%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG218+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 : n022.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 04:08:16 PM UTC 2026
% Result : Theorem 1.39s 1.76s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 121 ( 39 unt; 0 def)
% Number of atoms : 495 ( 52 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 580 ( 206 ~; 188 |; 148 &)
% ( 6 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 157 ( 4 sgn 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t10_rmod_5,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v4_group_1(X2)
& v7_group_1(X2)
& v6_vectsp_1(X2)
& v7_vectsp_1(X2)
& v8_vectsp_1(X2)
& ~ v10_vectsp_1(X2)
& v2_vectsp_2(X2)
& l3_vectsp_1(X2) )
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v3_rlvect_1(X3)
& v4_rlvect_1(X3)
& v5_rlvect_1(X3)
& v6_rlvect_1(X3)
& v5_vectsp_2(X3,X2)
& l1_vectsp_2(X3,X2) )
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))
=> ( r2_hidden(X1,X4)
=> r1_rlvect_1(k1_rmod_5(X2,X3,X4),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_rmod_5) ).
fof(t12_rmod_5,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ~ ( k1_rmod_5(X1,X2,X3) = k1_rmod_2(X1,X2)
& X3 != k1_xboole_0
& X3 != k7_rlvect_2(X2,k1_rlvect_1(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_rmod_5) ).
fof(t46_rmod_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v4_group_1(X2)
& v6_vectsp_1(X2)
& v7_vectsp_1(X2)
& v8_vectsp_1(X2)
& l3_vectsp_1(X2) )
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v3_rlvect_1(X3)
& v4_rlvect_1(X3)
& v5_rlvect_1(X3)
& v6_rlvect_1(X3)
& v5_vectsp_2(X3,X2)
& l1_vectsp_2(X3,X2) )
=> ( r1_rlvect_1(k1_rmod_2(X2,X3),X1)
<=> X1 = k1_rlvect_1(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_rmod_2) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = k1_tarski(X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( r1_tarski(X1,X2)
& r1_tarski(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
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(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ v1_xboole_0(k1_tarski(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(redefinition_k7_rlvect_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k7_rlvect_2(X1,X2) = k1_tarski(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_rlvect_2) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(dt_l1_vectsp_2,axiom,
! [X1] :
( l1_struct_0(X1)
=> ! [X2] :
( l1_vectsp_2(X2,X1)
=> l1_rlvect_1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).
fof(dt_l1_rlvect_1,axiom,
! [X1] :
( l1_rlvect_1(X1)
=> l2_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
fof(dt_l2_struct_0,axiom,
! [X1] :
( l2_struct_0(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(dt_l1_vectsp_1,axiom,
! [X1] :
( l1_vectsp_1(X1)
=> l1_group_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
fof(dt_l2_vectsp_1,axiom,
! [X1] :
( l2_vectsp_1(X1)
=> ( l1_vectsp_1(X1)
& l2_struct_0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
fof(dt_l3_vectsp_1,axiom,
! [X1] :
( l3_vectsp_1(X1)
=> ( l1_rlvect_1(X1)
& l2_vectsp_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(c_0_20,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v4_group_1(X2)
& v7_group_1(X2)
& v6_vectsp_1(X2)
& v7_vectsp_1(X2)
& v8_vectsp_1(X2)
& ~ v10_vectsp_1(X2)
& v2_vectsp_2(X2)
& l3_vectsp_1(X2) )
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v3_rlvect_1(X3)
& v4_rlvect_1(X3)
& v5_rlvect_1(X3)
& v6_rlvect_1(X3)
& v5_vectsp_2(X3,X2)
& l1_vectsp_2(X3,X2) )
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))
=> ( r2_hidden(X1,X4)
=> r1_rlvect_1(k1_rmod_5(X2,X3,X4),X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[t10_rmod_5]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ~ ( k1_rmod_5(X1,X2,X3) = k1_rmod_2(X1,X2)
& X3 != k1_xboole_0
& X3 != k7_rlvect_2(X2,k1_rlvect_1(X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t12_rmod_5])]) ).
fof(c_0_22,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v4_group_1(X2)
& v6_vectsp_1(X2)
& v7_vectsp_1(X2)
& v8_vectsp_1(X2)
& l3_vectsp_1(X2) )
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v3_rlvect_1(X3)
& v4_rlvect_1(X3)
& v5_rlvect_1(X3)
& v6_rlvect_1(X3)
& v5_vectsp_2(X3,X2)
& l1_vectsp_2(X3,X2) )
=> ( r1_rlvect_1(k1_rmod_2(X2,X3),X1)
<=> X1 = k1_rlvect_1(X3) ) ) ),
inference(fof_simplification,[status(thm)],[t46_rmod_2]) ).
fof(c_0_23,plain,
! [X283,X284,X285,X286] :
( v3_struct_0(X284)
| ~ v3_rlvect_1(X284)
| ~ v4_rlvect_1(X284)
| ~ v5_rlvect_1(X284)
| ~ v6_rlvect_1(X284)
| ~ v4_group_1(X284)
| ~ v7_group_1(X284)
| ~ v6_vectsp_1(X284)
| ~ v7_vectsp_1(X284)
| ~ v8_vectsp_1(X284)
| v10_vectsp_1(X284)
| ~ v2_vectsp_2(X284)
| ~ l3_vectsp_1(X284)
| v3_struct_0(X285)
| ~ v3_rlvect_1(X285)
| ~ v4_rlvect_1(X285)
| ~ v5_rlvect_1(X285)
| ~ v6_rlvect_1(X285)
| ~ v5_vectsp_2(X285,X284)
| ~ l1_vectsp_2(X285,X284)
| ~ m1_subset_1(X286,k1_zfmisc_1(u1_struct_0(X285)))
| ~ r2_hidden(X283,X286)
| r1_rlvect_1(k1_rmod_5(X284,X285,X286),X283) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_24,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v3_rlvect_1(esk1_0)
& v4_rlvect_1(esk1_0)
& v5_rlvect_1(esk1_0)
& v6_rlvect_1(esk1_0)
& v4_group_1(esk1_0)
& v7_group_1(esk1_0)
& v6_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v8_vectsp_1(esk1_0)
& ~ v10_vectsp_1(esk1_0)
& v2_vectsp_2(esk1_0)
& l3_vectsp_1(esk1_0)
& ~ v3_struct_0(esk2_0)
& v3_rlvect_1(esk2_0)
& v4_rlvect_1(esk2_0)
& v5_rlvect_1(esk2_0)
& v6_rlvect_1(esk2_0)
& v5_vectsp_2(esk2_0,esk1_0)
& l1_vectsp_2(esk2_0,esk1_0)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& k1_rmod_5(esk1_0,esk2_0,esk3_0) = k1_rmod_2(esk1_0,esk2_0)
& esk3_0 != k1_xboole_0
& esk3_0 != k7_rlvect_2(esk2_0,k1_rlvect_1(esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_25,plain,
! [X293,X294,X295] :
( ( ~ r1_rlvect_1(k1_rmod_2(X294,X295),X293)
| X293 = k1_rlvect_1(X295)
| v3_struct_0(X295)
| ~ v3_rlvect_1(X295)
| ~ v4_rlvect_1(X295)
| ~ v5_rlvect_1(X295)
| ~ v6_rlvect_1(X295)
| ~ v5_vectsp_2(X295,X294)
| ~ l1_vectsp_2(X295,X294)
| v3_struct_0(X294)
| ~ v3_rlvect_1(X294)
| ~ v4_rlvect_1(X294)
| ~ v5_rlvect_1(X294)
| ~ v6_rlvect_1(X294)
| ~ v4_group_1(X294)
| ~ v6_vectsp_1(X294)
| ~ v7_vectsp_1(X294)
| ~ v8_vectsp_1(X294)
| ~ l3_vectsp_1(X294) )
& ( X293 != k1_rlvect_1(X295)
| r1_rlvect_1(k1_rmod_2(X294,X295),X293)
| v3_struct_0(X295)
| ~ v3_rlvect_1(X295)
| ~ v4_rlvect_1(X295)
| ~ v5_rlvect_1(X295)
| ~ v6_rlvect_1(X295)
| ~ v5_vectsp_2(X295,X294)
| ~ l1_vectsp_2(X295,X294)
| v3_struct_0(X294)
| ~ v3_rlvect_1(X294)
| ~ v4_rlvect_1(X294)
| ~ v5_rlvect_1(X294)
| ~ v6_rlvect_1(X294)
| ~ v4_group_1(X294)
| ~ v6_vectsp_1(X294)
| ~ v7_vectsp_1(X294)
| ~ v8_vectsp_1(X294)
| ~ l3_vectsp_1(X294) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
cnf(c_0_26,plain,
( v3_struct_0(X1)
| v10_vectsp_1(X1)
| v3_struct_0(X2)
| r1_rlvect_1(k1_rmod_5(X1,X2,X3),X4)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v7_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ r2_hidden(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,esk3_0) = k1_rmod_2(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
v2_vectsp_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,negated_conjecture,
v7_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_39,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_40,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_41,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_42,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_43,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_44,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_45,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_46,negated_conjecture,
~ v10_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_47,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_48,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_49,plain,
! [X303,X304] :
( ~ r2_hidden(X303,X304)
| ~ v1_xboole_0(X304) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_50,plain,
! [X177,X178,X179,X180,X181] :
( ( ~ r1_tarski(X177,X178)
| ~ r2_hidden(X179,X177)
| r2_hidden(X179,X178) )
& ( r2_hidden(esk5_2(X180,X181),X180)
| r1_tarski(X180,X181) )
& ( ~ r2_hidden(esk5_2(X180,X181),X181)
| r1_tarski(X180,X181) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
cnf(c_0_51,plain,
( X3 = k1_rlvect_1(X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ r1_rlvect_1(k1_rmod_2(X1,X2),X3)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_52,negated_conjecture,
( r1_rlvect_1(k1_rmod_2(esk1_0,esk2_0),X1)
| ~ r2_hidden(X1,esk3_0) ),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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_26,c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_42]),c_0_43]),c_0_44]),c_0_45])]),c_0_46]),c_0_47]),c_0_48]) ).
fof(c_0_53,plain,
! [X170,X171,X172,X173,X174,X175] :
( ( ~ r2_hidden(X172,X171)
| X172 = X170
| X171 != k1_tarski(X170) )
& ( X173 != X170
| r2_hidden(X173,X171)
| X171 != k1_tarski(X170) )
& ( ~ r2_hidden(esk4_2(X174,X175),X175)
| esk4_2(X174,X175) != X174
| X175 = k1_tarski(X174) )
& ( r2_hidden(esk4_2(X174,X175),X175)
| esk4_2(X174,X175) = X174
| X175 = k1_tarski(X174) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).
fof(c_0_54,plain,
! [X168,X169] :
( ( r1_tarski(X168,X169)
| X168 != X169 )
& ( r1_tarski(X169,X168)
| X168 != X169 )
& ( ~ r1_tarski(X168,X169)
| ~ r1_tarski(X169,X168)
| X168 = X169 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_55,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
( r2_hidden(esk5_2(X1,X2),X1)
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( X1 = k1_rlvect_1(esk2_0)
| ~ r2_hidden(X1,esk3_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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_51,c_0_52]),c_0_29]),c_0_30]),c_0_31]),c_0_33]),c_0_34]),c_0_35]),c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_42]),c_0_43]),c_0_44]),c_0_45])]),c_0_47]),c_0_48]) ).
fof(c_0_58,plain,
! [X289,X290] :
( ~ m1_subset_1(X289,X290)
| v1_xboole_0(X290)
| r2_hidden(X289,X290) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_59,plain,
( r2_hidden(X1,X3)
| X1 != X2
| X3 != k1_tarski(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( X1 = X2
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,plain,
( r1_tarski(X1,X2)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( esk5_2(esk3_0,X1) = k1_rlvect_1(esk2_0)
| r1_tarski(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_63,plain,
( r1_tarski(X1,X2)
| ~ r2_hidden(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_64,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_65,plain,
! [X287,X288] :
( ~ r2_hidden(X287,X288)
| m1_subset_1(X287,X288) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_66,plain,
( r2_hidden(X1,X2)
| X2 != k1_tarski(X1) ),
inference(er,[status(thm)],[c_0_59]) ).
fof(c_0_67,plain,
! [X1] : ~ v1_xboole_0(k1_tarski(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(c_0_68,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k7_rlvect_2(X1,X2) = k1_tarski(X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k7_rlvect_2]) ).
fof(c_0_69,plain,
! [X296,X297,X298] :
( ~ r2_hidden(X296,X297)
| ~ m1_subset_1(X297,k1_zfmisc_1(X298))
| m1_subset_1(X296,X298) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_70,plain,
( X1 = X2
| ~ v1_xboole_0(X2)
| ~ r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,negated_conjecture,
( r1_tarski(esk3_0,X1)
| r2_hidden(k1_rlvect_1(esk2_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_62]) ).
cnf(c_0_72,plain,
( v1_xboole_0(X1)
| r1_tarski(X2,X1)
| ~ m1_subset_1(esk5_2(X2,X1),X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_73,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
r2_hidden(X1,k1_tarski(X1)),
inference(er,[status(thm)],[c_0_66]) ).
fof(c_0_75,plain,
! [X241] : ~ v1_xboole_0(k1_tarski(X241)),
inference(variable_rename,[status(thm)],[c_0_67]) ).
cnf(c_0_76,plain,
( X1 = X3
| ~ r2_hidden(X1,X2)
| X2 != k1_tarski(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_77,plain,
! [X277,X278] :
( v3_struct_0(X277)
| ~ l1_struct_0(X277)
| ~ m1_subset_1(X278,u1_struct_0(X277))
| k7_rlvect_2(X277,X278) = k1_tarski(X278) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])]) ).
cnf(c_0_78,plain,
( m1_subset_1(X1,X3)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( esk3_0 = X1
| r2_hidden(k1_rlvect_1(esk2_0),esk3_0)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_81,negated_conjecture,
esk3_0 != k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_82,negated_conjecture,
( v1_xboole_0(X1)
| r1_tarski(esk3_0,X1)
| ~ m1_subset_1(k1_rlvect_1(esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_62]) ).
cnf(c_0_83,plain,
m1_subset_1(X1,k1_tarski(X1)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_84,plain,
~ v1_xboole_0(k1_tarski(X1)),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_85,plain,
( esk5_2(X1,X2) = X3
| r1_tarski(X1,X2)
| X1 != k1_tarski(X3) ),
inference(spm,[status(thm)],[c_0_76,c_0_56]) ).
fof(c_0_86,plain,
! [X199,X200] :
( ~ l1_struct_0(X199)
| ~ l1_vectsp_2(X200,X199)
| l1_rlvect_1(X200) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_vectsp_2])])]) ).
cnf(c_0_87,negated_conjecture,
esk3_0 != k7_rlvect_2(esk2_0,k1_rlvect_1(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_88,plain,
( v3_struct_0(X1)
| k7_rlvect_2(X1,X2) = k1_tarski(X2)
| ~ l1_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_89,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk2_0))
| ~ r2_hidden(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_78,c_0_28]) ).
cnf(c_0_90,negated_conjecture,
r2_hidden(k1_rlvect_1(esk2_0),esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_91,negated_conjecture,
r1_tarski(esk3_0,k1_tarski(k1_rlvect_1(esk2_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_92,plain,
( esk5_2(k1_tarski(X1),X2) = X1
| r1_tarski(k1_tarski(X1),X2) ),
inference(er,[status(thm)],[c_0_85]) ).
fof(c_0_93,plain,
! [X197] :
( ~ l1_rlvect_1(X197)
| l2_struct_0(X197) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1])]) ).
cnf(c_0_94,plain,
( l1_rlvect_1(X2)
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_95,negated_conjecture,
( k1_tarski(k1_rlvect_1(esk2_0)) != esk3_0
| ~ l1_struct_0(esk2_0)
| ~ m1_subset_1(k1_rlvect_1(esk2_0),u1_struct_0(esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_48]) ).
cnf(c_0_96,negated_conjecture,
m1_subset_1(k1_rlvect_1(esk2_0),u1_struct_0(esk2_0)),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( k1_tarski(k1_rlvect_1(esk2_0)) = esk3_0
| ~ r1_tarski(k1_tarski(k1_rlvect_1(esk2_0)),esk3_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_91]) ).
cnf(c_0_98,plain,
( r1_tarski(k1_tarski(X1),X2)
| ~ r2_hidden(X1,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_92]) ).
fof(c_0_99,plain,
! [X201] :
( ~ l2_struct_0(X201)
| l1_struct_0(X201) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])]) ).
cnf(c_0_100,plain,
( l2_struct_0(X1)
| ~ l1_rlvect_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_101,negated_conjecture,
( l1_rlvect_1(esk2_0)
| ~ l1_struct_0(esk1_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_29]) ).
fof(c_0_102,plain,
! [X196] :
( ~ l1_group_1(X196)
| l1_struct_0(X196) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
fof(c_0_103,plain,
! [X198] :
( ~ l1_vectsp_1(X198)
| l1_group_1(X198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_vectsp_1])]) ).
fof(c_0_104,plain,
! [X202] :
( ( l1_vectsp_1(X202)
| ~ l2_vectsp_1(X202) )
& ( l2_struct_0(X202)
| ~ l2_vectsp_1(X202) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_vectsp_1])])]) ).
fof(c_0_105,plain,
! [X203] :
( ( l1_rlvect_1(X203)
| ~ l3_vectsp_1(X203) )
& ( l2_vectsp_1(X203)
| ~ l3_vectsp_1(X203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1])])]) ).
cnf(c_0_106,negated_conjecture,
( k1_tarski(k1_rlvect_1(esk2_0)) != esk3_0
| ~ l1_struct_0(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).
cnf(c_0_107,negated_conjecture,
k1_tarski(k1_rlvect_1(esk2_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_90])]) ).
cnf(c_0_108,plain,
( l1_struct_0(X1)
| ~ l2_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_109,negated_conjecture,
( l2_struct_0(esk2_0)
| ~ l1_struct_0(esk1_0) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_110,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_111,plain,
( l1_group_1(X1)
| ~ l1_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,plain,
( l1_vectsp_1(X1)
| ~ l2_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_113,plain,
( l2_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_114,negated_conjecture,
~ l1_struct_0(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107])]) ).
cnf(c_0_115,negated_conjecture,
( l1_struct_0(esk2_0)
| ~ l1_struct_0(esk1_0) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,plain,
( l1_struct_0(X1)
| ~ l1_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_117,plain,
( l1_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_118,negated_conjecture,
~ l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_119,plain,
( l1_struct_0(X1)
| ~ l3_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG218+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n022.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 10:24:36 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.39/1.76 % Version : CSE_E---1.7
% 1.39/1.76 % Problem : theBenchmark.p
% 1.39/1.76 % SZS status Theorem for theBenchmark.p
% 1.39/1.76 % SZS output start CNFRefutation
% See solution above
% 1.39/1.76 % Total time : 1.372s
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