%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU028+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:10:31 PM UTC 2026
% Result : Theorem 162.62s 118.10s
% Output : CNFRefutation 171.40s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_299)
% Comments :
%------------------------------------------------------------------------------
fof(t61_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
& relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(fc6_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(t57_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(t56_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_dom(X2)) )
=> ( X1 = apply(function_inverse(X2),apply(X2,X1))
& X1 = apply(relation_composition(X2,function_inverse(X2)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t59_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(function_inverse(X1),X1)) = relation_rng(X1)
& relation_rng(relation_composition(function_inverse(X1),X1)) = relation_rng(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
fof(t58_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
& relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(fc9_relat_1,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(fc10_relat_1,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(cc2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc8_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_45,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
& relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ) ),
inference(assume_negation,[status(cth)],[t61_funct_1]) ).
fof(i_0_46,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_47,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_48,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[fc6_relat_1]) ).
fof(i_0_49,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(i_0_50,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_51,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_52,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_53,plain,
! [X108,X109,X110] :
( ( relation_dom(X109) = X108
| X109 != identity_relation(X108)
| ~ relation(X109)
| ~ function(X109) )
& ( ~ in(X110,X108)
| apply(X109,X110) = X110
| X109 != identity_relation(X108)
| ~ relation(X109)
| ~ function(X109) )
& ( in(esk12_2(X108,X109),X108)
| relation_dom(X109) != X108
| X109 = identity_relation(X108)
| ~ relation(X109)
| ~ function(X109) )
& ( apply(X109,esk12_2(X108,X109)) != esk12_2(X108,X109)
| relation_dom(X109) != X108
| X109 = identity_relation(X108)
| ~ relation(X109)
| ~ function(X109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(i_0_54,plain,
! [X119,X120] :
( ( X119 = apply(X120,apply(function_inverse(X120),X119))
| ~ one_to_one(X120)
| ~ in(X119,relation_rng(X120))
| ~ relation(X120)
| ~ function(X120) )
& ( X119 = apply(relation_composition(function_inverse(X120),X120),X119)
| ~ one_to_one(X120)
| ~ in(X119,relation_rng(X120))
| ~ relation(X120)
| ~ function(X120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_funct_1])])]) ).
fof(i_0_55,plain,
! [X117,X118] :
( ( X117 = apply(function_inverse(X118),apply(X118,X117))
| ~ one_to_one(X118)
| ~ in(X117,relation_dom(X118))
| ~ relation(X118)
| ~ function(X118) )
& ( X117 = apply(relation_composition(X118,function_inverse(X118)),X117)
| ~ one_to_one(X118)
| ~ in(X117,relation_dom(X118))
| ~ relation(X118)
| ~ function(X118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t56_funct_1])])]) ).
fof(i_0_56,negated_conjecture,
( relation(esk13_0)
& function(esk13_0)
& one_to_one(esk13_0)
& ( relation_composition(esk13_0,function_inverse(esk13_0)) != identity_relation(relation_dom(esk13_0))
| relation_composition(function_inverse(esk13_0),esk13_0) != identity_relation(relation_rng(esk13_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_45])])]) ).
fof(i_0_57,plain,
! [X114,X115,X116] :
( ~ in(X114,X115)
| ~ element(X115,powerset(X116))
| element(X114,X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_58,plain,
! [X122] :
( ( relation_dom(relation_composition(function_inverse(X122),X122)) = relation_rng(X122)
| ~ one_to_one(X122)
| ~ relation(X122)
| ~ function(X122) )
& ( relation_rng(relation_composition(function_inverse(X122),X122)) = relation_rng(X122)
| ~ one_to_one(X122)
| ~ relation(X122)
| ~ function(X122) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t59_funct_1])])]) ).
fof(i_0_59,plain,
! [X121] :
( ( relation_dom(relation_composition(X121,function_inverse(X121))) = relation_dom(X121)
| ~ one_to_one(X121)
| ~ relation(X121)
| ~ function(X121) )
& ( relation_rng(relation_composition(X121,function_inverse(X121))) = relation_dom(X121)
| ~ one_to_one(X121)
| ~ relation(X121)
| ~ function(X121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t58_funct_1])])]) ).
fof(i_0_60,plain,
! [X123,X124,X125] :
( ~ in(X123,X124)
| ~ element(X124,powerset(X125))
| ~ empty(X125) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_61,plain,
! [X81,X82] :
( ( relation(relation_composition(X81,X82))
| ~ relation(X81)
| ~ function(X81)
| ~ relation(X82)
| ~ function(X82) )
& ( function(relation_composition(X81,X82))
| ~ relation(X81)
| ~ function(X81)
| ~ relation(X82)
| ~ function(X82) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
fof(i_0_62,plain,
! [X112,X113] :
( ( ~ element(X112,powerset(X113))
| subset(X112,X113) )
& ( ~ subset(X112,X113)
| element(X112,powerset(X113)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_63,plain,
! [X68,X69] :
( ~ in(X68,X69)
| ~ in(X69,X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_46])]) ).
fof(i_0_64,plain,
! [X74,X75] :
( ~ relation(X74)
| ~ relation(X75)
| relation(relation_composition(X74,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
fof(i_0_65,plain,
! [X89,X90] :
( ( empty(relation_composition(X89,X90))
| ~ empty(X89)
| ~ relation(X90) )
& ( relation(relation_composition(X89,X90))
| ~ empty(X89)
| ~ relation(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_relat_1])])]) ).
fof(i_0_66,plain,
! [X79,X80] :
( ( empty(relation_composition(X80,X79))
| ~ empty(X79)
| ~ relation(X80) )
& ( relation(relation_composition(X80,X79))
| ~ empty(X79)
| ~ relation(X80) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc10_relat_1])])]) ).
fof(i_0_67,plain,
! [X106,X107] :
( ~ element(X106,X107)
| empty(X107)
| in(X106,X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_68,plain,
! [X104,X105] :
( ~ in(X104,X105)
| element(X104,X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_69,plain,
! [X93] :
( ( element(esk4_1(X93),powerset(X93))
| empty(X93) )
& ( ~ empty(esk4_1(X93))
| empty(X93) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_47])])])]) ).
fof(i_0_70,plain,
! [X128,X129] :
( ~ in(X128,X129)
| ~ empty(X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_71,plain,
! [X86] :
( empty(X86)
| ~ relation(X86)
| ~ empty(relation_rng(X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_48])]) ).
fof(i_0_72,plain,
! [X85] :
( empty(X85)
| ~ relation(X85)
| ~ empty(relation_dom(X85)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_49])]) ).
fof(i_0_73,plain,
! [X98] :
( element(esk8_1(X98),powerset(X98))
& empty(esk8_1(X98)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_74,plain,
! [X72] :
( ( relation(X72)
| ~ relation(X72)
| ~ empty(X72)
| ~ function(X72) )
& ( function(X72)
| ~ relation(X72)
| ~ empty(X72)
| ~ function(X72) )
& ( one_to_one(X72)
| ~ relation(X72)
| ~ empty(X72)
| ~ function(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_75,plain,
! [X73] :
( ( relation(function_inverse(X73))
| ~ relation(X73)
| ~ function(X73) )
& ( function(function_inverse(X73))
| ~ relation(X73)
| ~ function(X73) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(i_0_76,plain,
! [X77] : element(esk1_1(X77),X77),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_77,plain,
! [X88] :
( ( empty(relation_rng(X88))
| ~ empty(X88) )
& ( relation(relation_rng(X88))
| ~ empty(X88) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).
fof(i_0_78,plain,
! [X87] :
( ( empty(relation_dom(X87))
| ~ empty(X87) )
& ( relation(relation_dom(X87))
| ~ empty(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
fof(i_0_79,plain,
! [X83] : ~ empty(powerset(X83)),
inference(variable_rename,[status(thm)],[i_0_50]) ).
fof(i_0_80,plain,
! [X130,X131] :
( ~ empty(X130)
| X130 = X131
| ~ empty(X131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_81,plain,
! [X103] : subset(X103,X103),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_82,plain,
! [X71] :
( ~ empty(X71)
| relation(X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_83,plain,
! [X70] :
( ~ empty(X70)
| function(X70) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_84,plain,
! [X84] :
( relation(identity_relation(X84))
& function(identity_relation(X84)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(i_0_85,plain,
! [X76] : relation(identity_relation(X76)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(i_0_86,plain,
! [X127] :
( ~ empty(X127)
| X127 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_87,plain,
~ empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_51])]) ).
fof(i_0_88,plain,
( ~ empty(esk7_0)
& relation(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_52])]) ).
fof(i_0_89,plain,
( relation(esk11_0)
& relation_empty_yielding(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_90,plain,
( relation(esk10_0)
& function(esk10_0)
& one_to_one(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_91,plain,
( relation(esk6_0)
& empty(esk6_0)
& function(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_92,plain,
( empty(esk3_0)
& relation(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_93,plain,
( relation(esk2_0)
& function(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_94,plain,
empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_95,plain,
( X1 = identity_relation(X2)
| apply(X1,esk12_2(X2,X1)) != esk12_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_96,plain,
( X1 = apply(relation_composition(function_inverse(X2),X2),X1)
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_97,plain,
( X1 = apply(relation_composition(X2,function_inverse(X2)),X1)
| ~ one_to_one(X2)
| ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_98,plain,
( X1 = apply(X2,apply(function_inverse(X2),X1))
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_99,plain,
( X1 = apply(function_inverse(X2),apply(X2,X1))
| ~ one_to_one(X2)
| ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_100,negated_conjecture,
( relation_composition(esk13_0,function_inverse(esk13_0)) != identity_relation(relation_dom(esk13_0))
| relation_composition(function_inverse(esk13_0),esk13_0) != identity_relation(relation_rng(esk13_0)) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_101,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_102,plain,
( in(esk12_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_103,plain,
( relation_rng(relation_composition(function_inverse(X1),X1)) = relation_rng(X1)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_104,plain,
( relation_dom(relation_composition(function_inverse(X1),X1)) = relation_rng(X1)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_105,plain,
( relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_106,plain,
( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_107,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_108,plain,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_109,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_110,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_111,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_112,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_113,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_114,plain,
( relation(relation_composition(X1,X2))
| ~ empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_115,plain,
( relation(relation_composition(X1,X2))
| ~ empty(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_116,plain,
( empty(relation_composition(X1,X2))
| ~ empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_117,plain,
( empty(relation_composition(X1,X2))
| ~ empty(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_118,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_119,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_120,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_121,plain,
( element(esk4_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_122,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_123,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_124,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_125,plain,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_126,plain,
element(esk8_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_127,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_128,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_129,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_130,plain,
( empty(X1)
| ~ empty(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_131,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_132,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_133,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_134,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_135,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_136,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_137,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_138,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_139,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_140,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_141,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_142,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_143,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_144,plain,
empty(esk8_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_145,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_146,plain,
~ empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_147,plain,
~ empty(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_148,plain,
relation_empty_yielding(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_149,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_150,negated_conjecture,
one_to_one(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_151,plain,
one_to_one(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_152,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_153,plain,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_154,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_155,plain,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_156,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_157,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_158,plain,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_159,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_160,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_161,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_162,plain,
function(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_163,plain,
function(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_164,plain,
function(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_165,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_166,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_167,plain,
empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_168,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_169,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_170,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_171,axiom,
X1 = X1 ).
cnf(i_0_172,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_173,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_174,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_175,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_176,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_177,axiom,
( X1 != X2
| esk12_2(X1,X3) = esk12_2(X2,X3) ) ).
cnf(i_0_178,axiom,
( X1 != X2
| esk12_2(X3,X1) = esk12_2(X3,X2) ) ).
cnf(i_0_179,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_180,axiom,
( X1 != X2
| relation_composition(X1,X3) = relation_composition(X2,X3) ) ).
cnf(i_0_181,axiom,
( X1 != X2
| relation_composition(X3,X1) = relation_composition(X3,X2) ) ).
cnf(i_0_182,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_183,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_184,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_185,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_186,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_187,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_188,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_189,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_190,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_191,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_192,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_193,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_2947,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_3023,plain,
subset(esk1_1(powerset(X1)),X1),
inference(rename_variables,[],[i_0_229]) ).
cnf(i_0_3101,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_3174,plain,
subset(esk8_1(X1),X1),
inference(rename_variables,[],[i_0_197]) ).
cnf(i_0_3254,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_3321,plain,
subset(esk1_1(powerset(X1)),X1),
inference(rename_variables,[],[i_0_229]) ).
cnf(i_0_3380,plain,
~ in(X1,esk1_1(powerset(esk6_0))),
inference(rename_variables,[],[i_0_349]) ).
cnf(i_0_3395,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_3466,plain,
subset(esk8_1(X1),X1),
inference(rename_variables,[],[i_0_197]) ).
cnf(i_0_3541,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_3623,plain,
subset(esk1_1(powerset(X1)),X1),
inference(rename_variables,[],[i_0_229]) ).
cnf(i_0_3694,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_3700,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_3830,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_3907,plain,
subset(esk8_1(X1),X1),
inference(rename_variables,[],[i_0_197]) ).
cnf(i_0_3975,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_4054,plain,
subset(esk1_1(powerset(X1)),X1),
inference(rename_variables,[],[i_0_229]) ).
cnf(i_0_4124,plain,
in(esk1_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_4197,plain,
subset(esk8_1(X1),X1),
inference(rename_variables,[],[i_0_197]) ).
cnf(i_0_224,plain,
relation(esk13_0),
inference(equality_inference,[],[216]) ).
cnf(i_0_225,plain,
function(esk13_0),
inference(equality_inference,[],[218]) ).
cnf(i_0_226,plain,
one_to_one(esk13_0),
inference(equality_inference,[],[219]) ).
cnf(i_0_227,plain,
~ in(powerset(X1),esk8_1(X1)),
inference(equality_inference,[],[220]) ).
cnf(i_0_228,plain,
relation_empty_yielding(esk11_0),
inference(equality_inference,[],[221]) ).
cnf(i_0_244,plain,
powerset(X1) != esk8_1(esk6_0),
inference(scs_inference,[],[i_0_209,i_0_206,i_0_131,i_0_230,i_0_239,i_0_147,i_0_167,i_0_144,i_0_111,i_0_122,i_0_139,i_0_140,i_0_107,i_0_119,i_0_187]) ).
cnf(i_0_246,plain,
esk3_0 != esk7_0,
inference(scs_inference,[],[i_0_209,i_0_206,i_0_131,i_0_230,i_0_239,i_0_147,i_0_167,i_0_144,i_0_111,i_0_122,i_0_139,i_0_140,i_0_107,i_0_119,i_0_187,i_0_190]) ).
cnf(i_0_247,plain,
one_to_one(esk3_0),
inference(scs_inference,[],[i_0_209,i_0_206,i_0_131,i_0_230,i_0_239,i_0_147,i_0_157,i_0_167,i_0_144,i_0_111,i_0_122,i_0_139,i_0_140,i_0_107,i_0_119,i_0_187,i_0_190,i_0_127]) ).
cnf(i_0_249,plain,
~ in(esk7_0,esk1_1(esk7_0)),
inference(scs_inference,[],[i_0_209,i_0_206,i_0_131,i_0_230,i_0_239,i_0_147,i_0_157,i_0_167,i_0_144,i_0_111,i_0_122,i_0_139,i_0_140,i_0_107,i_0_119,i_0_187,i_0_190,i_0_127,i_0_112]) ).
cnf(i_0_274,plain,
powerset(X1) != esk1_1(powerset(esk3_0)),
inference(scs_inference,[],[i_0_209,i_0_238,i_0_170,i_0_131,i_0_269,i_0_146,i_0_140,i_0_122,i_0_119,i_0_107,i_0_187]) ).
cnf(i_0_275,plain,
~ in(X1,esk1_1(powerset(esk3_0))),
inference(rename_variables,[],[i_0_238]) ).
cnf(i_0_276,plain,
empty_set != esk9_0,
inference(scs_inference,[],[i_0_209,i_0_238,i_0_170,i_0_131,i_0_269,i_0_146,i_0_140,i_0_122,i_0_119,i_0_107,i_0_187,i_0_190]) ).
cnf(i_0_277,plain,
one_to_one(empty_set),
inference(scs_inference,[],[i_0_209,i_0_238,i_0_160,i_0_170,i_0_131,i_0_269,i_0_146,i_0_140,i_0_122,i_0_119,i_0_107,i_0_187,i_0_190,i_0_127]) ).
cnf(i_0_279,plain,
~ in(esk9_0,esk1_1(esk9_0)),
inference(scs_inference,[],[i_0_209,i_0_238,i_0_160,i_0_170,i_0_131,i_0_269,i_0_146,i_0_140,i_0_122,i_0_119,i_0_107,i_0_187,i_0_190,i_0_127,i_0_112]) ).
cnf(i_0_306,plain,
powerset(X1) != esk3_0,
inference(scs_inference,[],[i_0_209,i_0_232,i_0_144,i_0_136,i_0_131,i_0_300,i_0_140,i_0_122,i_0_119,i_0_107,i_0_190,i_0_187]) ).
cnf(i_0_308,plain,
one_to_one(esk5_0),
inference(scs_inference,[],[i_0_209,i_0_232,i_0_144,i_0_166,i_0_201,i_0_203,i_0_136,i_0_131,i_0_300,i_0_140,i_0_122,i_0_119,i_0_107,i_0_190,i_0_187,i_0_127]) ).
cnf(i_0_310,plain,
~ in(powerset(X1),esk1_1(powerset(X1))),
inference(scs_inference,[],[i_0_209,i_0_232,i_0_144,i_0_166,i_0_201,i_0_203,i_0_136,i_0_131,i_0_300,i_0_140,i_0_122,i_0_119,i_0_107,i_0_190,i_0_187,i_0_127,i_0_112]) ).
cnf(i_0_332,plain,
powerset(X1) != esk1_1(powerset(empty_set)),
inference(scs_inference,[],[i_0_209,i_0_166,i_0_271,i_0_147,i_0_131,i_0_122,i_0_107,i_0_190,i_0_187]) ).
cnf(i_0_333,plain,
~ in(X1,esk1_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_271]) ).
cnf(i_0_334,plain,
one_to_one(esk8_1(X1)),
inference(scs_inference,[],[i_0_209,i_0_166,i_0_144,i_0_271,i_0_295,i_0_234,i_0_147,i_0_131,i_0_122,i_0_107,i_0_190,i_0_187,i_0_127]) ).
cnf(i_0_353,plain,
powerset(X1) != empty_set,
inference(scs_inference,[],[i_0_209,i_0_165,i_0_167,i_0_266,i_0_146,i_0_131,i_0_107,i_0_190,i_0_187]) ).
cnf(i_0_367,plain,
powerset(X1) != esk8_1(X2),
inference(scs_inference,[],[i_0_209,i_0_165,i_0_297,i_0_147,i_0_190,i_0_187]) ).
cnf(i_0_379,plain,
powerset(X1) != esk1_1(powerset(esk8_1(X2))),
inference(scs_inference,[],[i_0_170,i_0_209,i_0_302,i_0_136,i_0_190,i_0_187]) ).
cnf(i_0_380,plain,
~ in(X1,esk1_1(powerset(esk8_1(X2)))),
inference(rename_variables,[],[i_0_302]) ).
cnf(i_0_389,plain,
powerset(X1) != esk1_1(powerset(esk5_0)),
inference(scs_inference,[],[i_0_166,i_0_209,i_0_328,i_0_146,i_0_190,i_0_187]) ).
cnf(i_0_399,plain,
powerset(X1) != esk5_0,
inference(scs_inference,[],[i_0_170,i_0_209,i_0_326,i_0_147,i_0_190,i_0_187]) ).
cnf(i_0_407,plain,
powerset(X1) != esk1_1(powerset(esk6_0)),
inference(scs_inference,[],[i_0_165,i_0_209,i_0_349,i_0_136,i_0_190,i_0_187]) ).
cnf(i_0_2248,plain,
function(function_inverse(esk8_1(X1))),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_234,i_0_2246,i_0_295,i_0_131,i_0_146,i_0_147,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129]) ).
cnf(i_0_2251,plain,
relation(relation_composition(esk8_1(X1),esk8_1(X1))),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_146,i_0_147,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113]) ).
cnf(i_0_2253,plain,
relation(relation_composition(esk6_0,esk8_1(X1))),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_146,i_0_147,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114]) ).
cnf(i_0_2255,plain,
relation(relation_composition(esk8_1(X1),esk6_0)),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_146,i_0_147,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115]) ).
cnf(i_0_2257,plain,
empty(relation_composition(esk6_0,esk8_1(X1))),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_146,i_0_147,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116]) ).
cnf(i_0_2259,plain,
empty(relation_composition(esk8_1(X1),esk6_0)),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_146,i_0_147,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117]) ).
cnf(i_0_2261,plain,
relation_dom(identity_relation(X1)) = X1,
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_143,i_0_146,i_0_147,i_0_142,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196]) ).
cnf(i_0_2264,plain,
in(esk1_1(esk4_1(esk9_0)),esk4_1(esk9_0)),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_142,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119]) ).
cnf(i_0_2267,plain,
~ element(esk7_0,powerset(esk6_0)),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_241,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_142,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107]) ).
cnf(i_0_2269,plain,
~ in(X1,relation_dom(identity_relation(esk1_1(powerset(esk6_0))))),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_142,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187]) ).
cnf(i_0_2270,plain,
esk6_0 != esk4_1(esk9_0),
inference(scs_inference,[],[i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_142,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190]) ).
cnf(i_0_2271,plain,
relation_rng(relation_composition(function_inverse(esk13_0),esk13_0)) = relation_rng(esk13_0),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103]) ).
cnf(i_0_2273,plain,
relation_dom(relation_composition(function_inverse(esk13_0),esk13_0)) = relation_rng(esk13_0),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104]) ).
cnf(i_0_2275,plain,
relation_rng(relation_composition(esk13_0,function_inverse(esk13_0))) = relation_dom(esk13_0),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105]) ).
cnf(i_0_2277,plain,
relation_dom(relation_composition(esk13_0,function_inverse(esk13_0))) = relation_dom(esk13_0),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106]) ).
cnf(i_0_2279,plain,
function(relation_composition(esk8_1(X1),esk8_1(X1))),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110]) ).
cnf(i_0_2282,plain,
identity_relation(esk6_0) = identity_relation(empty_set),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174]) ).
cnf(i_0_2283,plain,
apply(esk6_0,X1) = apply(empty_set,X1),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175]) ).
cnf(i_0_2284,plain,
apply(X1,esk6_0) = apply(X1,empty_set),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176]) ).
cnf(i_0_2285,plain,
esk12_2(esk6_0,X1) = esk12_2(empty_set,X1),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177]) ).
cnf(i_0_2286,plain,
esk12_2(X1,esk6_0) = esk12_2(X1,empty_set),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178]) ).
cnf(i_0_2287,plain,
relation_dom(esk6_0) = relation_dom(empty_set),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179]) ).
cnf(i_0_2288,plain,
relation_composition(esk6_0,X1) = relation_composition(empty_set,X1),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180]) ).
cnf(i_0_2289,plain,
relation_composition(X1,esk6_0) = relation_composition(X1,empty_set),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181]) ).
cnf(i_0_2290,plain,
relation_rng(esk6_0) = relation_rng(empty_set),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182]) ).
cnf(i_0_2353,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_2417,plain,
~ empty(esk4_1(relation_rng(esk7_0))),
inference(scs_inference,[],[i_0_2241,i_0_130]) ).
cnf(i_0_2419,plain,
relation(relation_rng(relation_dom(esk6_0))),
inference(scs_inference,[],[i_0_2226,i_0_2241,i_0_130,i_0_132]) ).
cnf(i_0_2421,plain,
relation(relation_dom(relation_dom(esk6_0))),
inference(scs_inference,[],[i_0_2226,i_0_2241,i_0_130,i_0_132,i_0_133]) ).
cnf(i_0_2423,plain,
empty(relation_rng(relation_dom(esk6_0))),
inference(scs_inference,[],[i_0_2226,i_0_2241,i_0_130,i_0_132,i_0_133,i_0_134]) ).
cnf(i_0_2425,plain,
empty(relation_dom(relation_dom(esk6_0))),
inference(scs_inference,[],[i_0_2226,i_0_2241,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135]) ).
cnf(i_0_2427,plain,
element(esk4_1(relation_rng(esk7_0)),powerset(relation_rng(esk7_0))),
inference(scs_inference,[],[i_0_2226,i_0_2241,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_121]) ).
cnf(i_0_2462,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_2518,plain,
~ empty(esk4_1(relation_dom(esk7_0))),
inference(scs_inference,[],[i_0_2243,i_0_130]) ).
cnf(i_0_2563,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_2745,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_2831,plain,
~ in(X1,esk1_1(powerset(esk8_1(X2)))),
inference(rename_variables,[],[i_0_302]) ).
cnf(i_0_2940,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_3086,plain,
~ in(X1,esk1_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_271]) ).
cnf(i_0_3094,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_3162,plain,
~ in(X1,esk1_1(powerset(esk3_0))),
inference(rename_variables,[],[i_0_238]) ).
cnf(i_0_3245,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_3388,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_3534,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_3686,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_3824,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_3968,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_3987,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_4116,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_4258,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_2228]) ).
cnf(i_0_259,plain,
relation(esk11_0),
inference(equality_inference,[],[254]) ).
cnf(i_0_260,plain,
function(esk10_0),
inference(equality_inference,[],[255]) ).
cnf(i_0_261,plain,
one_to_one(esk6_0),
inference(equality_inference,[],[256]) ).
cnf(i_0_262,plain,
~ in(esk7_0,esk1_1(esk7_0)),
inference(equality_inference,[],[257]) ).
cnf(i_0_263,plain,
relation_empty_yielding(empty_set),
inference(equality_inference,[],[258]) ).
cnf(i_0_291,plain,
relation(esk8_1(X1)),
inference(equality_inference,[],[281]) ).
cnf(i_0_292,plain,
function(esk2_0),
inference(equality_inference,[],[282]) ).
cnf(i_0_322,plain,
relation(esk10_0),
inference(equality_inference,[],[312]) ).
cnf(i_0_323,plain,
function(esk5_0),
inference(equality_inference,[],[313]) ).
cnf(i_0_346,plain,
relation(esk7_0),
inference(equality_inference,[],[338]) ).
cnf(i_0_347,plain,
function(esk8_1(X1)),
inference(equality_inference,[],[339]) ).
cnf(i_0_363,plain,
relation(esk2_0),
inference(equality_inference,[],[355]) ).
cnf(i_0_364,plain,
function(esk3_0),
inference(equality_inference,[],[356]) ).
cnf(i_0_375,plain,
function(empty_set),
inference(equality_inference,[],[369]) ).
cnf(i_0_376,plain,
one_to_one(esk10_0),
inference(equality_inference,[],[370]) ).
cnf(i_0_377,plain,
relation(esk6_0),
inference(equality_inference,[],[371]) ).
cnf(i_0_386,plain,
function(esk6_0),
inference(equality_inference,[],[381]) ).
cnf(i_0_387,plain,
relation(esk3_0),
inference(equality_inference,[],[382]) ).
cnf(i_0_396,plain,
function(identity_relation(X1)),
inference(equality_inference,[],[391]) ).
cnf(i_0_397,plain,
relation(empty_set),
inference(equality_inference,[],[392]) ).
cnf(i_0_405,plain,
relation(esk5_0),
inference(equality_inference,[],[401]) ).
cnf(i_0_418,plain,
relation(identity_relation(X1)),
inference(equality_inference,[],[409]) ).
cnf(i_0_2291,plain,
~ in(esk7_0,esk1_1(powerset(powerset(esk6_0)))),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_251]) ).
cnf(i_0_2293,plain,
~ in(esk7_0,powerset(esk6_0)),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_251,i_0_120]) ).
cnf(i_0_2295,plain,
~ in(esk4_1(esk9_0),esk1_1(esk4_1(esk9_0))),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_251,i_0_120,i_0_112]) ).
cnf(i_0_2298,plain,
element(esk1_1(esk4_1(esk9_0)),esk9_0),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_251,i_0_120,i_0_112,i_0_173,i_0_101]) ).
cnf(i_0_2300,plain,
esk1_1(powerset(esk6_0)) != esk7_0,
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_299,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_251,i_0_120,i_0_112,i_0_173,i_0_101,i_0_186]) ).
cnf(i_0_2302,plain,
relation(relation_dom(empty_set)),
inference(scs_inference,[],[i_0_150,i_0_138,i_0_2238,i_0_205,i_0_241,i_0_299,i_0_349,i_0_234,i_0_2246,i_0_2249,i_0_295,i_0_131,i_0_2236,i_0_143,i_0_146,i_0_147,i_0_152,i_0_142,i_0_161,i_0_165,i_0_155,i_0_172,i_0_130,i_0_132,i_0_133,i_0_134,i_0_135,i_0_118,i_0_121,i_0_145,i_0_188,i_0_189,i_0_191,i_0_192,i_0_123,i_0_124,i_0_128,i_0_129,i_0_113,i_0_114,i_0_115,i_0_116,i_0_117,i_0_196,i_0_119,i_0_107,i_0_187,i_0_190,i_0_103,i_0_104,i_0_105,i_0_106,i_0_110,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_251,i_0_120,i_0_112,i_0_173,i_0_101,i_0_186,i_0_183]) ).
cnf(i_0_2307,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2309,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2337,plain,
function(relation_composition(esk8_1(X1),esk8_1(X1))),
inference(rename_variables,[],[i_0_2279]) ).
cnf(i_0_2340,plain,
function(relation_composition(esk8_1(X1),esk8_1(X1))),
inference(rename_variables,[],[i_0_2279]) ).
cnf(i_0_2357,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2365,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2367,plain,
~ in(X1,relation_dom(identity_relation(esk1_1(powerset(esk6_0))))),
inference(rename_variables,[],[i_0_2269]) ).
cnf(i_0_2369,plain,
relation_composition(esk6_0,X1) = relation_composition(empty_set,X1),
inference(rename_variables,[],[i_0_2288]) ).
cnf(i_0_2391,plain,
function(relation_composition(esk8_1(X1),esk8_1(X1))),
inference(rename_variables,[],[i_0_2279]) ).
cnf(i_0_2400,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2444,plain,
function(function_inverse(esk8_1(X1))),
inference(rename_variables,[],[i_0_2248]) ).
cnf(i_0_2447,plain,
function(function_inverse(esk8_1(X1))),
inference(rename_variables,[],[i_0_2248]) ).
cnf(i_0_2468,plain,
apply(X1,esk6_0) = apply(X1,empty_set),
inference(rename_variables,[],[i_0_2284]) ).
cnf(i_0_2478,plain,
relation_composition(X1,esk6_0) = relation_composition(X1,empty_set),
inference(rename_variables,[],[i_0_2289]) ).
cnf(i_0_2481,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2498,plain,
function(function_inverse(esk8_1(X1))),
inference(rename_variables,[],[i_0_2248]) ).
cnf(i_0_2570,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2590,plain,
function(relation_composition(esk8_1(X1),esk8_1(X1))),
inference(rename_variables,[],[i_0_2279]) ).
cnf(i_0_2660,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2663,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2687,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2699,plain,
~ empty(esk4_1(esk4_1(relation_rng(esk7_0)))),
inference(scs_inference,[],[i_0_2417,i_0_130]) ).
cnf(i_0_2755,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2788,plain,
~ empty(esk4_1(esk4_1(relation_dom(esk7_0)))),
inference(scs_inference,[],[i_0_2518,i_0_130]) ).
cnf(i_0_2852,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2855,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2878,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_2943,plain,
apply(X1,esk6_0) = apply(X1,empty_set),
inference(rename_variables,[],[i_0_2284]) ).
cnf(i_0_2945,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3028,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3031,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3097,plain,
esk12_2(esk6_0,X1) = esk12_2(empty_set,X1),
inference(rename_variables,[],[i_0_2285]) ).
cnf(i_0_3099,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3179,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3182,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3192,plain,
function(function_inverse(esk8_1(X1))),
inference(rename_variables,[],[i_0_2248]) ).
cnf(i_0_3258,plain,
relation_composition(X1,esk6_0) = relation_composition(X1,empty_set),
inference(rename_variables,[],[i_0_2289]) ).
cnf(i_0_3323,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3326,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3468,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3471,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3537,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3555,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3627,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3630,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3768,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3771,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3909,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(i_0_3912,plain,
relation_dom(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_2261]) ).
cnf(c_0_2292,plain,
( in(esk12_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
i_0_102 ).
cnf(c_0_2293,plain,
( identity_relation(relation_dom(X1)) = X1
| in(esk12_2(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[c_0_2292]) ).
cnf(c_0_2294,plain,
relation_dom(relation_composition(function_inverse(esk13_0),esk13_0)) = relation_rng(esk13_0),
i_0_2273 ).
cnf(c_0_2295,plain,
relation_dom(relation_composition(esk13_0,function_inverse(esk13_0))) = relation_dom(esk13_0),
i_0_2277 ).
cnf(c_0_2296,plain,
( relation_composition(function_inverse(esk13_0),esk13_0) = identity_relation(relation_rng(esk13_0))
| in(esk12_2(relation_rng(esk13_0),relation_composition(function_inverse(esk13_0),esk13_0)),relation_rng(esk13_0))
| ~ function(relation_composition(function_inverse(esk13_0),esk13_0))
| ~ relation(relation_composition(function_inverse(esk13_0),esk13_0)) ),
inference(spm,[status(thm)],[c_0_2293,c_0_2294]) ).
cnf(c_0_2297,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
i_0_110 ).
cnf(c_0_2298,negated_conjecture,
function(esk13_0),
i_0_161 ).
cnf(c_0_2299,negated_conjecture,
relation(esk13_0),
i_0_152 ).
cnf(c_0_2300,plain,
( relation_composition(esk13_0,function_inverse(esk13_0)) = identity_relation(relation_dom(esk13_0))
| in(esk12_2(relation_dom(esk13_0),relation_composition(esk13_0,function_inverse(esk13_0))),relation_dom(esk13_0))
| ~ function(relation_composition(esk13_0,function_inverse(esk13_0)))
| ~ relation(relation_composition(esk13_0,function_inverse(esk13_0))) ),
inference(spm,[status(thm)],[c_0_2293,c_0_2295]) ).
cnf(c_0_2301,plain,
( X1 = identity_relation(X2)
| apply(X1,esk12_2(X2,X1)) != esk12_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
i_0_95 ).
cnf(c_0_2302,plain,
( relation_composition(function_inverse(esk13_0),esk13_0) = identity_relation(relation_rng(esk13_0))
| in(esk12_2(relation_rng(esk13_0),relation_composition(function_inverse(esk13_0),esk13_0)),relation_rng(esk13_0))
| ~ function(function_inverse(esk13_0))
| ~ relation(relation_composition(function_inverse(esk13_0),esk13_0))
| ~ relation(function_inverse(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2296,c_0_2297]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2303,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
i_0_129 ).
cnf(c_0_2304,plain,
( relation_composition(esk13_0,function_inverse(esk13_0)) = identity_relation(relation_dom(esk13_0))
| in(esk12_2(relation_dom(esk13_0),relation_composition(esk13_0,function_inverse(esk13_0))),relation_dom(esk13_0))
| ~ function(function_inverse(esk13_0))
| ~ relation(relation_composition(esk13_0,function_inverse(esk13_0)))
| ~ relation(function_inverse(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2300,c_0_2297]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2305,plain,
( identity_relation(relation_dom(X1)) = X1
| apply(X1,esk12_2(relation_dom(X1),X1)) != esk12_2(relation_dom(X1),X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[c_0_2301]) ).
cnf(c_0_2306,plain,
( relation_composition(function_inverse(esk13_0),esk13_0) = identity_relation(relation_rng(esk13_0))
| in(esk12_2(relation_rng(esk13_0),relation_composition(function_inverse(esk13_0),esk13_0)),relation_rng(esk13_0))
| ~ relation(relation_composition(function_inverse(esk13_0),esk13_0))
| ~ relation(function_inverse(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2302,c_0_2303]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2307,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
i_0_128 ).
cnf(c_0_2308,plain,
( relation_composition(esk13_0,function_inverse(esk13_0)) = identity_relation(relation_dom(esk13_0))
| in(esk12_2(relation_dom(esk13_0),relation_composition(esk13_0,function_inverse(esk13_0))),relation_dom(esk13_0))
| ~ relation(relation_composition(esk13_0,function_inverse(esk13_0)))
| ~ relation(function_inverse(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2304,c_0_2303]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2309,plain,
( relation_composition(function_inverse(esk13_0),esk13_0) = identity_relation(relation_rng(esk13_0))
| apply(relation_composition(function_inverse(esk13_0),esk13_0),esk12_2(relation_rng(esk13_0),relation_composition(function_inverse(esk13_0),esk13_0))) != esk12_2(relation_rng(esk13_0),relation_composition(function_inverse(esk13_0),esk13_0))
| ~ function(relation_composition(function_inverse(esk13_0),esk13_0))
| ~ relation(relation_composition(function_inverse(esk13_0),esk13_0)) ),
inference(spm,[status(thm)],[c_0_2305,c_0_2294]) ).
cnf(c_0_2310,plain,
( X1 = apply(relation_composition(function_inverse(X2),X2),X1)
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
i_0_96 ).
cnf(c_0_2311,negated_conjecture,
one_to_one(esk13_0),
i_0_150 ).
cnf(c_0_2312,plain,
( relation_composition(function_inverse(esk13_0),esk13_0) = identity_relation(relation_rng(esk13_0))
| in(esk12_2(relation_rng(esk13_0),relation_composition(function_inverse(esk13_0),esk13_0)),relation_rng(esk13_0))
| ~ relation(relation_composition(function_inverse(esk13_0),esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2306,c_0_2307]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2313,plain,
( relation_composition(esk13_0,function_inverse(esk13_0)) = identity_relation(relation_dom(esk13_0))
| apply(relation_composition(esk13_0,function_inverse(esk13_0)),esk12_2(relation_dom(esk13_0),relation_composition(esk13_0,function_inverse(esk13_0)))) != esk12_2(relation_dom(esk13_0),relation_composition(esk13_0,function_inverse(esk13_0)))
| ~ function(relation_composition(esk13_0,function_inverse(esk13_0)))
| ~ relation(relation_composition(esk13_0,function_inverse(esk13_0))) ),
inference(spm,[status(thm)],[c_0_2305,c_0_2295]) ).
cnf(c_0_2314,plain,
( X1 = apply(relation_composition(X2,function_inverse(X2)),X1)
| ~ one_to_one(X2)
| ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
i_0_97 ).
cnf(c_0_2315,plain,
( relation_composition(esk13_0,function_inverse(esk13_0)) = identity_relation(relation_dom(esk13_0))
| in(esk12_2(relation_dom(esk13_0),relation_composition(esk13_0,function_inverse(esk13_0))),relation_dom(esk13_0))
| ~ relation(relation_composition(esk13_0,function_inverse(esk13_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2308,c_0_2307]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2316,plain,
( relation_composition(function_inverse(esk13_0),esk13_0) = identity_relation(relation_rng(esk13_0))
| ~ function(relation_composition(function_inverse(esk13_0),esk13_0))
| ~ relation(relation_composition(function_inverse(esk13_0),esk13_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2309,c_0_2310]),c_0_2311]),c_0_2298]),c_0_2299])]),c_0_2312]) ).
cnf(c_0_2317,plain,
( relation_composition(esk13_0,function_inverse(esk13_0)) = identity_relation(relation_dom(esk13_0))
| ~ function(relation_composition(esk13_0,function_inverse(esk13_0)))
| ~ relation(relation_composition(esk13_0,function_inverse(esk13_0))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2313,c_0_2314]),c_0_2311]),c_0_2298]),c_0_2299])]),c_0_2315]) ).
cnf(c_0_2318,plain,
( relation_composition(function_inverse(esk13_0),esk13_0) = identity_relation(relation_rng(esk13_0))
| ~ function(function_inverse(esk13_0))
| ~ relation(relation_composition(function_inverse(esk13_0),esk13_0))
| ~ relation(function_inverse(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2316,c_0_2297]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2319,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
i_0_113 ).
cnf(c_0_2320,plain,
( relation_composition(esk13_0,function_inverse(esk13_0)) = identity_relation(relation_dom(esk13_0))
| ~ function(function_inverse(esk13_0))
| ~ relation(relation_composition(esk13_0,function_inverse(esk13_0)))
| ~ relation(function_inverse(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2317,c_0_2297]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2321,negated_conjecture,
( relation_composition(esk13_0,function_inverse(esk13_0)) != identity_relation(relation_dom(esk13_0))
| relation_composition(function_inverse(esk13_0),esk13_0) != identity_relation(relation_rng(esk13_0)) ),
i_0_100 ).
cnf(c_0_2322,plain,
( relation_composition(function_inverse(esk13_0),esk13_0) = identity_relation(relation_rng(esk13_0))
| ~ function(function_inverse(esk13_0))
| ~ relation(function_inverse(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2318,c_0_2319]),c_0_2299])]) ).
cnf(c_0_2323,plain,
( relation_composition(esk13_0,function_inverse(esk13_0)) = identity_relation(relation_dom(esk13_0))
| ~ function(function_inverse(esk13_0))
| ~ relation(function_inverse(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2320,c_0_2319]),c_0_2299])]) ).
cnf(c_0_2324,negated_conjecture,
( ~ function(function_inverse(esk13_0))
| ~ relation(function_inverse(esk13_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_2321,c_0_2322]),c_0_2323]) ).
cnf(c_0_2325,plain,
~ relation(function_inverse(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2324,c_0_2303]),c_0_2298]),c_0_2299])]) ).
cnf(c_0_2326,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2325,c_0_2307]),c_0_2298]),c_0_2299])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU028+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n016.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:42:06 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 162.62/118.10 % Version : CSE_E---1.7
% 162.62/118.10 % Problem : theBenchmark.p
% 162.62/118.10 % SZS status Theorem for theBenchmark.p
% 162.62/118.10 % SZS output start CNFRefutation
% See solution above
% 171.40/126.86 % Total time : 117.735s
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