function(U_13)
| ~ relation(U_13)
| ~ function(U_14)
| ~ relation(U_14) ),
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_15] : ~ empty(powerset(U_15)),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
~ empty(powerset(U_15)),
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,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_14_2,plain,
! [U_16] :
( function(identity_relation(U_16))
& relation(identity_relation(U_16)) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_18] : function(identity_relation(U_18))
& ! [U_17] : relation(identity_relation(U_17)) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
relation(identity_relation(U_17)),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
function(identity_relation(U_18)),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_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]) ).
fof(f_16_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_16_2,plain,
! [U_19] :
( ~ empty(relation_dom(U_19))
| ~ relation(U_19)
| empty(U_19) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( ~ empty(relation_dom(U_19))
| ~ relation(U_19)
| empty(U_19) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_17_2,plain,
! [U_20] :
( ~ empty(relation_rng(U_20))
| ~ relation(U_20)
| empty(U_20) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( ~ empty(relation_rng(U_20))
| ~ relation(U_20)
| empty(U_20) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_18_2,plain,
! [U_21] :
( ( relation(relation_dom(U_21))
& empty(relation_dom(U_21)) )
| ~ empty(U_21) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( empty(relation_dom(U_21))
| ~ empty(U_21) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( relation(relation_dom(U_21))
| ~ empty(U_21) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_19_2,plain,
! [U_22] :
( ( relation(relation_rng(U_22))
& empty(relation_rng(U_22)) )
| ~ empty(U_22) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( empty(relation_rng(U_22))
| ~ empty(U_22) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( relation(relation_rng(U_22))
| ~ empty(U_22) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_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_20_1]) ).
cnf(f_20_3,plain,
( empty(relation_composition(U_24,U_23))
| ~ relation(U_23)
| ~ empty(U_24) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( relation(relation_composition(U_24,U_23))
| ~ relation(U_23)
| ~ empty(U_24) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_21_2,plain,
? [U_25] :
( function(U_25)
& relation(U_25) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_25,sK2)],[f_21_2]) ).
cnf(f_21_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_22_2,plain,
? [U_26] :
( relation(U_26)
& empty(U_26) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_26,sK3)],[f_22_2]) ).
cnf(f_22_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_23_2,plain,
! [U_28] :
( ? [U_27] :
( ~ empty(U_27)
& element(U_27,powerset(U_28)) )
| empty(U_28) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_28] :
( ( ~ empty(sK4(U_28))
& element(sK4(U_28),powerset(U_28)) )
| empty(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_27,sK4(U_28))],[f_23_2]) ).
cnf(f_23_4,plain,
( element(sK4(U_28),powerset(U_28))
| empty(U_28) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( ~ empty(sK4(U_28))
| empty(U_28) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_24_2,plain,
? [U_29] : empty(U_29),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_29,sK5)],[f_24_2]) ).
cnf(f_24_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_25_2,plain,
? [U_30] :
( function(U_30)
& empty(U_30)
& relation(U_30) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( function(sK6)
& empty(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_30,sK6)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
function(sK6),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_26_2,plain,
? [U_31] :
( relation(U_31)
& ~ empty(U_31) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( relation(sK7)
& ~ empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_31,sK7)],[f_26_2]) ).
cnf(f_26_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_27_2,plain,
! [U_33] :
? [U_32] :
( empty(U_32)
& element(U_32,powerset(U_33)) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_33] :
( empty(sK8(U_33))
& element(sK8(U_33),powerset(U_33)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_32,sK8(U_33))],[f_27_2]) ).
cnf(f_27_4,plain,
element(sK8(U_33),powerset(U_33)),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
empty(sK8(U_33)),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_28_2,plain,
? [U_34] : ~ empty(U_34),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_34,sK9)],[f_28_2]) ).
cnf(f_28_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_29_2,plain,
? [U_35] :
( one_to_one(U_35)
& function(U_35)
& relation(U_35) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_35,sK10)],[f_29_2]) ).
cnf(f_29_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
function(sK10),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_30_2,plain,
? [U_36] :
( relation_empty_yielding(U_36)
& relation(U_36) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( relation_empty_yielding(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_36,sK11)],[f_30_2]) ).
cnf(f_30_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
relation_empty_yielding(sK11),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_31_2,plain,
! [U_38,U_37] : subset(U_38,U_38),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_38] : subset(U_38,U_38),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
subset(U_38,U_38),
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_40,U_39] :
( element(U_40,U_39)
| ~ in(U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( element(U_40,U_39)
| ~ in(U_40,U_39) ),
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_42,U_41] :
( in(U_42,U_41)
| empty(U_41)
| ~ element(U_42,U_41) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( in(U_42,U_41)
| empty(U_41)
| ~ element(U_42,U_41) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t34_funct_1]) ).
fof(f_34_2,plain,
! [U_46,U_45] :
( ( ( U_45 = identity_relation(U_46)
| ? [U_44] :
( apply(U_45,U_44) != U_44
& in(U_44,U_46) )
| relation_dom(U_45) != U_46 )
& ( ( ! [U_43] :
( apply(U_45,U_43) = U_43
| ~ in(U_43,U_46) )
& relation_dom(U_45) = U_46 )
| U_45 != identity_relation(U_46) ) )
| ~ function(U_45)
| ~ relation(U_45) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_46,U_45] :
( ( ( U_45 = identity_relation(U_46)
| ( apply(U_45,sK12(U_46,U_45)) != sK12(U_46,U_45)
& in(sK12(U_46,U_45),U_46) )
| relation_dom(U_45) != U_46 )
& ( ( ! [U_43] :
( apply(U_45,U_43) = U_43
| ~ in(U_43,U_46) )
& relation_dom(U_45) = U_46 )
| U_45 != identity_relation(U_46) ) )
| ~ function(U_45)
| ~ relation(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_44,sK12(U_46,U_45))],[f_34_2]) ).
cnf(f_34_4,plain,
( relation_dom(U_45) = U_46
| U_45 != identity_relation(U_46)
| ~ function(U_45)
| ~ relation(U_45) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( apply(U_45,U_43) = U_43
| ~ in(U_43,U_46)
| U_45 != identity_relation(U_46)
| ~ function(U_45)
| ~ relation(U_45) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_6,plain,
( in(sK12(U_46,U_45),U_46)
| relation_dom(U_45) != U_46
| U_45 = identity_relation(U_46)
| ~ function(U_45)
| ~ relation(U_45) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_7,plain,
( apply(U_45,sK12(U_46,U_45)) != sK12(U_46,U_45)
| relation_dom(U_45) != U_46
| U_45 = identity_relation(U_46)
| ~ function(U_45)
| ~ relation(U_45) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_48,U_47] :
( ( element(U_48,powerset(U_47))
| ~ subset(U_48,U_47) )
& ( subset(U_48,U_47)
| ~ element(U_48,powerset(U_47)) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_52,U_50] :
( element(U_52,powerset(U_50))
| ~ subset(U_52,U_50) )
& ! [U_51,U_49] :
( subset(U_51,U_49)
| ~ element(U_51,powerset(U_49)) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( subset(U_51,U_49)
| ~ element(U_51,powerset(U_49)) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( element(U_52,powerset(U_50))
| ~ subset(U_52,U_50) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_36_2,plain,
! [U_55,U_54,U_53] :
( element(U_55,U_53)
| ~ element(U_54,powerset(U_53))
| ~ in(U_55,U_54) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( element(U_55,U_53)
| ~ element(U_54,powerset(U_53))
| ~ in(U_55,U_54) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [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)],[t56_funct_1]) ).
fof(f_37_2,plain,
! [U_57,U_56] :
( ( U_57 = apply(relation_composition(U_56,function_inverse(U_56)),U_57)
& U_57 = apply(function_inverse(U_56),apply(U_56,U_57)) )
| ~ in(U_57,relation_dom(U_56))
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_57 = apply(function_inverse(U_56),apply(U_56,U_57))
| ~ in(U_57,relation_dom(U_56))
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( U_57 = apply(relation_composition(U_56,function_inverse(U_56)),U_57)
| ~ in(U_57,relation_dom(U_56))
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_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_38_2,plain,
! [U_59,U_58] :
( ( U_59 = apply(relation_composition(function_inverse(U_58),U_58),U_59)
& U_59 = apply(U_58,apply(function_inverse(U_58),U_59)) )
| ~ in(U_59,relation_rng(U_58))
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( U_59 = apply(U_58,apply(function_inverse(U_58),U_59))
| ~ in(U_59,relation_rng(U_58))
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( U_59 = apply(relation_composition(function_inverse(U_58),U_58),U_59)
| ~ in(U_59,relation_rng(U_58))
| ~ one_to_one(U_58)
| ~ function(U_58)
| ~ relation(U_58) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A] :
( ( relation_rng(relation_composition(A,function_inverse(A))) = relation_dom(A)
& relation_dom(relation_composition(A,function_inverse(A))) = relation_dom(A) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t58_funct_1]) ).
fof(f_39_2,plain,
! [U_60] :
( ( relation_rng(relation_composition(U_60,function_inverse(U_60))) = relation_dom(U_60)
& relation_dom(relation_composition(U_60,function_inverse(U_60))) = relation_dom(U_60) )
| ~ one_to_one(U_60)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( relation_dom(relation_composition(U_60,function_inverse(U_60))) = relation_dom(U_60)
| ~ one_to_one(U_60)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(clausify,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( relation_rng(relation_composition(U_60,function_inverse(U_60))) = relation_dom(U_60)
| ~ one_to_one(U_60)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A] :
( ( relation_rng(relation_composition(function_inverse(A),A)) = relation_rng(A)
& relation_dom(relation_composition(function_inverse(A),A)) = relation_rng(A) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t59_funct_1]) ).
fof(f_40_2,plain,
! [U_61] :
( ( relation_rng(relation_composition(function_inverse(U_61),U_61)) = relation_rng(U_61)
& relation_dom(relation_composition(function_inverse(U_61),U_61)) = relation_rng(U_61) )
| ~ one_to_one(U_61)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( relation_dom(relation_composition(function_inverse(U_61),U_61)) = relation_rng(U_61)
| ~ one_to_one(U_61)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( relation_rng(relation_composition(function_inverse(U_61),U_61)) = relation_rng(U_61)
| ~ one_to_one(U_61)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_41_2,plain,
! [U_64,U_63,U_62] :
( ~ empty(U_62)
| ~ element(U_63,powerset(U_62))
| ~ in(U_64,U_63) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_64,U_63] :
( ! [U_62] :
( ~ empty(U_62)
| ~ element(U_63,powerset(U_62)) )
| ~ in(U_64,U_63) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( ~ empty(U_62)
| ~ element(U_63,powerset(U_62))
| ~ in(U_64,U_63) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A))
& relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A)) ) ) ),
inference(negate,[status(cth)],[t61_funct_1]) ).
fof(f_42_2,negated_conjecture,
? [A] :
( ( relation_composition(function_inverse(A),A) != identity_relation(relation_rng(A))
| relation_composition(A,function_inverse(A)) != identity_relation(relation_dom(A)) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_42_1]) ).
fof(f_42_3,negated_conjecture,
? [U_65] :
( ( relation_composition(function_inverse(U_65),U_65) != identity_relation(relation_rng(U_65))
| relation_composition(U_65,function_inverse(U_65)) != identity_relation(relation_dom(U_65)) )
& one_to_one(U_65)
& function(U_65)
& relation(U_65) ),
inference(variable_rename,[status(thm)],[f_42_2]) ).
fof(f_42_4,negated_conjecture,
( ( relation_composition(function_inverse(sK13),sK13) != identity_relation(relation_rng(sK13))
| relation_composition(sK13,function_inverse(sK13)) != identity_relation(relation_dom(sK13)) )
& one_to_one(sK13)
& function(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_65,sK13)],[f_42_3]) ).
cnf(f_42_5,negated_conjecture,
relation(sK13),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,negated_conjecture,
function(sK13),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_7,negated_conjecture,
one_to_one(sK13),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_8,negated_conjecture,
( relation_composition(function_inverse(sK13),sK13) != identity_relation(relation_rng(sK13))
| relation_composition(sK13,function_inverse(sK13)) != identity_relation(relation_dom(sK13)) ),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_43_2,plain,
! [U_66] :
( U_66 = empty_set
| ~ empty(U_66) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( U_66 = empty_set
| ~ empty(U_66) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_44_2,plain,
! [U_68,U_67] :
( ~ empty(U_67)
| ~ in(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( ~ empty(U_67)
| ~ in(U_68,U_67) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_45_2,plain,
! [U_70,U_69] :
( ~ empty(U_69)
| U_70 = U_69
| ~ empty(U_70) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_70] :
( ! [U_69] :
( ~ empty(U_69)
| U_70 = U_69 )
| ~ empty(U_70) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( ~ empty(U_69)
| U_70 = U_69
| ~ empty(U_70) ),
inference(clausify,[status(thm)],[f_45_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,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( relation_dom(Eq_x_0) = relation_dom(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,
( 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_11,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,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_16,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,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_20,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_21,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_22,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 : SEU028+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 23:16:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 257.64/257.92 % SZS status Theorem for theBenchmark
% 257.64/257.92 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------