%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP641+3 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 04:26:40 PM UTC 2026
% Result : Theorem 9.90s 9.68s
% Output : CNFRefutation 9.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 16 unt; 0 def)
% Number of atoms : 234 ( 5 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 284 ( 100 ~; 93 |; 59 &)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> v4_group_1(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',cc1_group_2) ).
fof(t19_latsubgr,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_latsubgr) ).
fof(dt_m1_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',dt_m1_group_2) ).
fof(dt_k2_group_1,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',dt_k2_group_1) ).
fof(t63_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_group_2(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',t63_group_2) ).
fof(t53_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> k2_group_1(X2) = k2_group_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',t53_group_2) ).
fof(t18_latsubgr,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
<=> r1_rlvect_1(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_latsubgr) ).
fof(t55_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> r1_rlvect_1(X2,k2_group_1(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',t55_group_2) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> v4_group_1(X2) ) ),
inference(fof_simplification,[status(thm)],[cc1_group_2]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t19_latsubgr])]) ).
fof(c_0_10,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_group_2]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k2_group_1]) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_group_2(X1,X1) ),
inference(fof_simplification,[status(thm)],[t63_group_2]) ).
fof(c_0_13,plain,
! [X593,X594] :
( v3_struct_0(X593)
| ~ v3_group_1(X593)
| ~ v4_group_1(X593)
| ~ l1_group_1(X593)
| ~ m1_group_2(X594,X593)
| v4_group_1(X594) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_14,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v3_group_1(esk1_0)
& v4_group_1(esk1_0)
& l1_group_1(esk1_0)
& v1_group_1(esk2_0)
& m1_group_2(esk2_0,esk1_0)
& ~ r2_hidden(k2_group_1(esk1_0),k1_funct_1(k1_latsubgr(esk1_0),esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_15,plain,
! [X605,X606] :
( ( ~ v3_struct_0(X606)
| ~ m1_group_2(X606,X605)
| v3_struct_0(X605)
| ~ v3_group_1(X605)
| ~ l1_group_1(X605) )
& ( v3_group_1(X606)
| ~ m1_group_2(X606,X605)
| v3_struct_0(X605)
| ~ v3_group_1(X605)
| ~ l1_group_1(X605) )
& ( l1_group_1(X606)
| ~ m1_group_2(X606,X605)
| v3_struct_0(X605)
| ~ v3_group_1(X605)
| ~ l1_group_1(X605) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_16,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> k2_group_1(X2) = k2_group_1(X1) ) ),
inference(fof_simplification,[status(thm)],[t53_group_2]) ).
fof(c_0_17,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
<=> r1_rlvect_1(X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t18_latsubgr]) ).
fof(c_0_18,plain,
! [X579] :
( v3_struct_0(X579)
| ~ l1_group_1(X579)
| m1_subset_1(k2_group_1(X579),u1_struct_0(X579)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> r1_rlvect_1(X2,k2_group_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[t55_group_2]) ).
fof(c_0_20,plain,
! [X598] :
( v3_struct_0(X598)
| ~ v3_group_1(X598)
| ~ v4_group_1(X598)
| ~ l1_group_1(X598)
| m1_group_2(X598,X598) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_21,plain,
( v3_struct_0(X1)
| v4_group_1(X2)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
m1_group_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,plain,
( v3_group_1(X1)
| v3_struct_0(X2)
| ~ m1_group_2(X1,X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,plain,
( l1_group_1(X1)
| v3_struct_0(X2)
| ~ m1_group_2(X1,X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,plain,
( v3_struct_0(X2)
| ~ v3_struct_0(X1)
| ~ m1_group_2(X1,X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_30,plain,
! [X583,X584] :
( v3_struct_0(X583)
| ~ v3_group_1(X583)
| ~ v4_group_1(X583)
| ~ l1_group_1(X583)
| ~ m1_group_2(X584,X583)
| k2_group_1(X584) = k2_group_1(X583) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_31,plain,
! [X566,X567,X568] :
( ( ~ r2_hidden(X568,k1_funct_1(k1_latsubgr(X566),X567))
| r1_rlvect_1(X567,X568)
| ~ m1_subset_1(X568,u1_struct_0(X566))
| ~ v1_group_1(X567)
| ~ m1_group_2(X567,X566)
| v3_struct_0(X566)
| ~ v3_group_1(X566)
| ~ v4_group_1(X566)
| ~ l1_group_1(X566) )
& ( ~ r1_rlvect_1(X567,X568)
| r2_hidden(X568,k1_funct_1(k1_latsubgr(X566),X567))
| ~ m1_subset_1(X568,u1_struct_0(X566))
| ~ v1_group_1(X567)
| ~ m1_group_2(X567,X566)
| v3_struct_0(X566)
| ~ v3_group_1(X566)
| ~ v4_group_1(X566)
| ~ l1_group_1(X566) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_32,plain,
( v3_struct_0(X1)
| m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_33,plain,
! [X588,X589] :
( v3_struct_0(X588)
| ~ v3_group_1(X588)
| ~ v4_group_1(X588)
| ~ l1_group_1(X588)
| ~ m1_group_2(X589,X588)
| r1_rlvect_1(X589,k2_group_1(X588)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_34,plain,
( v3_struct_0(X1)
| m1_group_2(X1,X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_35,negated_conjecture,
v4_group_1(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_21,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_36,negated_conjecture,
v3_group_1(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_37,negated_conjecture,
l1_group_1(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_38,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_39,plain,
( v3_struct_0(X1)
| k2_group_1(X2) = k2_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
( r2_hidden(X2,k1_funct_1(k1_latsubgr(X3),X1))
| v3_struct_0(X3)
| ~ r1_rlvect_1(X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X3))
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X3)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
m1_subset_1(k2_group_1(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_26]) ).
cnf(c_0_42,plain,
( v3_struct_0(X1)
| r1_rlvect_1(X2,k2_group_1(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,negated_conjecture,
m1_group_2(esk2_0,esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_44,negated_conjecture,
k2_group_1(esk2_0) = k2_group_1(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_39,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_45,negated_conjecture,
~ r2_hidden(k2_group_1(esk1_0),k1_funct_1(k1_latsubgr(esk1_0),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_46,negated_conjecture,
( r2_hidden(k2_group_1(esk1_0),k1_funct_1(k1_latsubgr(esk1_0),X1))
| ~ m1_group_2(X1,esk1_0)
| ~ v1_group_1(X1)
| ~ r1_rlvect_1(X1,k2_group_1(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_40,c_0_41]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_47,negated_conjecture,
v1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_48,negated_conjecture,
r1_rlvect_1(esk2_0,k2_group_1(esk1_0)),
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_42,c_0_43]),c_0_44]),c_0_35]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_22]),c_0_47]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP641+3 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:54:00 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 9.90/9.68 % Version : CSE_E---1.7
% 9.90/9.68 % Problem : theBenchmark.p
% 9.90/9.68 % SZS status Theorem for theBenchmark.p
% 9.90/9.68 % SZS output start CNFRefutation
% See solution above
% 9.90/9.69 % Total time : 9.158s
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