%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : TOP036+1 : TPTP v9.2.1. Released v3.4.0.
% 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 : n019.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 05:56:41 PM UTC 2026
% Result : Theorem 5.87s 4.38s
% Output : CNFRefutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 159 ( 42 unt; 0 def)
% Number of atoms : 624 ( 82 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 733 ( 268 ~; 266 |; 144 &)
% ( 4 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 4 con; 0-4 aty)
% Number of variables : 261 ( 7 sgn 175 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_tsp_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m2_tsp_1(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k4_pre_topc(X1,X2,k3_tsp_2(X1,X2),k1_struct_0(X1,X3)) = k4_pre_topc(X1,X2,k3_tsp_2(X1,X2),k4_tex_4(X1,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_tsp_2) ).
fof(redefinition_k1_struct_0,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k1_struct_0(X1,X2) = k1_tarski(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
fof(dt_l1_pre_topc,axiom,
! [X1] :
( l1_pre_topc(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(redefinition_k3_tsp_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m1_pre_topc(X2,X1) )
=> k3_tsp_2(X1,X2) = k1_tsp_2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_tsp_2) ).
fof(redefinition_m2_tsp_1,axiom,
! [X1] :
( l1_pre_topc(X1)
=> ! [X2] :
( m2_tsp_1(X2,X1)
<=> m1_pre_topc(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_tsp_1) ).
fof(dt_k1_struct_0,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k1_struct_0(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).
fof(dt_k1_tsp_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m1_pre_topc(X2,X1) )
=> ( v1_funct_1(k1_tsp_2(X1,X2))
& v1_funct_2(k1_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2))
& v5_pre_topc(k1_tsp_2(X1,X2),X1,X2)
& m2_relset_1(k1_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tsp_2) ).
fof(dt_k3_tsp_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m1_pre_topc(X2,X1) )
=> ( v1_funct_1(k3_tsp_2(X1,X2))
& v1_funct_2(k3_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2))
& v5_pre_topc(k3_tsp_2(X1,X2),X1,X2)
& m2_relset_1(k3_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tsp_2) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& v1_xboole_0(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ v1_xboole_0(k1_tarski(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(t27_tsp_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m2_tsp_1(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k5_pre_topc(X1,X2,k3_tsp_2(X1,X2),k1_struct_0(X2,k8_funct_2(u1_struct_0(X1),u1_struct_0(X2),k3_tsp_2(X1,X2),X3))) = k4_tex_4(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tsp_2) ).
fof(redefinition_k8_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,X1,X2)
& m1_relset_1(X3,X1,X2)
& m1_subset_1(X4,X1) )
=> k8_funct_2(X1,X2,X3,X4) = k1_funct_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_m2_tsp_1,axiom,
! [X1] :
( l1_pre_topc(X1)
=> ! [X2] :
( m2_tsp_1(X2,X1)
=> l1_pre_topc(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_tsp_1) ).
fof(dt_k8_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,X1,X2)
& m1_relset_1(X3,X1,X2)
& m1_subset_1(X4,X1) )
=> m1_subset_1(k8_funct_2(X1,X2,X3,X4),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
fof(t51_tops_2,axiom,
! [X1] :
( l1_struct_0(X1)
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& l1_struct_0(X2) )
=> ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
& m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2)) )
=> ( k1_relat_1(X3) = k2_pre_topc(X1)
& r1_tarski(k2_relat_1(X3),k2_pre_topc(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_2) ).
fof(redefinition_k5_pre_topc,axiom,
! [X1,X2,X3,X4] :
( ( l1_struct_0(X1)
& l1_struct_0(X2)
& v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
& m1_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2)) )
=> k5_pre_topc(X1,X2,X3,X4) = k10_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_pre_topc) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> v1_relat_1(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_k4_pre_topc,axiom,
! [X1,X2,X3,X4] :
( ( l1_struct_0(X1)
& l1_struct_0(X2)
& v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
& m1_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2)) )
=> k4_pre_topc(X1,X2,X3,X4) = k9_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_pre_topc) ).
fof(t39_zfmisc_1,axiom,
! [X1,X2] :
( r1_tarski(X1,k1_tarski(X2))
<=> ( X1 = k1_xboole_0
| X1 = k1_tarski(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(t145_funct_1,axiom,
! [X1,X2] :
( ( v1_relat_1(X2)
& v1_funct_1(X2) )
=> r1_tarski(k9_relat_1(X2,k10_relat_1(X2,X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(t152_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ~ ( X1 != k1_xboole_0
& r1_tarski(X1,k1_relat_1(X2))
& k9_relat_1(X2,X1) = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
fof(t117_funct_1,axiom,
! [X1,X2] :
( ( v1_relat_1(X2)
& v1_funct_1(X2) )
=> ( r2_hidden(X1,k1_relat_1(X2))
=> k9_relat_1(X2,k1_tarski(X1)) = k1_tarski(k1_funct_1(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(redefinition_k4_tex_4,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k4_tex_4(X1,X2) = k2_tex_4(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_tex_4) ).
fof(dt_k2_tex_4,axiom,
! [X1,X2] :
( ( l1_pre_topc(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k2_tex_4(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tex_4) ).
fof(t12_pre_topc,axiom,
! [X1] :
( l1_struct_0(X1)
=> k2_pre_topc(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(dt_k4_tex_4,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> ( ~ v1_xboole_0(k4_tex_4(X1,X2))
& m1_subset_1(k4_tex_4(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tex_4) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(fc6_membered,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
fof(c_0_32,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m2_tsp_1(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k4_pre_topc(X1,X2,k3_tsp_2(X1,X2),k1_struct_0(X1,X3)) = k4_pre_topc(X1,X2,k3_tsp_2(X1,X2),k4_tex_4(X1,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t28_tsp_2])]) ).
fof(c_0_33,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k1_struct_0(X1,X2) = k1_tarski(X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_struct_0]) ).
fof(c_0_34,plain,
! [X332] :
( ~ l1_pre_topc(X332)
| l1_struct_0(X332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])]) ).
fof(c_0_35,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v2_pre_topc(esk1_0)
& l1_pre_topc(esk1_0)
& ~ v3_struct_0(esk2_0)
& v2_tsp_2(esk2_0,esk1_0)
& m2_tsp_1(esk2_0,esk1_0)
& m1_subset_1(esk3_0,u1_struct_0(esk1_0))
& k4_pre_topc(esk1_0,esk2_0,k3_tsp_2(esk1_0,esk2_0),k1_struct_0(esk1_0,esk3_0)) != k4_pre_topc(esk1_0,esk2_0,k3_tsp_2(esk1_0,esk2_0),k4_tex_4(esk1_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
fof(c_0_36,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m1_pre_topc(X2,X1) )
=> k3_tsp_2(X1,X2) = k1_tsp_2(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_tsp_2]) ).
fof(c_0_37,plain,
! [X411,X412] :
( ( ~ m2_tsp_1(X412,X411)
| m1_pre_topc(X412,X411)
| ~ l1_pre_topc(X411) )
& ( ~ m1_pre_topc(X412,X411)
| m2_tsp_1(X412,X411)
| ~ l1_pre_topc(X411) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_tsp_1])])])]) ).
fof(c_0_38,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k1_struct_0(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k1_struct_0]) ).
fof(c_0_39,plain,
! [X390,X391] :
( v3_struct_0(X390)
| ~ l1_struct_0(X390)
| ~ m1_subset_1(X391,u1_struct_0(X390))
| k1_struct_0(X390,X391) = k1_tarski(X391) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_40,plain,
( l1_struct_0(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
l1_pre_topc(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_42,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m1_pre_topc(X2,X1) )
=> ( v1_funct_1(k1_tsp_2(X1,X2))
& v1_funct_2(k1_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2))
& v5_pre_topc(k1_tsp_2(X1,X2),X1,X2)
& m2_relset_1(k1_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2)) ) ),
inference(fof_simplification,[status(thm)],[dt_k1_tsp_2]) ).
fof(c_0_43,plain,
! [X392,X393] :
( v3_struct_0(X392)
| ~ v2_pre_topc(X392)
| ~ l1_pre_topc(X392)
| v3_struct_0(X393)
| ~ v2_tsp_2(X393,X392)
| ~ m1_pre_topc(X393,X392)
| k3_tsp_2(X392,X393) = k1_tsp_2(X392,X393) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
cnf(c_0_44,plain,
( m1_pre_topc(X1,X2)
| ~ m2_tsp_1(X1,X2)
| ~ l1_pre_topc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
m2_tsp_1(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_46,plain,
! [X309,X310] :
( v3_struct_0(X309)
| ~ l1_struct_0(X309)
| ~ m1_subset_1(X310,u1_struct_0(X309))
| m1_subset_1(k1_struct_0(X309,X310),k1_zfmisc_1(u1_struct_0(X309))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
cnf(c_0_47,plain,
( v3_struct_0(X1)
| k1_struct_0(X1,X2) = k1_tarski(X2)
| ~ l1_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,negated_conjecture,
l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_51,plain,
! [X311,X312] :
( ( v1_funct_1(k1_tsp_2(X311,X312))
| v3_struct_0(X311)
| ~ v2_pre_topc(X311)
| ~ l1_pre_topc(X311)
| v3_struct_0(X312)
| ~ v2_tsp_2(X312,X311)
| ~ m1_pre_topc(X312,X311) )
& ( v1_funct_2(k1_tsp_2(X311,X312),u1_struct_0(X311),u1_struct_0(X312))
| v3_struct_0(X311)
| ~ v2_pre_topc(X311)
| ~ l1_pre_topc(X311)
| v3_struct_0(X312)
| ~ v2_tsp_2(X312,X311)
| ~ m1_pre_topc(X312,X311) )
& ( v5_pre_topc(k1_tsp_2(X311,X312),X311,X312)
| v3_struct_0(X311)
| ~ v2_pre_topc(X311)
| ~ l1_pre_topc(X311)
| v3_struct_0(X312)
| ~ v2_tsp_2(X312,X311)
| ~ m1_pre_topc(X312,X311) )
& ( m2_relset_1(k1_tsp_2(X311,X312),u1_struct_0(X311),u1_struct_0(X312))
| v3_struct_0(X311)
| ~ v2_pre_topc(X311)
| ~ l1_pre_topc(X311)
| v3_struct_0(X312)
| ~ v2_tsp_2(X312,X311)
| ~ m1_pre_topc(X312,X311) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
cnf(c_0_52,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| k3_tsp_2(X1,X2) = k1_tsp_2(X1,X2)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1)
| ~ v2_tsp_2(X2,X1)
| ~ m1_pre_topc(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,negated_conjecture,
m1_pre_topc(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_41])]) ).
cnf(c_0_54,negated_conjecture,
v2_tsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_55,negated_conjecture,
v2_pre_topc(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_56,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_57,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m1_pre_topc(X2,X1) )
=> ( v1_funct_1(k3_tsp_2(X1,X2))
& v1_funct_2(k3_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2))
& v5_pre_topc(k3_tsp_2(X1,X2),X1,X2)
& m2_relset_1(k3_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_tsp_2]) ).
fof(c_0_58,plain,
! [X438,X439,X440] :
( ~ r2_hidden(X438,X439)
| ~ m1_subset_1(X439,k1_zfmisc_1(X440))
| ~ v1_xboole_0(X440) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_59,plain,
( v3_struct_0(X1)
| m1_subset_1(k1_struct_0(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_60,negated_conjecture,
k1_struct_0(esk1_0,esk3_0) = k1_tarski(esk3_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]),c_0_50]) ).
fof(c_0_61,plain,
! [X426,X427] :
( ~ m1_subset_1(X426,X427)
| v1_xboole_0(X427)
| r2_hidden(X426,X427) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_62,plain,
! [X347] : m1_subset_1(esk8_1(X347),X347),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_63,plain,
! [X1] : ~ v1_xboole_0(k1_tarski(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(c_0_64,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_tsp_2(X2,X1)
& m2_tsp_1(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k5_pre_topc(X1,X2,k3_tsp_2(X1,X2),k1_struct_0(X2,k8_funct_2(u1_struct_0(X1),u1_struct_0(X2),k3_tsp_2(X1,X2),X3))) = k4_tex_4(X1,X3) ) ) ),
inference(fof_simplification,[status(thm)],[t27_tsp_2]) ).
fof(c_0_65,plain,
! [X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,X1,X2)
& m1_relset_1(X3,X1,X2)
& m1_subset_1(X4,X1) )
=> k8_funct_2(X1,X2,X3,X4) = k1_funct_1(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k8_funct_2]) ).
fof(c_0_66,plain,
! [X408,X409,X410] :
( ( ~ m2_relset_1(X410,X408,X409)
| m1_relset_1(X410,X408,X409) )
& ( ~ m1_relset_1(X410,X408,X409)
| m2_relset_1(X410,X408,X409) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_67,plain,
( m2_relset_1(k1_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2))
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1)
| ~ v2_tsp_2(X2,X1)
| ~ m1_pre_topc(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_68,negated_conjecture,
k1_tsp_2(esk1_0,esk2_0) = k3_tsp_2(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_41]),c_0_55])]),c_0_56]),c_0_50]) ).
fof(c_0_69,plain,
! [X316,X317] :
( ( v1_funct_1(k3_tsp_2(X316,X317))
| v3_struct_0(X316)
| ~ v2_pre_topc(X316)
| ~ l1_pre_topc(X316)
| v3_struct_0(X317)
| ~ v2_tsp_2(X317,X316)
| ~ m1_pre_topc(X317,X316) )
& ( v1_funct_2(k3_tsp_2(X316,X317),u1_struct_0(X316),u1_struct_0(X317))
| v3_struct_0(X316)
| ~ v2_pre_topc(X316)
| ~ l1_pre_topc(X316)
| v3_struct_0(X317)
| ~ v2_tsp_2(X317,X316)
| ~ m1_pre_topc(X317,X316) )
& ( v5_pre_topc(k3_tsp_2(X316,X317),X316,X317)
| v3_struct_0(X316)
| ~ v2_pre_topc(X316)
| ~ l1_pre_topc(X316)
| v3_struct_0(X317)
| ~ v2_tsp_2(X317,X316)
| ~ m1_pre_topc(X317,X316) )
& ( m2_relset_1(k3_tsp_2(X316,X317),u1_struct_0(X316),u1_struct_0(X317))
| v3_struct_0(X316)
| ~ v2_pre_topc(X316)
| ~ l1_pre_topc(X316)
| v3_struct_0(X317)
| ~ v2_tsp_2(X317,X316)
| ~ m1_pre_topc(X317,X316) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
cnf(c_0_70,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_71,negated_conjecture,
m1_subset_1(k1_tarski(esk3_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_48]),c_0_60]),c_0_49])]),c_0_50]) ).
cnf(c_0_72,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_73,plain,
m1_subset_1(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_74,plain,
! [X359] : ~ v1_xboole_0(k1_tarski(X359)),
inference(variable_rename,[status(thm)],[c_0_63]) ).
fof(c_0_75,plain,
! [X423,X424,X425] :
( v3_struct_0(X423)
| ~ v2_pre_topc(X423)
| ~ l1_pre_topc(X423)
| v3_struct_0(X424)
| ~ v2_tsp_2(X424,X423)
| ~ m2_tsp_1(X424,X423)
| ~ m1_subset_1(X425,u1_struct_0(X423))
| k5_pre_topc(X423,X424,k3_tsp_2(X423,X424),k1_struct_0(X424,k8_funct_2(u1_struct_0(X423),u1_struct_0(X424),k3_tsp_2(X423,X424),X425))) = k4_tex_4(X423,X425) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
fof(c_0_76,plain,
! [X404,X405,X406,X407] :
( v1_xboole_0(X404)
| ~ v1_funct_1(X406)
| ~ v1_funct_2(X406,X404,X405)
| ~ m1_relset_1(X406,X404,X405)
| ~ m1_subset_1(X407,X404)
| k8_funct_2(X404,X405,X406,X407) = k1_funct_1(X406,X407) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])]) ).
cnf(c_0_77,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_78,negated_conjecture,
m2_relset_1(k3_tsp_2(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_53]),c_0_68]),c_0_54]),c_0_41]),c_0_55])]),c_0_56]),c_0_50]) ).
cnf(c_0_79,plain,
( v1_funct_2(k3_tsp_2(X1,X2),u1_struct_0(X1),u1_struct_0(X2))
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1)
| ~ v2_tsp_2(X2,X1)
| ~ m1_pre_topc(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_80,plain,
( v1_funct_1(k3_tsp_2(X1,X2))
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1)
| ~ v2_tsp_2(X2,X1)
| ~ m1_pre_topc(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_81,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ r2_hidden(X1,k1_tarski(esk3_0)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_82,plain,
( v1_xboole_0(X1)
| r2_hidden(esk8_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
~ v1_xboole_0(k1_tarski(X1)),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_84,plain,
! [X338,X339] :
( ~ l1_pre_topc(X338)
| ~ m2_tsp_1(X339,X338)
| l1_pre_topc(X339) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_tsp_1])])]) ).
fof(c_0_85,plain,
! [X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,X1,X2)
& m1_relset_1(X3,X1,X2)
& m1_subset_1(X4,X1) )
=> m1_subset_1(k8_funct_2(X1,X2,X3,X4),X2) ),
inference(fof_simplification,[status(thm)],[dt_k8_funct_2]) ).
cnf(c_0_86,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| k5_pre_topc(X1,X2,k3_tsp_2(X1,X2),k1_struct_0(X2,k8_funct_2(u1_struct_0(X1),u1_struct_0(X2),k3_tsp_2(X1,X2),X3))) = k4_tex_4(X1,X3)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1)
| ~ v2_tsp_2(X2,X1)
| ~ m2_tsp_1(X2,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_87,plain,
( v1_xboole_0(X1)
| k8_funct_2(X1,X3,X2,X4) = k1_funct_1(X2,X4)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X1,X3)
| ~ m1_relset_1(X2,X1,X3)
| ~ m1_subset_1(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_88,negated_conjecture,
m1_relset_1(k3_tsp_2(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_89,negated_conjecture,
v1_funct_2(k3_tsp_2(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_53]),c_0_54]),c_0_41]),c_0_55])]),c_0_56]),c_0_50]) ).
cnf(c_0_90,negated_conjecture,
v1_funct_1(k3_tsp_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_53]),c_0_54]),c_0_41]),c_0_55])]),c_0_56]),c_0_50]) ).
cnf(c_0_91,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_92,plain,
( l1_pre_topc(X2)
| ~ l1_pre_topc(X1)
| ~ m2_tsp_1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_93,plain,
! [X328,X329,X330,X331] :
( v1_xboole_0(X328)
| ~ v1_funct_1(X330)
| ~ v1_funct_2(X330,X328,X329)
| ~ m1_relset_1(X330,X328,X329)
| ~ m1_subset_1(X331,X328)
| m1_subset_1(k8_funct_2(X328,X329,X330,X331),X329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])]) ).
fof(c_0_94,plain,
! [X1] :
( l1_struct_0(X1)
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& l1_struct_0(X2) )
=> ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
& m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2)) )
=> ( k1_relat_1(X3) = k2_pre_topc(X1)
& r1_tarski(k2_relat_1(X3),k2_pre_topc(X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t51_tops_2]) ).
fof(c_0_95,plain,
! [X400,X401,X402,X403] :
( ~ l1_struct_0(X400)
| ~ l1_struct_0(X401)
| ~ v1_funct_1(X402)
| ~ v1_funct_2(X402,u1_struct_0(X400),u1_struct_0(X401))
| ~ m1_relset_1(X402,u1_struct_0(X400),u1_struct_0(X401))
| k5_pre_topc(X400,X401,X402,X403) = k10_relat_1(X402,X403) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_pre_topc])]) ).
cnf(c_0_96,negated_conjecture,
( k5_pre_topc(esk1_0,X1,k3_tsp_2(esk1_0,X1),k1_struct_0(X1,k8_funct_2(u1_struct_0(esk1_0),u1_struct_0(X1),k3_tsp_2(esk1_0,X1),esk3_0))) = k4_tex_4(esk1_0,esk3_0)
| v3_struct_0(X1)
| ~ m2_tsp_1(X1,esk1_0)
| ~ v2_tsp_2(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_48]),c_0_41]),c_0_55])]),c_0_50]) ).
cnf(c_0_97,negated_conjecture,
( k8_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),k3_tsp_2(esk1_0,esk2_0),X1) = k1_funct_1(k3_tsp_2(esk1_0,esk2_0),X1)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_90])]),c_0_91]) ).
cnf(c_0_98,negated_conjecture,
l1_pre_topc(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_45]),c_0_41])]) ).
cnf(c_0_99,plain,
( v1_xboole_0(X1)
| m1_subset_1(k8_funct_2(X1,X3,X2,X4),X3)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X1,X3)
| ~ m1_relset_1(X2,X1,X3)
| ~ m1_subset_1(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_100,plain,
! [X262,X263,X264] :
( ~ m1_subset_1(X264,k1_zfmisc_1(k2_zfmisc_1(X262,X263)))
| v1_relat_1(X264) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_101,plain,
! [X335,X336,X337] :
( ~ m2_relset_1(X337,X335,X336)
| m1_subset_1(X337,k1_zfmisc_1(k2_zfmisc_1(X335,X336))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_102,plain,
! [X435,X436,X437] :
( ( k1_relat_1(X437) = k2_pre_topc(X435)
| ~ v1_funct_1(X437)
| ~ v1_funct_2(X437,u1_struct_0(X435),u1_struct_0(X436))
| ~ m2_relset_1(X437,u1_struct_0(X435),u1_struct_0(X436))
| v3_struct_0(X436)
| ~ l1_struct_0(X436)
| ~ l1_struct_0(X435) )
& ( r1_tarski(k2_relat_1(X437),k2_pre_topc(X436))
| ~ v1_funct_1(X437)
| ~ v1_funct_2(X437,u1_struct_0(X435),u1_struct_0(X436))
| ~ m2_relset_1(X437,u1_struct_0(X435),u1_struct_0(X436))
| v3_struct_0(X436)
| ~ l1_struct_0(X436)
| ~ l1_struct_0(X435) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])])]) ).
cnf(c_0_103,negated_conjecture,
k4_pre_topc(esk1_0,esk2_0,k3_tsp_2(esk1_0,esk2_0),k1_struct_0(esk1_0,esk3_0)) != k4_pre_topc(esk1_0,esk2_0,k3_tsp_2(esk1_0,esk2_0),k4_tex_4(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_104,plain,
! [X394,X395,X396,X397] :
( ~ l1_struct_0(X394)
| ~ l1_struct_0(X395)
| ~ v1_funct_1(X396)
| ~ v1_funct_2(X396,u1_struct_0(X394),u1_struct_0(X395))
| ~ m1_relset_1(X396,u1_struct_0(X394),u1_struct_0(X395))
| k4_pre_topc(X394,X395,X396,X397) = k9_relat_1(X396,X397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_pre_topc])]) ).
fof(c_0_105,plain,
! [X428,X429] :
( ( ~ r1_tarski(X428,k1_tarski(X429))
| X428 = k1_xboole_0
| X428 = k1_tarski(X429) )
& ( X428 != k1_xboole_0
| r1_tarski(X428,k1_tarski(X429)) )
& ( X428 != k1_tarski(X429)
| r1_tarski(X428,k1_tarski(X429)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(c_0_106,plain,
! [X417,X418] :
( ~ v1_relat_1(X418)
| ~ v1_funct_1(X418)
| r1_tarski(k9_relat_1(X418,k10_relat_1(X418,X417)),X417) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t145_funct_1])]) ).
cnf(c_0_107,plain,
( k5_pre_topc(X1,X2,X3,X4) = k10_relat_1(X3,X4)
| ~ l1_struct_0(X1)
| ~ l1_struct_0(X2)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
| ~ m1_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_108,negated_conjecture,
k5_pre_topc(esk1_0,esk2_0,k3_tsp_2(esk1_0,esk2_0),k1_struct_0(esk2_0,k1_funct_1(k3_tsp_2(esk1_0,esk2_0),esk3_0))) = k4_tex_4(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_45]),c_0_54]),c_0_48])]),c_0_56]) ).
cnf(c_0_109,negated_conjecture,
l1_struct_0(esk2_0),
inference(spm,[status(thm)],[c_0_40,c_0_98]) ).
cnf(c_0_110,negated_conjecture,
( m1_subset_1(k1_funct_1(k3_tsp_2(esk1_0,esk2_0),X1),u1_struct_0(esk2_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_97]),c_0_88]),c_0_89]),c_0_90])]),c_0_91]) ).
cnf(c_0_111,plain,
( v1_relat_1(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_112,plain,
( m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_113,plain,
( k1_relat_1(X1) = k2_pre_topc(X2)
| v3_struct_0(X3)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X3))
| ~ m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X3))
| ~ l1_struct_0(X3)
| ~ l1_struct_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_114,negated_conjecture,
k4_pre_topc(esk1_0,esk2_0,k3_tsp_2(esk1_0,esk2_0),k4_tex_4(esk1_0,esk3_0)) != k4_pre_topc(esk1_0,esk2_0,k3_tsp_2(esk1_0,esk2_0),k1_tarski(esk3_0)),
inference(rw,[status(thm)],[c_0_103,c_0_60]) ).
cnf(c_0_115,plain,
( k4_pre_topc(X1,X2,X3,X4) = k9_relat_1(X3,X4)
| ~ l1_struct_0(X1)
| ~ l1_struct_0(X2)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
| ~ m1_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_116,plain,
( X1 = k1_xboole_0
| X1 = k1_tarski(X2)
| ~ r1_tarski(X1,k1_tarski(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_117,plain,
( r1_tarski(k9_relat_1(X1,k10_relat_1(X1,X2)),X2)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_118,negated_conjecture,
k10_relat_1(k3_tsp_2(esk1_0,esk2_0),k1_struct_0(esk2_0,k1_funct_1(k3_tsp_2(esk1_0,esk2_0),esk3_0))) = k4_tex_4(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_88]),c_0_89]),c_0_90]),c_0_109]),c_0_49])]) ).
cnf(c_0_119,negated_conjecture,
( k1_struct_0(esk2_0,k1_funct_1(k3_tsp_2(esk1_0,esk2_0),X1)) = k1_tarski(k1_funct_1(k3_tsp_2(esk1_0,esk2_0),X1))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_110]),c_0_109])]),c_0_56]) ).
cnf(c_0_120,plain,
( v1_relat_1(X1)
| ~ m2_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
fof(c_0_121,plain,
! [X419,X420] :
( ~ v1_relat_1(X420)
| X419 = k1_xboole_0
| ~ r1_tarski(X419,k1_relat_1(X420))
| k9_relat_1(X420,X419) != k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t152_relat_1])]) ).
cnf(c_0_122,negated_conjecture,
( k1_relat_1(k3_tsp_2(esk1_0,esk2_0)) = k2_pre_topc(esk1_0)
| ~ v1_funct_2(k3_tsp_2(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk2_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_78]),c_0_90]),c_0_109]),c_0_49])]),c_0_56]) ).
cnf(c_0_123,negated_conjecture,
k4_pre_topc(esk1_0,esk2_0,k3_tsp_2(esk1_0,esk2_0),k1_tarski(esk3_0)) != k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k4_tex_4(esk1_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_90]),c_0_109]),c_0_49])]),c_0_88]),c_0_89])]) ).
cnf(c_0_124,plain,
( k9_relat_1(X1,k10_relat_1(X1,k1_tarski(X2))) = k1_tarski(X2)
| k9_relat_1(X1,k10_relat_1(X1,k1_tarski(X2))) = k1_xboole_0
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
k10_relat_1(k3_tsp_2(esk1_0,esk2_0),k1_tarski(k1_funct_1(k3_tsp_2(esk1_0,esk2_0),esk3_0))) = k4_tex_4(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_48])]) ).
cnf(c_0_126,negated_conjecture,
v1_relat_1(k3_tsp_2(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_120,c_0_78]) ).
cnf(c_0_127,plain,
( X2 = k1_xboole_0
| ~ v1_relat_1(X1)
| ~ r1_tarski(X2,k1_relat_1(X1))
| k9_relat_1(X1,X2) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_128,negated_conjecture,
k1_relat_1(k3_tsp_2(esk1_0,esk2_0)) = k2_pre_topc(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_89])]) ).
cnf(c_0_129,negated_conjecture,
k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k4_tex_4(esk1_0,esk3_0)) != k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k1_tarski(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_115]),c_0_88]),c_0_89]),c_0_90]),c_0_109]),c_0_49])]) ).
cnf(c_0_130,negated_conjecture,
( k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k4_tex_4(esk1_0,esk3_0)) = k1_tarski(k1_funct_1(k3_tsp_2(esk1_0,esk2_0),esk3_0))
| k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k4_tex_4(esk1_0,esk3_0)) = k1_xboole_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_90]),c_0_126])]) ).
fof(c_0_131,plain,
! [X414,X415] :
( ~ v1_relat_1(X415)
| ~ v1_funct_1(X415)
| ~ r2_hidden(X414,k1_relat_1(X415))
| k9_relat_1(X415,k1_tarski(X414)) = k1_tarski(k1_funct_1(X415,X414)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_funct_1])]) ).
fof(c_0_132,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k4_tex_4(X1,X2) = k2_tex_4(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_tex_4]) ).
cnf(c_0_133,negated_conjecture,
( X1 = k1_xboole_0
| k9_relat_1(k3_tsp_2(esk1_0,esk2_0),X1) != k1_xboole_0
| ~ r1_tarski(X1,k2_pre_topc(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_126])]) ).
cnf(c_0_134,negated_conjecture,
( k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k4_tex_4(esk1_0,esk3_0)) = k1_xboole_0
| k1_tarski(k1_funct_1(k3_tsp_2(esk1_0,esk2_0),esk3_0)) != k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k1_tarski(esk3_0)) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,plain,
( k9_relat_1(X1,k1_tarski(X2)) = k1_tarski(k1_funct_1(X1,X2))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1)
| ~ r2_hidden(X2,k1_relat_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
fof(c_0_136,plain,
! [X314,X315] :
( ~ l1_pre_topc(X314)
| ~ m1_subset_1(X315,u1_struct_0(X314))
| m1_subset_1(k2_tex_4(X314,X315),k1_zfmisc_1(u1_struct_0(X314))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_tex_4])]) ).
fof(c_0_137,plain,
! [X398,X399] :
( v3_struct_0(X398)
| ~ v2_pre_topc(X398)
| ~ l1_pre_topc(X398)
| ~ m1_subset_1(X399,u1_struct_0(X398))
| k4_tex_4(X398,X399) = k2_tex_4(X398,X399) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])]) ).
cnf(c_0_138,negated_conjecture,
( k4_tex_4(esk1_0,esk3_0) = k1_xboole_0
| k1_tarski(k1_funct_1(k3_tsp_2(esk1_0,esk2_0),esk3_0)) != k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k1_tarski(esk3_0))
| ~ r1_tarski(k4_tex_4(esk1_0,esk3_0),k2_pre_topc(esk1_0)) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_139,negated_conjecture,
( k1_tarski(k1_funct_1(k3_tsp_2(esk1_0,esk2_0),X1)) = k9_relat_1(k3_tsp_2(esk1_0,esk2_0),k1_tarski(X1))
| ~ r2_hidden(X1,k2_pre_topc(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_128]),c_0_90])]),c_0_126])]) ).
fof(c_0_140,plain,
! [X416] :
( ~ l1_struct_0(X416)
| k2_pre_topc(X416) = u1_struct_0(X416) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_pre_topc])]) ).
cnf(c_0_141,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| r2_hidden(esk3_0,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_72,c_0_48]) ).
cnf(c_0_142,plain,
( m1_subset_1(k2_tex_4(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_pre_topc(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_143,plain,
( v3_struct_0(X1)
| k4_tex_4(X1,X2) = k2_tex_4(X1,X2)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
fof(c_0_144,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> ( ~ v1_xboole_0(k4_tex_4(X1,X2))
& m1_subset_1(k4_tex_4(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_k4_tex_4]) ).
cnf(c_0_145,negated_conjecture,
( k4_tex_4(esk1_0,esk3_0) = k1_xboole_0
| ~ r1_tarski(k4_tex_4(esk1_0,esk3_0),k2_pre_topc(esk1_0))
| ~ r2_hidden(esk3_0,k2_pre_topc(esk1_0)) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_146,plain,
( k2_pre_topc(X1) = u1_struct_0(X1)
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_147,negated_conjecture,
r2_hidden(esk3_0,u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[c_0_141,c_0_91]) ).
fof(c_0_148,plain,
! [X430,X431] :
( ( ~ m1_subset_1(X430,k1_zfmisc_1(X431))
| r1_tarski(X430,X431) )
& ( ~ r1_tarski(X430,X431)
| m1_subset_1(X430,k1_zfmisc_1(X431)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_149,negated_conjecture,
m1_subset_1(k2_tex_4(esk1_0,esk3_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_48]),c_0_41])]) ).
cnf(c_0_150,negated_conjecture,
k2_tex_4(esk1_0,esk3_0) = k4_tex_4(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_48]),c_0_41]),c_0_55])]),c_0_50]) ).
fof(c_0_151,plain,
! [X322,X323] :
( ( ~ v1_xboole_0(k4_tex_4(X322,X323))
| v3_struct_0(X322)
| ~ v2_pre_topc(X322)
| ~ l1_pre_topc(X322)
| ~ m1_subset_1(X323,u1_struct_0(X322)) )
& ( m1_subset_1(k4_tex_4(X322,X323),k1_zfmisc_1(u1_struct_0(X322)))
| v3_struct_0(X322)
| ~ v2_pre_topc(X322)
| ~ l1_pre_topc(X322)
| ~ m1_subset_1(X323,u1_struct_0(X322)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])])]) ).
cnf(c_0_152,negated_conjecture,
( k4_tex_4(esk1_0,esk3_0) = k1_xboole_0
| ~ r1_tarski(k4_tex_4(esk1_0,esk3_0),u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]),c_0_49])]) ).
cnf(c_0_153,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_154,negated_conjecture,
m1_subset_1(k4_tex_4(esk1_0,esk3_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(rw,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_155,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(k4_tex_4(X1,X2))
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_156,negated_conjecture,
k4_tex_4(esk1_0,esk3_0) = k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154])]) ).
cnf(c_0_157,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc6_membered]) ).
cnf(c_0_158,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]),c_0_48]),c_0_41]),c_0_55])]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP036+1 : TPTP v9.2.1. Released v3.4.0.
% 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
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 09:59:44 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 5.87/4.38 % Version : CSE_E---1.7
% 5.87/4.38 % Problem : theBenchmark.p
% 5.87/4.38 % SZS status Theorem for theBenchmark.p
% 5.87/4.38 % SZS output start CNFRefutation
% See solution above
% 5.87/4.39 % Total time : 3.426s
%------------------------------------------------------------------------------