%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP629+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:40:26 PM UTC 2026
% Result : Theorem 24.36s 4.38s
% Output : CNFRefutation 24.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 152 ( 26 equ)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 192 ( 67 ~; 59 |; 44 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-5 aty)
% Number of variables : 40 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t26_autgroup,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k3_group_1(X1,X2)),k6_autgroup(X1,X2)) = k6_autgroup(X1,k2_group_1(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_autgroup) ).
fof(t23_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_autgroup) ).
fof(d6_group_1,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( X3 = k3_group_1(X1,X2)
<=> ( k1_group_1(X1,X3,X2) = k2_group_1(X1)
& k1_group_1(X1,X2,X3) = k2_group_1(X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',d6_group_1) ).
fof(dt_k3_group_1,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',dt_k3_group_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k3_group_1(X1,X2)),k6_autgroup(X1,X2)) = k6_autgroup(X1,k2_group_1(X1)) ) ),
inference(assume_negation,[status(cth)],[t26_autgroup]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k3_group_1(X1,X2)),k6_autgroup(X1,X2)) = k6_autgroup(X1,k2_group_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t23_autgroup]) ).
fof(c_0_7,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( X3 = k3_group_1(X1,X2)
<=> ( k1_group_1(X1,X3,X2) = k2_group_1(X1)
& k1_group_1(X1,X2,X3) = k2_group_1(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d6_group_1]) ).
fof(c_0_8,plain,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k3_group_1]) ).
fof(c_0_9,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k3_group_1(esk1_0,esk2_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,k2_group_1(esk1_0))
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& v1_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_10,plain,
! [X22,X23,X24] :
( k6_autgroup(X22,k1_group_1(X22,X23,X24)) = k7_funct_2(u1_struct_0(X22),u1_struct_0(X22),u1_struct_0(X22),k6_autgroup(X22,X23),k6_autgroup(X22,X24))
| ~ m1_subset_1(X24,u1_struct_0(X22))
| ~ m1_subset_1(X23,u1_struct_0(X22))
| ~ l1_group_1(X22)
| ~ v4_group_1(X22)
| ~ v3_group_1(X22)
| ~ v1_group_1(X22)
| v3_struct_0(X22) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,plain,
! [X31,X32,X33] :
( ( ~ l1_group_1(X31)
| ~ v4_group_1(X31)
| ~ v3_group_1(X31)
| v3_struct_0(X31)
| ~ m1_subset_1(X32,u1_struct_0(X31))
| ~ m1_subset_1(X33,u1_struct_0(X31))
| X33 = k3_group_1(X31,X32)
| k1_group_1(X31,X33,X32) != k2_group_1(X31)
| k1_group_1(X31,X32,X33) != k2_group_1(X31) )
& ( ~ l1_group_1(X31)
| ~ v4_group_1(X31)
| ~ v3_group_1(X31)
| v3_struct_0(X31)
| ~ m1_subset_1(X32,u1_struct_0(X31))
| ~ m1_subset_1(X33,u1_struct_0(X31))
| X33 != k3_group_1(X31,X32)
| k1_group_1(X31,X33,X32) = k2_group_1(X31) )
& ( ~ l1_group_1(X31)
| ~ v4_group_1(X31)
| ~ v3_group_1(X31)
| v3_struct_0(X31)
| ~ m1_subset_1(X32,u1_struct_0(X31))
| ~ m1_subset_1(X33,u1_struct_0(X31))
| X33 != k3_group_1(X31,X32)
| k1_group_1(X31,X32,X33) = k2_group_1(X31) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_12,plain,
! [X152,X153] :
( m1_subset_1(k3_group_1(X152,X153),u1_struct_0(X152))
| ~ m1_subset_1(X153,u1_struct_0(X152))
| ~ l1_group_1(X152)
| ~ v4_group_1(X152)
| ~ v3_group_1(X152)
| v3_struct_0(X152) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,negated_conjecture,
k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k3_group_1(esk1_0,esk2_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,k2_group_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| X2 != k3_group_1(X1,X3)
| v3_struct_0(X1)
| k1_group_1(X1,X2,X3) = k2_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
( ~ m1_subset_1(k3_group_1(esk1_0,esk2_0),u1_struct_0(esk1_0))
| k6_autgroup(esk1_0,k1_group_1(esk1_0,k3_group_1(esk1_0,esk2_0),esk2_0)) != k6_autgroup(esk1_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_24,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| v3_struct_0(X1)
| k1_group_1(X1,k3_group_1(X1,X2),X2) = k2_group_1(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ m1_subset_1(k3_group_1(esk1_0,esk2_0),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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]),c_0_16]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_26,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_25,c_0_22]),c_0_15]),c_0_16]),c_0_18]),c_0_19])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP629+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n003.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 20:23:15 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.36/4.38 % Version: 3.5.1
% 24.36/4.38 % Preprocessing class: FMLMSMMLSSSNFFN.
% 24.36/4.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.36/4.38 % Starting new_bool_3 with 900s (3) cores
% 24.36/4.38 % Starting new_bool_1 with 900s (3) cores
% 24.36/4.38 % Starting sh5l with 300s (1) cores
% 24.36/4.38 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S032N with 300s (1) cores
% 24.36/4.38 % new_bool_3 with pid 2515891 completed with status 0
% 24.36/4.38 % Result found by new_bool_3
% 24.36/4.38 % Preprocessing class: FMLMSMMLSSSNFFN.
% 24.36/4.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.36/4.38 % Starting new_bool_3 with 900s (3) cores
% 24.36/4.38 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 24.36/4.38 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 24.36/4.38 % Search class: FGHSM-SMLM32-MFFFFFNN
% 24.36/4.38 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 24.36/4.38 % Starting SubtermCWHack with 82s (1) cores
% 24.36/4.38 % Starting new_bool_3 with 91s (1) cores
% 24.36/4.38 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 24.36/4.38 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 2515898 completed with status 0
% 24.36/4.38 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 24.36/4.38 % Preprocessing class: FMLMSMMLSSSNFFN.
% 24.36/4.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.36/4.38 % Starting new_bool_3 with 900s (3) cores
% 24.36/4.38 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 24.36/4.38 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 24.36/4.38 % Search class: FGHSM-SMLM32-MFFFFFNN
% 24.36/4.38 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 24.36/4.38 % Starting SubtermCWHack with 82s (1) cores
% 24.36/4.38 % Starting new_bool_3 with 91s (1) cores
% 24.36/4.38 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 24.36/4.38 % Preprocessing time : 0.054 s
% 24.36/4.38 % Presaturation interreduction done
% 24.36/4.38
% 24.36/4.38 % Proof found!
% 24.36/4.38 % SZS status Theorem
% 24.36/4.38 % SZS output start CNFRefutation
% See solution above
% 24.36/4.38 % Parsed axioms : 3841
% 24.36/4.38 % Removed by relevancy pruning/SinE : 3051
% 24.36/4.38 % Initial clauses : 1644
% 24.36/4.38 % Removed in clause preprocessing : 72
% 24.36/4.38 % Initial clauses in saturation : 1572
% 24.36/4.38 % Processed clauses : 12279
% 24.36/4.38 % ...of these trivial : 32
% 24.36/4.38 % ...subsumed : 7991
% 24.36/4.38 % ...remaining for further processing : 4256
% 24.36/4.38 % Other redundant clauses eliminated : 508
% 24.36/4.38 % Clauses deleted for lack of memory : 0
% 24.36/4.38 % Backward-subsumed : 155
% 24.36/4.38 % Backward-rewritten : 44
% 24.36/4.38 % Generated clauses : 54329
% 24.36/4.38 % ...of the previous two non-redundant : 49644
% 24.36/4.38 % ...aggressively subsumed : 0
% 24.36/4.38 % Contextual simplify-reflections : 76
% 24.36/4.38 % Paramodulations : 53796
% 24.36/4.38 % Factorizations : 12
% 24.36/4.38 % NegExts : 0
% 24.36/4.38 % Equation resolutions : 531
% 24.36/4.38 % Disequality decompositions : 0
% 24.36/4.38 % Total rewrite steps : 17115
% 24.36/4.38 % ...of those cached : 15973
% 24.36/4.38 % Propositional unsat checks : 0
% 24.36/4.38 % Propositional check models : 0
% 24.36/4.38 % Propositional check unsatisfiable : 0
% 24.36/4.38 % Propositional clauses : 0
% 24.36/4.38 % Propositional clauses after purity: 0
% 24.36/4.38 % Propositional unsat core size : 0
% 24.36/4.38 % Propositional preprocessing time : 0.000
% 24.36/4.38 % Propositional encoding time : 0.000
% 24.36/4.38 % Propositional solver time : 0.000
% 24.36/4.38 % Success case prop preproc time : 0.000
% 24.36/4.38 % Success case prop encoding time : 0.000
% 24.36/4.38 % Success case prop solver time : 0.000
% 24.36/4.38 % Current number of processed clauses : 2449
% 24.36/4.38 % Positive orientable unit clauses : 182
% 24.36/4.38 % Positive unorientable unit clauses: 2
% 24.36/4.38 % Negative unit clauses : 279
% 24.36/4.38 % Non-unit-clauses : 1986
% 24.36/4.38 % Current number of unprocessed clauses: 40007
% 24.36/4.38 % ...number of literals in the above : 197714
% 24.36/4.38 % Current number of archived formulas : 0
% 24.36/4.38 % Current number of archived clauses : 1658
% 24.36/4.38 % Clause-clause subsumption calls (NU) : 1842271
% 24.36/4.38 % Rec. Clause-clause subsumption calls : 362296
% 24.36/4.38 % Non-unit clause-clause subsumptions : 4959
% 24.36/4.38 % Unit Clause-clause subsumption calls : 29592
% 24.36/4.38 % Rewrite failures with RHS unbound : 0
% 24.36/4.38 % BW rewrite match attempts : 162
% 24.36/4.38 % BW rewrite match successes : 95
% 24.36/4.38 % Condensation attempts : 0
% 24.36/4.38 % Condensation successes : 0
% 24.36/4.38 % Termbank termtop insertions : 1008535
% 24.36/4.38 % Search garbage collected termcells : 56165
% 24.36/4.38
% 24.36/4.38 % -------------------------------------------------
% 24.36/4.38 % User time : 3.403 s
% 24.36/4.38 % System time : 0.107 s
% 24.36/4.38 % Total time : 3.510 s
% 24.36/4.38 % Maximum resident set size: 14256 pages
% 24.36/4.38
% 24.36/4.38 % -------------------------------------------------
% 24.36/4.38 % User time : 10.040 s
% 24.36/4.38 % System time : 0.341 s
% 24.36/4.38 % Total time : 10.380 s
% 24.36/4.38 % Maximum resident set size: 9472 pages
% 24.36/4.38 % E exiting
%------------------------------------------------------------------------------